Scalable parallel prefix solvers for discrete ordinates transport
International Nuclear Information System (INIS)
Pautz, S.; Pandya, T.; Adams, M.
2009-01-01
The well-known 'sweep' algorithm for inverting the streaming-plus-collision term in first-order deterministic radiation transport calculations has some desirable numerical properties. However, it suffers from parallel scaling issues caused by a lack of concurrency. The maximum degree of concurrency, and thus the maximum parallelism, grows more slowly than the problem size for sweeps-based solvers. We investigate a new class of parallel algorithms that involves recasting the streaming-plus-collision problem in prefix form and solving via cyclic reduction. This method, although computationally more expensive at low levels of parallelism than the sweep algorithm, offers better theoretical scalability properties. Previous work has demonstrated this approach for one-dimensional calculations; we show how to extend it to multidimensional calculations. Notably, for multiple dimensions it appears that this approach is limited to long-characteristics discretizations; other discretizations cannot be cast in prefix form. We implement two variants of the algorithm within the radlib/SCEPTRE transport code library at Sandia National Laboratories and show results on two different massively parallel systems. Both the 'forward' and 'symmetric' solvers behave similarly, scaling well to larger degrees of parallelism then sweeps-based solvers. We do observe some issues at the highest levels of parallelism (relative to the system size) and discuss possible causes. We conclude that this approach shows good potential for future parallel systems, but the parallel scalability will depend heavily on the architecture of the communication networks of these systems. (authors)
International Nuclear Information System (INIS)
Fischer, J.W.; Azmy, Y.Y.
2003-01-01
A previously reported parallel performance model for Angular Domain Decomposition (ADD) of the Discrete Ordinates method for solving multidimensional neutron transport problems is revisited for further validation. Three communication schemes: native MPI, the bucket algorithm, and the distributed bucket algorithm, are included in the validation exercise that is successfully conducted on a Beowulf cluster. The parallel performance model is comprised of three components: serial, parallel, and communication. The serial component is largely independent of the number of participating processors, P, while the parallel component decreases like 1/P. These two components are independent of the communication scheme, in contrast with the communication component that typically increases with P in a manner highly dependent on the global reduced algorithm. Correct trends for each component and each communication scheme were measured for the Arbitrarily High Order Transport (AHOT) code, thus validating the performance models. Furthermore, extensive experiments illustrate the superiority of the bucket algorithm. The primary question addressed in this research is: for a given problem size, which domain decomposition method, angular or spatial, is best suited to parallelize Discrete Ordinates methods on a specific computational platform? We address this question for three-dimensional applications via parallel performance models that include parameters specifying the problem size and system performance: the above-mentioned ADD, and a previously constructed and validated Spatial Domain Decomposition (SDD) model. We conclude that for large problems the parallel component dwarfs the communication component even on moderately large numbers of processors. The main advantages of SDD are: (a) scalability to higher numbers of processors of the order of the number of computational cells; (b) smaller memory requirement; (c) better performance than ADD on high-end platforms and large number of
Development of parallel 3D discrete ordinates transport program on JASMIN framework
International Nuclear Information System (INIS)
Cheng, T.; Wei, J.; Shen, H.; Zhong, B.; Deng, L.
2015-01-01
A parallel 3D discrete ordinates radiation transport code JSNT-S is developed, aiming at simulating real-world radiation shielding and reactor physics applications in a reasonable time. Through the patch-based domain partition algorithm, the memory requirement is shared among processors and a space-angle parallel sweeping algorithm is developed based on data-driven algorithm. Acceleration methods such as partial current rebalance are implemented. The correctness is proved through the VENUS-3 and other benchmark models. In the radiation shielding calculation of the Qinshan-II reactor pressure vessel model with 24.3 billion DoF, only 88 seconds is required and the overall parallel efficiency of 44% is achieved on 1536 CPU cores. (author)
A massively parallel discrete ordinates response matrix method for neutron transport
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1992-01-01
In this paper a discrete ordinates response matrix method is formulated with anisotropic scattering for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices that result from the diamond-differenced equations are utilized in a factored form that minimizes memory requirements and significantly reduces the number of arithmetic operations required per node. The red-black solution algorithm utilizes massive parallelism by assigning each spatial node to one or more processors. The algorithm is accelerated by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red-black iterations. The method is implemented on a 16K Connection Machine-2, and S 8 and S 16 solutions are obtained for fixed-source benchmark problems in x-y geometry
Analysis of Massively Parallel Discrete-Ordinates Transport Sweep Algorithms with Collisions
International Nuclear Information System (INIS)
Bailey, T.S.; Falgout, R.D.
2008-01-01
We present theoretical scaling models for a variety of discrete-ordinates sweep algorithms. In these models, we pay particular attention to the way each algorithm handles collisions. A collision is defined as a processor having multiple angles with ready to be swept during one stage of the sweep. The models also take into account how subdomains are assigned to processors and how angles are grouped during the sweep. We describe a data driven algorithm that resolves collisions efficiently during the sweep as well as other algorithms that have been designed to avoid collisions completely. Our models are validated using the ARGES and AMTRAN transport codes. We then use the models to study and predict scaling trends in all of the sweep algorithms
Zerr, Robert Joseph
2011-12-01
The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of
Recent developments in discrete ordinates electron transport
International Nuclear Information System (INIS)
Morel, J.E.; Lorence, L.J. Jr.
1986-01-01
The discrete ordinates method is a deterministic method for numerically solving the Boltzmann equation. It was originally developed for neutron transport calculations, but is routinely used for photon and coupled neutron-photon transport calculations as well. The computational state of the art for coupled electron-photon transport (CEPT) calculations is not as developed as that for neutron transport calculations. The only production codes currently available for CEPT calculations are condensed-history Monte Carlo codes such as the ETRAN and ITS codes. A deterministic capability for production calculations is clearly needed. In response to this need, we have begun the development of a production discrete ordinates code for CEPT calculations. The purpose of this paper is to describe the basic approach we are taking, discuss the current status of the project, and present some new computational results. Although further characterization of the coupled electron-photon discrete ordinates method remains to be done, the results to date indicate that the discrete ordinates method can be just as accurate and from 10 to 100 times faster than the Monte Carlo method for a wide variety of problems. We stress that these results are obtained with standard discrete ordinates codes such as ONETRAN. It is clear that even greater efficiency can be obtained by developing a new generation of production discrete ordinates codes specifically designed to solve the Boltzmann-Fokker-Planck equation. However, the prospects for such development in the near future appear to be remote
Parallel Implementation and Scaling of an Adaptive Mesh Discrete Ordinates Algorithm for Transport
International Nuclear Information System (INIS)
Howell, L H
2004-01-01
Block-structured adaptive mesh refinement (AMR) uses a mesh structure built up out of locally-uniform rectangular grids. In the BoxLib parallel framework used by the Raptor code, each processor operates on one or more of these grids at each refinement level. The decomposition of the mesh into grids and the distribution of these grids among processors may change every few timesteps as a calculation proceeds. Finer grids use smaller timesteps than coarser grids, requiring additional work to keep the system synchronized and ensure conservation between different refinement levels. In a paper for NECDC 2002 I presented preliminary results on implementation of parallel transport sweeps on the AMR mesh, conjugate gradient acceleration, accuracy of the AMR solution, and scalar speedup of the AMR algorithm compared to a uniform fully-refined mesh. This paper continues with a more in-depth examination of the parallel scaling properties of the scheme, both in single-level and multi-level calculations. Both sweeping and setup costs are considered. The algorithm scales with acceptable performance to several hundred processors. Trends suggest, however, that this is the limit for efficient calculations with traditional transport sweeps, and that modifications to the sweep algorithm will be increasingly needed as job sizes in the thousands of processors become common
Parallel ray tracing for one-dimensional discrete ordinate computations
International Nuclear Information System (INIS)
Jarvis, R.D.; Nelson, P.
1996-01-01
The ray-tracing sweep in discrete-ordinates, spatially discrete numerical approximation methods applied to the linear, steady-state, plane-parallel, mono-energetic, azimuthally symmetric, neutral-particle transport equation can be reduced to a parallel prefix computation. In so doing, the often severe penalty in convergence rate of the source iteration, suffered by most current parallel algorithms using spatial domain decomposition, can be avoided while attaining parallelism in the spatial domain to whatever extent desired. In addition, the reduction implies parallel algorithm complexity limits for the ray-tracing sweep. The reduction applies to all closed, linear, one-cell functional (CLOF) spatial approximation methods, which encompasses most in current popular use. Scalability test results of an implementation of the algorithm on a 64-node nCube-2S hypercube-connected, message-passing, multi-computer are described. (author)
Energy-pointwise discrete ordinates transport methods
International Nuclear Information System (INIS)
Williams, M.L.; Asgari, M.; Tashakorri, R.
1997-01-01
A very brief description is given of a one-dimensional code, CENTRM, which computes a detailed, space-dependent flux spectrum in a pointwise-energy representation within the resolved resonance range. The code will become a component in the SCALE system to improve computation of self-shielded cross sections, thereby enhancing the accuracy of codes such as KENO. CENTRM uses discrete-ordinates transport theory with an arbitrary angular quadrature order and a Legendre expansion of scattering anisotropy for moderator materials and heavy nuclides. The CENTRM program provides capability to deterministically compute full energy range, space-dependent angular flux spectra, rigorously accounting for resonance fine-structure and scattering anisotropy effects
A discrete ordinate response matrix method for massively parallel computers
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1991-01-01
A discrete ordinate response matrix method is formulated for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices which result from the diamond-differenced equations are utilized in a factored form which minimizes memory requirements and significantly reduces the required number of algorithm utilizes massive parallelism by assigning each spatial node to a processor. The algorithm is accelerated effectively by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red/black iterations. The method has been implemented on a 16k Connection Machine-2, and S 8 and S 16 solutions have been obtained for fixed-source benchmark problems in X--Y geometry
Multidimensional electron-photon transport with standard discrete ordinates codes
International Nuclear Information System (INIS)
Drumm, C.R.
1995-01-01
A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electronphoton transport problems
The adaptive collision source method for discrete ordinates radiation transport
International Nuclear Information System (INIS)
Walters, William J.; Haghighat, Alireza
2017-01-01
Highlights: • A new adaptive quadrature method to solve the discrete ordinates transport equation. • The adaptive collision source (ACS) method splits the flux into n’th collided components. • Uncollided flux requires high quadrature; this is lowered with number of collisions. • ACS automatically applies appropriate quadrature order each collided component. • The adaptive quadrature is 1.5–4 times more efficient than uniform quadrature. - Abstract: A novel collision source method has been developed to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order used for each. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This method allows for an optimal use of processing power, by using a high order quadrature for the first iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and is referred to as the adaptive collision source (ACS) method. The ACS methodology has been implemented in the 3-D, parallel, multigroup discrete ordinates code TITAN. This code was tested on a several simple and complex fixed-source problems. The ACS implementation in TITAN has shown a reduction in computation time by a factor of 1.5–4 on the fixed-source test problems, for the same desired level of accuracy, as compared to the standard TITAN code.
KIM, Jong Woon; LEE, Young-Ouk
2017-09-01
As computing power gets better and better, computer codes that use a deterministic method seem to be less useful than those using the Monte Carlo method. In addition, users do not like to think about space, angles, and energy discretization for deterministic codes. However, a deterministic method is still powerful in that we can obtain a solution of the flux throughout the problem, particularly as when particles can barely penetrate, such as in a deep penetration problem with small detection volumes. Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed and has been widely used in several applications. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. Since 2009, we have been developing our own code by benchmarking ATTILA. AETIUS is a discrete ordinates code that uses an unstructured tetrahedral mesh such as ATTILA. For pre- and post- processing, Gmsh is used to generate an unstructured tetrahedral mesh by importing a CAD file (*.step) and visualizing the calculation results of AETIUS. Using a CAD tool, the geometry can be modeled very easily. In this paper, we describe a brief overview of AETIUS and provide numerical results from both AETIUS and a Monte Carlo code, MCNP5, in a deep penetration problem with small detection volumes. The results demonstrate the effectiveness and efficiency of AETIUS for such calculations.
Multidimensional electron-photon transport with standard discrete ordinates codes
International Nuclear Information System (INIS)
Drumm, C.R.
1997-01-01
A method is described for generating electron cross sections that are comparable with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electron-photon transport problems. The key to the method is a simultaneous solution of the continuous-slowing-down (CSD) portion and elastic-scattering portion of the scattering source by the Goudsmit-Saunderson theory. The resulting multigroup-Legendre cross sections are much smaller than the true scattering cross sections that they represent. Under certain conditions, the cross sections are guaranteed positive and converge with a low-order Legendre expansion
Multidimensional electron-photon transport with standard discrete ordinates codes
International Nuclear Information System (INIS)
Drumm, C.R.
1997-01-01
A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages to using an established discrete ordinates solver, e.g., immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and synthetic radiation environments. The cross sections have been successfully used in the DORT, TWODANT, and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electron-photon transport problems. The key to the method is a simultaneous solution of the continuous-slowing-down and elastic-scattering portions of the scattering source by the Goudsmit-Saunderson theory. The resulting multigroup-Legendre cross sections are much smaller than the true scattering cross sections that they represent. Under certain conditions, the cross sections are guaranteed positive and converge with a low-order Legendre expansion
High order discrete ordinates transport in two dimensions
International Nuclear Information System (INIS)
Arkuszewski, J.J.
1980-01-01
A two-dimensional neutron transport equation in (x,y) geometry is solved by the subdomain version of the weighted residual method. The weight functions are chosen to be characteristic functions of computational boxes (subdomains). In the case of bilinear interpolant the conventional diamond relations are obtained, while the quadratic one produces generalized diamond relations containing first derivatives of the solution. The balance equation remains the same. The derivation yields also additional relations for extrapolating boundary values of derivatives and leaves the room for supplementing the interpolant with specially curtailed higher order polynomials. The method requires only slight modifications in inner iteration process used by conventional discrete ordinates programs, and has been introduced as an option into the program DOT2. The paper contains comparisons of the proposed method with conventional one based on calculations of IAEA-CRP transport theory benchmarks. (author)
ASOP, Shield Calculation, 1-D, Discrete Ordinates Transport
International Nuclear Information System (INIS)
1993-01-01
1 - Nature of physical problem solved: ASOP is a shield optimization calculational system based on the one-dimensional discrete ordinates transport program ANISN. It has been used to design optimum shields for space applications of SNAP zirconium-hydride-uranium- fueled reactors and uranium-oxide fueled thermionic reactors and to design beam stops for the ORELA facility. 2 - Method of solution: ASOP generates coefficients of linear equations describing the logarithm of the dose and dose-weight derivatives as functions of position from data obtained in an automated sequence of ANISN calculations. With the dose constrained to a design value and all dose-weight derivatives required to be equal, the linear equations may be solved for a new set of shield dimensions. Since changes in the shield dimensions may cause the linear functions to change, the entire procedure is repeated until convergence is obtained. The detailed calculations of the radiation transport through shield configurations for every step in the procedure distinguish ASOP from other shield optimization computer code systems which rely on multiple component sources and attenuation coefficients to describe the transport. 3 - Restrictions on the complexity of the problem: Problem size is limited only by machine size
International Nuclear Information System (INIS)
Chalhoub, Ezzat Selim
1997-01-01
The method of discrete ordinates is applied to the solution of the slab albedo problem with azimuthal dependence in transport theory. A new set of quadratures appropriate to the problem is introduced. In addition to the ANISN code, modified to include the proposed formalism, two new programs, PEESNC and PEESNA, which were created on the basis of the discrete ordinates formalism, using the direct integration method and the analytic solution method respectively, are used in the generation of results for a few sample problems. Program PEESNC was created to validate the results obtained with the discrete ordinates method and the finite difference approximation (ANISN), while program PEESNA was developed in order to implement an analytical discrete ordinates formalism, which provides more accurate results. The obtained results for selected sample problems are compared with highly accurate numerical results published in the literature. Compared to ANISN and PEESNC, program PEESNA presents a greater efficiency in execution time and much more precise numerical results. (author)
Time dependence linear transport III convergence of the discrete ordinate method
International Nuclear Information System (INIS)
Wilson, D.G.
1983-01-01
In this paper the uniform pointwise convergence of the discrete ordinate method for weak and strong solutions of the time dependent, linear transport equation posed in a multidimensional, rectangular parallelepiped with partially reflecting walls is established. The first result is that a sequence of discrete ordinate solutions converges uniformly on the quadrature points to a solution of the continuous problem provided that the corresponding sequence of truncation errors for the solution of the continuous problem converges to zero in the same manner. The second result is that continuity of the solution with respect to the velocity variables guarantees that the truncation erros in the quadrature formula go the zero and hence that the discrete ordinate approximations converge to the solution of the continuous problem as the discrete ordinate become dense. An existence theory for strong solutions of the the continuous problem follows as a result
Experiences in the parallelization of the discrete ordinates method using OpenMP and MPI
Energy Technology Data Exchange (ETDEWEB)
Pautz, A. [TUV Hannover/Sachsen-Anhalt e.V. (Germany); Langenbuch, S. [Gesellschaft fur Anlagen- und Reaktorsicherheit (GRS) mbH (Germany)
2003-07-01
The method of Discrete Ordinates is in principle parallelizable to a high degree, since the transport 'mesh sweeps' are mutually independent for all angular directions. However, in the well-known production code Dort such a type of angular domain decomposition has to be done on a spatial line-byline basis, causing the parallelism in the code to be very fine-grained. The construction of scalar fluxes and moments requires a large effort for inter-thread or inter-process communication. We have implemented two different parallelization approaches in Dort: firstly, we have used a shared-memory model suitable for SMP (Symmetric Multiprocessor) machines based on the standard OpenMP. The second approach uses the well-known Message Passing Interface (MPI) to establish communication between parallel processes running in a distributed-memory environment. We investigate the benefits and drawbacks of both models and show first results on performance and scaling behaviour of the parallel Dort code. (authors)
Experiences in the parallelization of the discrete ordinates method using OpenMP and MPI
International Nuclear Information System (INIS)
Pautz, A.; Langenbuch, S.
2003-01-01
The method of Discrete Ordinates is in principle parallelizable to a high degree, since the transport 'mesh sweeps' are mutually independent for all angular directions. However, in the well-known production code Dort such a type of angular domain decomposition has to be done on a spatial line-byline basis, causing the parallelism in the code to be very fine-grained. The construction of scalar fluxes and moments requires a large effort for inter-thread or inter-process communication. We have implemented two different parallelization approaches in Dort: firstly, we have used a shared-memory model suitable for SMP (Symmetric Multiprocessor) machines based on the standard OpenMP. The second approach uses the well-known Message Passing Interface (MPI) to establish communication between parallel processes running in a distributed-memory environment. We investigate the benefits and drawbacks of both models and show first results on performance and scaling behaviour of the parallel Dort code. (authors)
Shared memory parallelism for 3D cartesian discrete ordinates solver
International Nuclear Information System (INIS)
Moustafa, S.; Dutka-Malen, I.; Plagne, L.; Poncot, A.; Ramet, P.
2013-01-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multi-core + SIMD - Single Instruction on Multiple Data) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46*10 6 spatial cells and 1*10 12 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40.74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool. (authors)
Parallel discrete ordinates algorithms on distributed and common memory systems
International Nuclear Information System (INIS)
Wienke, B.R.; Hiromoto, R.E.; Brickner, R.G.
1987-01-01
The S/sub n/ algorithm employs iterative techniques in solving the linear Boltzmann equation. These methods, both ordered and chaotic, were compared on both the Denelcor HEP and the Intel hypercube. Strategies are linked to the organization and accessibility of memory (common memory versus distributed memory architectures), with common concern for acquisition of global information. Apart from this, the inherent parallelism of the algorithm maps directly onto the two architectures. Results comparing execution times, speedup, and efficiency are based on a representative 16-group (full upscatter and downscatter) sample problem. Calculations were performed on both the Los Alamos National Laboratory (LANL) Denelcor HEP and the LANL Intel hypercube. The Denelcor HEP is a 64-bit multi-instruction, multidate MIMD machine consisting of up to 16 process execution modules (PEMs), each capable of executing 64 processes concurrently. Each PEM can cooperate on a job, or run several unrelated jobs, and share a common global memory through a crossbar switch. The Intel hypercube, on the other hand, is a distributed memory system composed of 128 processing elements, each with its own local memory. Processing elements are connected in a nearest-neighbor hypercube configuration and sharing of data among processors requires execution of explicit message-passing constructs
International Nuclear Information System (INIS)
Won, Jong Hyuck; Cho, Nam Zin
2010-01-01
In group condensation for transport method, it is well-known that angle-dependent total cross section is generated. To remove this difficulty on angledependent total cross section, we normally perform the group condensation on total cross section by using scalar flux weight as used in neutron diffusion method. In this study, angle-dependent total cross section is directly applied to the discrete ordinates method. In addition, angle collapsing concept is introduced based on equivalence to reduce calculational burden of transport computation. We also show numerical results for a heterogeneous 1-D slab problem with local/global iteration, in which fine-group discrete ordinates calculation is used in local problem while few-group angle collapsed discrete ordinates calculation is used in global problem iteratively
International Nuclear Information System (INIS)
Zerr, R.J.; Azmy, Y.Y.
2010-01-01
A spatial domain decomposition with a parallel block Jacobi solution algorithm has been developed based on the integral transport matrix formulation of the discrete ordinates approximation for solving the within-group transport equation. The new methodology abandons the typical source iteration scheme and solves directly for the fully converged scalar flux. Four matrix operators are constructed based upon the integral form of the discrete ordinates equations. A single differential mesh sweep is performed to construct these operators. The method is parallelized by decomposing the problem domain into several smaller sub-domains, each treated as an independent problem. The scalar flux of each sub-domain is solved exactly given incoming angular flux boundary conditions. Sub-domain boundary conditions are updated iteratively, and convergence is achieved when the scalar flux error in all cells meets a pre-specified convergence criterion. The method has been implemented in a computer code that was then employed for strong scaling studies of the algorithm's parallel performance via a fixed-size problem in tests ranging from one domain up to one cell per sub-domain. Results indicate that the best parallel performance compared to source iterations occurs for optically thick, highly scattering problems, the variety that is most difficult for the traditional SI scheme to solve. Moreover, the minimum execution time occurs when each sub-domain contains a total of four cells. (authors)
Hydrogen transport in a toroidal plasma using multigroup discrete-ordinates methodology
International Nuclear Information System (INIS)
Wienke, B.R.; Miller, W.F. Jr.; Seed, T.J.
1979-01-01
Neutral hydrogen transport in a fully ionized two-dimensional tokamak plasma was examined using discrete ordinates and contrasted with earlier analyses. In particular, curvature effects induced by toroidal geometries and ray effects caused by possible source localization were investigated. From an overview of the multigroup discrete-ordinates approximation, methodology in two-dimensional cylindrical geometry is detailed, mesh and plasma zoning procedures are sketched, and the piecewise polynomial solution algorithm on a triangular domain is obtained. Toroidal effects and comparisons as related to reaction rates and perticle spectra are examined for various model and source configurations
International Nuclear Information System (INIS)
Zazula, J.M.
1983-01-01
The general purpose code BALTORO was written for coupling the three-dimensional Monte-Carlo /MC/ with the one-dimensional Discrete Ordinates /DO/ radiation transport calculations. The quantity of a radiation-induced /neutrons or gamma-rays/ nuclear effect or the score from a radiation-yielding nuclear effect can be analysed in this way. (author)
Sarvari, S. M. Hosseini
2017-09-01
The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.
A parallel algorithm for solving the integral form of the discrete ordinates equations
International Nuclear Information System (INIS)
Zerr, R. J.; Azmy, Y. Y.
2009-01-01
The integral form of the discrete ordinates equations involves a system of equations that has a large, dense coefficient matrix. The serial construction methodology is presented and properties that affect the execution times to construct and solve the system are evaluated. Two approaches for massively parallel implementation of the solution algorithm are proposed and the current results of one of these are presented. The system of equations May be solved using two parallel solvers-block Jacobi and conjugate gradient. Results indicate that both methods can reduce overall wall-clock time for execution. The conjugate gradient solver exhibits better performance to compete with the traditional source iteration technique in terms of execution time and scalability. The parallel conjugate gradient method is synchronous, hence it does not increase the number of iterations for convergence compared to serial execution, and the efficiency of the algorithm demonstrates an apparent asymptotic decline. (authors)
C5 Benchmark Problem with Discrete Ordinate Radiation Transport Code DENOVO
Energy Technology Data Exchange (ETDEWEB)
Yesilyurt, Gokhan [ORNL; Clarno, Kevin T [ORNL; Evans, Thomas M [ORNL; Davidson, Gregory G [ORNL; Fox, Patricia B [ORNL
2011-01-01
The C5 benchmark problem proposed by the Organisation for Economic Co-operation and Development/Nuclear Energy Agency was modeled to examine the capabilities of Denovo, a three-dimensional (3-D) parallel discrete ordinates (S{sub N}) radiation transport code, for problems with no spatial homogenization. Denovo uses state-of-the-art numerical methods to obtain accurate solutions to the Boltzmann transport equation. Problems were run in parallel on Jaguar, a high-performance supercomputer located at Oak Ridge National Laboratory. Both the two-dimensional (2-D) and 3-D configurations were analyzed, and the results were compared with the reference MCNP Monte Carlo calculations. For an additional comparison, SCALE/KENO-V.a Monte Carlo solutions were also included. In addition, a sensitivity analysis was performed for the optimal angular quadrature and mesh resolution for both the 2-D and 3-D infinite lattices of UO{sub 2} fuel pin cells. Denovo was verified with the C5 problem. The effective multiplication factors, pin powers, and assembly powers were found to be in good agreement with the reference MCNP and SCALE/KENO-V.a Monte Carlo calculations.
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
International Nuclear Information System (INIS)
FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov
2002-01-01
The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
Fan, W C; Powell, J L
2002-01-01
The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.
Discrete ordinates cross-section generation in parallel plane geometry -- 2: Computational results
International Nuclear Information System (INIS)
Yavuz, M.
1998-01-01
In Ref. 1, the author presented inverse discrete ordinates (S N ) methods for cross-section generation with an arbitrary scattering anisotropy of order L (L ≤ N - 1) in parallel plane geometry. The solution techniques depend on the S N eigensolutions. The eigensolutions are determined by the inverse simplified S N method (ISS N ), which uses the surface Green's function matrices (T and R). Inverse problems are generally designed so that experimentally measured physical quantities can be used in the formulations. In the formulations, although T and R (TR matrices) are measurable quantities, the author does not have such data to check the adequacy and accuracy of the methods. However, it is possible to compute TR matrices by S N methods. The author presents computational results and computationally observed properties
Uniform Gauss-Weight Quadratures for Discrete Ordinate Transport Calculations
International Nuclear Information System (INIS)
Carew, John F.; Hu, Kai; Zamonsky, Gabriel
2000-01-01
Recently, a uniform equal-weight quadrature set, UE n , and a uniform Gauss-weight quadrature set, UG n , have been derived. These quadratures have the advantage over the standard level-symmetric LQ n quadrature sets in that the weights are positive for all orders,and the transport solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased,the points approach a uniform continuous distribution on the unit sphere,and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased.The numerical characteristics of the UE n quadrature set have been investigated previously. In this paper, numerical calculations are performed to evaluate the application of the UG n quadrature set in typical transport analyses. A series of DORT transport calculations of the >1-MeV neutron flux have been performed for a set of pressure-vessel fluence benchmark problems. These calculations employed the UG n (n = 8, 12, 16, 24, and 32) quadratures and indicate that the UG n solutions have converged to within ∼0.25%. The converged UG n solutions are found to be comparable to the UE n results and are more accurate than the level-symmetric S 16 predictions
The three-dimensional, discrete ordinates neutral particle transport code TORT: An overview
International Nuclear Information System (INIS)
Azmy, Y.Y.
1996-01-01
The centerpiece of the Discrete Ordinates Oak Ridge System (DOORS), the three-dimensional neutral particle transport code TORT is reviewed. Its most prominent features pertaining to large applications, such as adjustable problem parameters, memory management, and coarse mesh methods, are described. Advanced, state-of-the-art capabilities including acceleration and multiprocessing are summarized here. Future enhancement of existing graphics and visualization tools is briefly presented
Discrete-ordinates electron transport calculations using standard neutron transport codes
International Nuclear Information System (INIS)
Morel, J.E.
1979-01-01
The primary purpose of this work was to develop a method for using standard neutron transport codes to perform electron transport calculations. The method is to develop approximate electron cross sections which are sufficiently well-behaved to be treated with standard S/sub n/ methods, but which nonetheless yield flux solutions which are very similar to the exact solutions. The main advantage of this approach is that, once the approximate cross sections are constructed, their multigroup Legendre expansion coefficients can be calculated and input to any standard S/sub n/ code. Discrete-ordinates calculations were performed to determine the accuracy of the flux solutions for problems corresponding to 1.0-MeV electrons incident upon slabs of aluminum and gold. All S/sub n/ calculations were compared with similar calculations performed with an electron Monte Carlo code, considered to be exact. In all cases, the discrete-ordinates solutions for integral flux quantities (i.e., scalar flux, energy deposition profiles, etc.) are generally in agreement with the Monte Carlo solutions to within approximately 5% or less. The central conclusion is that integral electron flux quantities can be efficiently and accurately calculated using standard S/sub n/ codes in conjunction with approximate cross sections. Furthermore, if group structures and approximate cross section construction are optimized, accurate differential flux energy spectra may also be obtainable without having to use an inordinately large number of energy groups. 1 figure
National Research Council Canada - National Science Library
Labowski, Kristofer
2001-01-01
The Linear Characteristic (LC) method on rectangular boxoid meshes is a discrete ordinate neutron transport technique that uses both zeroth and first moments of the angular neutron flux to construct a relatively accurate...
International Nuclear Information System (INIS)
Wu Hongchun; Xie Zhongsheng; Zhu Xuehua
1994-01-01
The nodal discrete-ordinate transport calculating model of anisotropy scattering problem in three-dimensional cartesian geometry is given. The computing code NOTRAN/3D has been encoded and the satisfied conclusion is gained
Numerical solution of neutron transport equations in discrete ordinates and slab geometry
International Nuclear Information System (INIS)
Serrano Pedraza, F.
1985-01-01
An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used
Generalized perturbation theory using two-dimensional, discrete ordinates transport theory
International Nuclear Information System (INIS)
Childs, R.L.
1979-01-01
Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions
GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method
International Nuclear Information System (INIS)
Gong Chunye; Liu Jie; Chi Lihua; Huang Haowei; Fang Jingyue; Gong Zhenghu
2011-01-01
Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates (S n ) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.
GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method
Gong, Chunye; Liu, Jie; Chi, Lihua; Huang, Haowei; Fang, Jingyue; Gong, Zhenghu
2011-07-01
Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates ( Sn) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.
The ADO-nodal method for solving two-dimensional discrete ordinates transport problems
International Nuclear Information System (INIS)
Barichello, L.B.; Picoloto, C.B.; Cunha, R.D. da
2017-01-01
Highlights: • Two-dimensional discrete ordinates neutron transport. • Analytical Discrete Ordinates (ADO) nodal method. • Heterogeneous media fixed source problems. • Local solutions. - Abstract: In this work, recent results on the solution of fixed-source two-dimensional transport problems, in Cartesian geometry, are reported. Homogeneous and heterogeneous media problems are considered in order to incorporate the idea of arbitrary number of domain division into regions (nodes) when applying the ADO method, which is a method of analytical features, to those problems. The ADO-nodal formulation is developed, for each node, following previous work devoted to heterogeneous media problem. Here, however, the numerical procedure is extended to higher number of domain divisions. Such extension leads, in some cases, to the use of an iterative method for solving the general linear system which defines the arbitrary constants of the general solution. In addition to solve alternative heterogeneous media configurations than reported in previous works, the present approach allows comparisons with results provided by other metodologies generated with refined meshes. Numerical results indicate the ADO solution may achieve a prescribed accuracy using coarser meshes than other schemes.
A linear multiple balance method for discrete ordinates neutron transport equations
International Nuclear Information System (INIS)
Park, Chang Je; Cho, Nam Zin
2000-01-01
A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient
International Nuclear Information System (INIS)
Seed, T.J.; Miller, W.F. Jr.; Brinkley, F.W. Jr.
1977-03-01
TRIDENT solves the two-dimensional-multigroup-transport equations in rectangular (x-y) and cylindrical (r-z) geometries using a regular triangular mesh. Regular and adjoint, inhomogeneous and homogeneous (k/sub eff/ and eigenvalue searches) problems subject to vacuum, reflective, white, or source boundary conditions are solved. General anisotropic scattering is allowed and anisotropic-distributed sources are permitted. The discrete-ordinates approximation is used for the neutron directional variables. An option is included to append a fictitious source to the discrete-ordinates equations that is defined such that spherical-harmonics solutions (in x-y geometry) or spherical-harmonics-like solutions (in r-z geometry) are obtained. A spatial-finite-element method is used in which the angular flux is expressed as a linear polynomial in each triangle that is discontinous at triangle boundaries. Unusual Features of the program: Provision is made for creation of standard interface output files for S/sub N/ constants, angle-integrated (scalar) fluxes, and angular fluxes. Standard interface input files for S/sub N/ constants, inhomogeneous sources, cross sections, and the scalar flux may be read. Flexible edit options as well as a dump and restart capability are provided
International Nuclear Information System (INIS)
Asadzadeh, M.; Thevenot, L.
2010-01-01
The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (D G) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ??in R3 with a polygonal convex cross-section ? The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.
Program to solve the multigroup discrete ordinates transport equation in (x,y,z) geometry
International Nuclear Information System (INIS)
Lathrop, K.D.
1976-04-01
Numerical formulations and programming algorithms are given for the THREETRAN computer program which solves the discrete ordinates, multigroup transport equation in (x,y,z) geometry. An efficient, flexible, and general data-handling strategy is derived to make use of three hierarchies of storage: small core memory, large core memory, and disk file. Data management, input instructions, and sample problem output are described. A six-group, S 4 , 18 502 mesh point, 2 800 zone, k/sub eff/ calculation of the ZPPR-4 critical assembly required 144 min of CDC-7600 time to execute to a convergence tolerance of 5 x 10 -4 and gave results in good qualitative agreement with experiment and other calculations. 6 references
High-order discrete ordinate transport in hexagonal geometry: A new capability in ERANOS
International Nuclear Information System (INIS)
Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J.M.
2010-01-01
This paper presents the implementation of an arbitrary order discontinuous Galerkin scheme within the framework of a discrete ordinate solver of the neutron transport equation for nuclear reactor calculations. More precisely, it deals with non-conforming spatial meshes for the 2 D and 3 D modeling of core geometries based on hexagonal assemblies. This work aims at improving the capabilities of the ERANOS code system dedicated to fast reactor analysis and design. Both the angular quadrature and spatial scheme peculiarities for hexagonal geometries are presented. A particular focus is set on the spatial non-conforming mesh and variable order capabilities of this scheme in anticipation to the development of spatial adaptiveness algorithms. These features are illustrated on a 3 D numerical benchmark with comparison to a Monte Carlo reference and a 2 D benchmark that shows the potential of this scheme for both h-and p-adaptation.
International Nuclear Information System (INIS)
Zazula, J.M.
1984-01-01
This work concerns calculation of a neutron response, caused by a neutron field perturbed by materials surrounding the source or the detector. Solution of a problem is obtained using coupling of the Monte Carlo radiation transport computation for the perturbed region and the discrete ordinates transport computation for the unperturbed system. (author). 62 refs
Longoni, Gianluca
In the nuclear science and engineering field, radiation transport calculations play a key-role in the design and optimization of nuclear devices. The linear Boltzmann equation describes the angular, energy and spatial variations of the particle or radiation distribution. The discrete ordinates method (S N) is the most widely used technique for solving the linear Boltzmann equation. However, for realistic problems, the memory and computing time require the use of supercomputers. This research is devoted to the development of new formulations for the SN method, especially for highly angular dependent problems, in parallel environments. The present research work addresses two main issues affecting the accuracy and performance of SN transport theory methods: quadrature sets and acceleration techniques. New advanced quadrature techniques which allow for large numbers of angles with a capability for local angular refinement have been developed. These techniques have been integrated into the 3-D SN PENTRAN (Parallel Environment Neutral-particle TRANsport) code and applied to highly angular dependent problems, such as CT-Scan devices, that are widely used to obtain detailed 3-D images for industrial/medical applications. In addition, the accurate simulation of core physics and shielding problems with strong heterogeneities and transport effects requires the numerical solution of the transport equation. In general, the convergence rate of the solution methods for the transport equation is reduced for large problems with optically thick regions and scattering ratios approaching unity. To remedy this situation, new acceleration algorithms based on the Even-Parity Simplified SN (EP-SSN) method have been developed. A new stand-alone code system, PENSSn (Parallel Environment Neutral-particle Simplified SN), has been developed based on the EP-SSN method. The code is designed for parallel computing environments with spatial, angular and hybrid (spatial/angular) domain
International Nuclear Information System (INIS)
Ching, J.; Oblow, E.M.; Goldstein, H.
1976-01-01
An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab
The TORT three-dimensional discrete ordinates neutron/photon transport code (TORT version 3)
Energy Technology Data Exchange (ETDEWEB)
Rhoades, W.A.; Simpson, D.B.
1997-10-01
TORT calculates the flux or fluence of neutrons and/or photons throughout three-dimensional systems due to particles incident upon the system`s external boundaries, due to fixed internal sources, or due to sources generated by interaction with the system materials. The transport process is represented by the Boltzman transport equation. The method of discrete ordinates is used to treat the directional variable, and a multigroup formulation treats the energy dependence. Anisotropic scattering is treated using a Legendre expansion. Various methods are used to treat spatial dependence, including nodal and characteristic procedures that have been especially adapted to resist numerical distortion. A method of body overlay assists in material zone specification, or the specification can be generated by an external code supplied by the user. Several special features are designed to concentrate machine resources where they are most needed. The directional quadrature and Legendre expansion can vary with energy group. A discontinuous mesh capability has been shown to reduce the size of large problems by a factor of roughly three in some cases. The emphasis in this code is a robust, adaptable application of time-tested methods, together with a few well-tested extensions.
Discrete ordinates transport methods for problems with highly forward-peaked scattering
International Nuclear Information System (INIS)
Pautz, S.D.
1998-04-01
The author examines the solutions of the discrete ordinates (S N ) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S N equations. This analysis shows that in this asymptotic limit the S N solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S N equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method
International Nuclear Information System (INIS)
Mathews, K.; Sjoden, G.; Minor, B.
1994-01-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in slab geometry is derived and compared with current methods. It is similar to the linear characteristic (or, in slab geometry, the linear nodal) quadrature but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx), whose parameters are root-solved to match the known (from the previous iteration) average and first moment of the source over the cell. Like the linear adaptive method, the exponential characteristic method is positive and nonlinear but more accurate and more readily extended to other cell shapes. The nonlinearity has not interfered with convergence. The authors introduce the ''exponential moment functions,'' a generalization of the functions used by Walters in the linear nodal method, and use them to avoid numerical ill-conditioning. The method exhibits O(Δx 4 ) truncation error on fine enough meshes; the error is insensitive to mesh size for coarse meshes. In a shielding problem, it is accurate to 10% using 16-mfp-thick cells; conventional methods err by 8 to 15 orders of magnitude. The exponential characteristic method is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems
International Nuclear Information System (INIS)
Garcia, R.D.M.
2015-01-01
Highlights: • An improved 1-D model of 3-D particle transport in ducts is studied. • The cases of isotropic and directional incidence are treated with the ADO method. • Accurate numerical results are reported for ducts of circular cross section. • A comparison with results of other authors is included. • The ADO method is found to be very efficient. - Abstract: An analytical discrete-ordinates solution is developed for the problem of particle transport in ducts, as described by a one-dimensional model constructed with two basis functions. Two types of particle incidence are considered: isotropic incidence and incidence described by the Dirac delta distribution. Accurate numerical results are tabulated for the reflection probabilities of semi-infinite ducts and the reflection and transmission probabilities of finite ducts. It is concluded that the developed solution is more efficient than commonly used numerical implementations of the discrete-ordinates method.
International Nuclear Information System (INIS)
Abreu, Marcos Pimenta de
1998-01-01
We describe a numerical method applied to the first-order form of one-speed slab-geometry discrete ordinates equations modelling time-independent neutron transport problems with anisotropic scattering, with no interior source and defined in a nonmultiplying homogeneous host medium. Our numerical method is concerned with the generation of the spectrum and of a vector basis for the null space of the one-speed slab-geometry discrete ordinates operator. Moreover, it allows us to overcome the difficulties introduced in previous methods by anisotropic scattering and by angular quadrature sets of high order. To illustrate the positive features of our numerical method, we present numerical results for one-speed slab-geometry neutron transport model problems with anisotropic scattering
International Nuclear Information System (INIS)
Minor, B.; Mathews, K.
1995-01-01
The exponential characteristic (EC) spatial quadrature for discrete ordinates neutral particle transport previously introduced in slab geometry is extended here to x-y geometry with rectangular cells. The method is derived and compared with current methods. It is similar to the linear characteristic (LC) quadrature (a linear-linear moments method) but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx + cy), whose parameters are rootsolved to match the known (from the previous iteration) spatial average and first moments of the source over the cell. Similarly, EC assumes exponential distributions of flux along cell edges through which particles enter the cell, with parameters chosen to match the average and first moments of flux, as passed from the adjacent, upstream cells (or as determined by boundary conditions). Like the linear adaptive (LA) method, EC is positive and nonlinear. It is more accurate than LA and does not require subdivision of cells. The nonlinearity has not interfered with convergence. The exponential moment functions, which were introduced with the slab geometry method, are extended to arbitrary dimensions (numbers of arguments) and used to avoid numerical ill conditioning. As in slab geometry, the method approaches O(Δx 4 ) global truncation error on fine-enough meshes, while the error is insensitive to mesh size for coarse meshes. Performance of the method is compared with that of the step characteristic, LC, linear nodal, step adaptive, and LA schemes. The EC method is a strong performer with scattering ratios ranging from 0 to 0.9 (the range tested), particularly so for lower scattering ratios. As in slab geometry, EC is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems
International Nuclear Information System (INIS)
Godoy, William F.; Liu Xu
2012-01-01
The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.
International Nuclear Information System (INIS)
Filho, J. F. P.; Barichello, L. B.
2013-01-01
In this work, an analytical discrete ordinates method is used to solve a nodal formulation of a neutron transport problem in x, y-geometry. The proposed approach leads to an important reduction in the order of the associated eigenvalue systems, when combined with the classical level symmetric quadrature scheme. Auxiliary equations are proposed, as usually required for nodal methods, to express the unknown fluxes at the boundary introduced as additional unknowns in the integrated equations. Numerical results, for the problem defined by a two-dimensional region with a spatially constant and isotropically emitting source, are presented and compared with those available in the literature. (authors)
International Nuclear Information System (INIS)
Yoo, Han Jong; Won, Jong Hyuck; Cho, Nam Zin
2011-01-01
In computational studies of neutron transport equations, the fine-group to few-group condensation procedure leads to equivalent total cross section that becomes angle dependent. The difficulty of this angle dependency has been traditionally treated by consistent P or extended transport approximation in the literature. In a previous study, we retained the angle dependency of the total cross section and applied directly to the discrete ordinates equation, with additional concept of angle-collapsing, and tested in a one-dimensional slab problem. In this study, we provide further results of this discrete ordinates-like method in comparison with the typical traditional methods. In addition, IRAM acceleration (based on Krylov subspace method) is tested for the purpose of further reducing the computational burden of few-group calculation. From the test results, it is ascertained that the angle-dependent total cross section with angle-collapsing gives excellent estimation of k_e_f_f and flux distribution and that IRAM acceleration effectively reduces the number of outer iterations. However, since IRAM requires sufficient convergence in inner iterations, speedup in total computer time is not significant for problems with upscattering. (author)
High-order discrete ordinate transport in non-conforming 2D Cartesian meshes
International Nuclear Information System (INIS)
Gastaldo, L.; Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J. M.
2009-01-01
We present in this paper a numerical scheme for solving the time-independent first-order form of the Boltzmann equation in non-conforming 2D Cartesian meshes. The flux solution technique used here is the discrete ordinate method and the spatial discretization is based on discontinuous finite elements. In order to have p-refinement capability, we have chosen a hierarchical polynomial basis based on Legendre polynomials. The h-refinement capability is also available and the element interface treatment has been simplified by the use of special functions decomposed over the mesh entities of an element. The comparison to a classical S N method using the Diamond Differencing scheme as spatial approximation confirms the good behaviour of the method. (authors)
International Nuclear Information System (INIS)
Daskalov, G.M.; Baker, R.S.; Little, R.C.; Rogers, D.W.O.; Williamson, J.F.
2000-01-01
The DANTSYS discrete ordinates computer code system is applied to quantitative estimation of water kerma rate distributions in the vicinity of discrete photon sources with energies in the 20- to 800-keV range in two-dimensional cylindrical r-z geometry. Unencapsulated sources immersed in cylindrical water phantoms of 40-cm diameter and 40-cm height are modeled in either homogeneous phantoms or shielded by Ti, Fe, and Pb filters with thicknesses of 1 and 2 mean free paths. The obtained dose results are compared with corresponding photon Monte Carlo simulations. A 210-group photon cross-section library for applications in this energy range is developed and applied, together with a general-purpose 42-group library developed at Los Alamos National Laboratory, for DANTSYS calculations. The accuracy of DANTSYS with the 42-group library relative to Monte Carlo exhibits large pointwise fluctuations from -42 to +84%. The major cause for the observed discrepancies is determined to be the inadequacy of the weighting function used for the 42-group library derivation. DANTSYS simulations with a finer 210-group library show excellent accuracy on and off the source transverse plane relative to Monte Carlo kerma calculations, varying from minus4.9 to 3.7%. The P 3 Legendre polynomial expansion of the angular scattering function is shown to be sufficient for accurate calculations. The results demonstrate that DANTSYS is capable of calculating photon doses in very good agreement with Monte Carlo and that the multigroup cross-section library and efficient techniques for mitigation of ray effects are critical for accurate discrete ordinates implementation
Discrete ordinates cross-sections generation in parallel plane geometry -- 1: Concept
International Nuclear Information System (INIS)
Yavuz, M.
1998-01-01
Cross-section formulations derived from the linear Boltzman transport equation have been the subjects of several studies. In these studies, theoretical foundations and concepts are provided, and the solution techniques are derived. The author presents new methods for generating cross-section sets for transport problems, with an arbitrary scattering anisotropy of order L (L ≤ N - 1), approximated by the S N (and P N-1 ) methods. The formulations require knowledge of the eigensolutions, which may be determined by a recent eigenvalue equation found in Yavuz. The motivation for this study is to generate few-group cross sections for pin cells (and/or assemblies) using a Monte Carlo code, for example, MCNP, with a continuous-energy cross-section library. However, this work is a first step, and it describes a new concept to perform inverse transport calculations, provided that the surface Green's functions over desired angular and energy intervals are known
TDTORT: Time-Dependent, 3-D, Discrete Ordinates, Neutron Transport Code System with Delayed Neutrons
International Nuclear Information System (INIS)
2002-01-01
1 - Description of program or function: TDTORT solves the time-dependent, three-dimensional neutron transport equation with explicit representation of delayed neutrons to estimate the fission yield from fissionable material transients. This release includes a modified version of TORT from the C00650MFMWS01 DOORS3.1 code package plus the time-dependent TDTORT code. GIP is also included for cross-section preparation. TORT calculates the flux or fluence of particles due to particles incident upon the system from extraneous sources or generated internally as a result of interaction with the system in two- or three-dimensional geometric systems. The principle application is to the deep-penetration transport of neutrons and photons. Reactor eigenvalue problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis. TDTORT reads ANISN-format cross-section libraries, which are not included in the package. Users may choose from several available in RSICC's data library collection which can be identified by the keyword 'ANISN FORMAT'. 2 - Methods:The time-dependent spatial flux is expressed as a product of a space-, energy-, and angle-dependent shape function, which is usually slowly varying in time and a purely time-dependent amplitude function. The shape equation is solved for the shape using TORT; and the result is used to calculate the point kinetics parameters (e.g., reactivity) by using their inner product definitions, which are then used to solve the time-dependent amplitude and precursor equations. The amplitude function is calculated by solving the kinetics equations using the LSODE solver. When a new shape calculation is needed, the flux is calculated using the newly computed amplitude function. The Boltzmann transport equation is solved using the method of discrete ordinates to treat the directional variable and weighted finite-difference methods, in addition to Linear Nodal
International Nuclear Information System (INIS)
Brockmann, H.
1992-01-01
Using the discrete ordinates method for the treatment of neutral particle transport through voids serious flux distortions may occur due to the restricted streaming of particles along discrete directions. For mitigating this type of ray effect the method of view factors is proposed which has been developed in the theory of thermal radiation for describing the radiant exchange among surfaces. In order to apply this method to transport theory generalized view factors are defined which regard the angular dependence of the radiation leaving the surfaces. The generalized view factors are calculated analytically for r-z cylinder geometries and by applying the view factor algebra. The method was realized in the discrete ordinates transport code DOT 4.2 and applied to an r-z analogue of the S I S (Square-In-Square) sample problem. The results of the proposed method are compared with those calculated by the common discrete ordinates method and the Monte Carlo method
International Nuclear Information System (INIS)
Ching, J.T.
1975-01-01
An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated which allows the development of a discrete-energy, discrete-ordinates method for the solution of radiation transport problems. The method utilizes a modified version of a cross section processing scheme devised for the moments method code BMT and the transport equation solution algorithm from the one-dimensional discrete-ordinates transport code ANISN. The combined system, identified as MOMANS, computes fluxes directly from point cross sections in a single operation. In the cross-section processing, the group averaging required for multigroup calculations is replaced by a fast numerical scheme capable of generating a set of transfer cross sections containing all the physical features of interest, thereby increasing the detail in the calculated results. Test calculations in which the discrete-energy method was compared with the multigroup method have shown that for the same energy grid (number of points = number of groups), the discrete-energy method is faster but somewhat less accurate than the multigroup method. However, the accuracy of the discrete-energy method increases rapidly as the spacing between energy points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum the discrete-energy method has therefore proven to be as accurate as, and more economical than, the multigroup technique. This was demonstrated by the application of the method to the study of the transport of neutrons in an iron sphere. Using the capability of the discrete-energy method for rapidly treating changes in cross-section sets, the propagation of neutrons from a 14 MeV source in a 22 cm radius sphere of iron was analyzed for sensitivity to changes in the microscopic scattering mechanisms
International Nuclear Information System (INIS)
Masiello, Emiliano; Martin, Brunella; Do, Jean-Michel
2011-01-01
A new development for the IDT solver is presented for large reactor core applications in XYZ geometries. The multigroup discrete-ordinate neutron transport equation is solved using a Domain-Decomposition (DD) method coupled with the Coarse-Mesh Finite Differences (CMFD). The later is used for accelerating the DD convergence rate. In particular, the external power iterations are preconditioned for stabilizing the oscillatory behavior of the DD iterative process. A set of critical 2-D and 3-D numerical tests on a single processor will be presented for the analysis of the performances of the method. The results show that the application of the CMFD to the DD can be a good candidate for large 3D full-core parallel applications. (author)
International Nuclear Information System (INIS)
Homma, Y.; Moriwaki, H.; Ikeda, K.; Ohdi, S.
2013-01-01
This paper deals with the verification of the 3 dimensional triangular prismatic discrete ordinates transport calculation code ENSEMBLE-TRIZ by comparison with the multi-group Monte Carlo calculation code GMVP in a large fast breeder reactor. The reactor is a 750 MWe electric power sodium cooled reactor. Nuclear characteristics are calculated at the beginning of cycle of an initial core and at the beginning and the end of cycle of an equilibrium core. According to the calculations, the differences between the two methodologies are smaller than 0.0002 Δk in the multiplication factor, relatively about 1% in the control rod reactivity, and 1% in the sodium void reactivity. (authors)
Energy Technology Data Exchange (ETDEWEB)
Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Prolo Filho, Joao Francisco [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica, Estatistica e Fisica; Dias da Cunha, Rudnei; Basso Barichello, Liliane [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica
2014-04-15
In this work a study of two-dimensional fixed-source neutron transport problems, in Cartesian geometry, is reported. The approach reduces the complexity of the multidimensional problem using a combination of nodal schemes and the Analytical Discrete Ordinates Method (ADO). The unknown leakage terms on the boundaries that appear from the use of the derivation of the nodal scheme are incorporated to the problem source term, such as to couple the one-dimensional integrated solutions, made explicit in terms of the x and y spatial variables. The formulation leads to a considerable reduction of the order of the associated eigenvalue problems when combined with the usual symmetric quadratures, thereby providing solutions that have a higher degree of computational efficiency. Reflective-type boundary conditions are introduced to represent the domain on a simpler form than that previously considered in connection with the ADO method. Numerical results obtained with the technique are provided and compared to those present in the literature. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Oliva, Amaury M.; Filho, Hermes A.; Silva, Davi M.; Garcia, Carlos R., E-mail: aoliva@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: davijmsilva@yahoo.com.br, E-mail: cgh@instec.cu [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional; Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2017-07-01
In this paper, we propose a numerical methodology for the development of a method of the spectral nodal class that will generate numerical solutions free from spatial truncation errors. This method, denominated Spectral Deterministic Method (SDM), is tested as an initial study of the solutions (spectral analysis) of neutron transport equations in the discrete ordinates (S{sub N}) formulation, in one-dimensional slab geometry, multigroup approximation, with linearly anisotropic scattering, considering homogeneous and heterogeneous domains with fixed source. The unknowns in the methodology are the cell-edge, and cell average angular fluxes, the numerical values calculated for these quantities coincide with the analytic solution of the equations. These numerical results are shown and compared with the traditional ne- mesh method Diamond Difference (DD) and the coarse-mesh method spectral Green's function (SGF) to illustrate the method's accuracy and stability. The solution algorithms problems are implemented in a computer simulator made in C++ language, the same that was used to generate the results of the reference work. (author)
International Nuclear Information System (INIS)
Ryman, J.C.; Eckerman, K.F.; Shultis, J.K.; Faw, R.E.; Dillman, L.T.
1996-01-01
Federal Guidance Report No. 12 tabulates dose coefficients for external exposure to photons and electrons emitted by radionuclides distributed in air, water, and soil. Although the dose coefficients of this report are based on previously developed dosimetric methodologies, they are derived from new, detailed calculations of energy and angular distributions of the radiations incident on the body and the transport of these radiations within the body. Effort was devoted to expanding the information available for assessment of radiation dose from radionuclides distributed on or below the surface of the ground. A companion paper (External Exposure to Radionuclides in Air, Water, and Soil) discusses the significance of the new tabulations of coefficients and provides detiled comparisons to previously published values. This paper discusses details of the photon transport calculations
A posteriori error estimator and AMR for discrete ordinates nodal transport methods
International Nuclear Information System (INIS)
Duo, Jose I.; Azmy, Yousry Y.; Zikatanov, Ludmil T.
2009-01-01
In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems' simulation. In this regard, error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). In this paper, we derive an a posteriori error estimator based on the nodal solution of the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N). Furthermore, by making assumptions on the regularity of the solution, we represent the error estimator as a function of computable volume and element-edges residuals. The global L 2 error norm is proved to be bound by the estimator. To lighten the computational load, we present a numerical approximation to the aforementioned residuals and split the global norm error estimator into local error indicators. These indicators are used to drive an AMR strategy for the spatial discretization. However, the indicators based on forward solution residuals alone do not bound the cell-wise error. The estimator and AMR strategy are tested in two problems featuring strong heterogeneity and highly transport streaming regime with strong flux gradients. The results show that the error estimator indeed bounds the global error norms and that the error indicator follows the cell-error's spatial distribution pattern closely. The AMR strategy proves beneficial to optimize resources, primarily by reducing the number of unknowns solved for to achieve prescribed solution accuracy in global L 2 error norm. Likewise, AMR achieves higher accuracy compared to uniform refinement when resolving sharp flux gradients, for the same number of unknowns
International Nuclear Information System (INIS)
Maertens, H.D.
1982-01-01
The inhomogenious structure of modern heavy water reactor fuel elements result in a strong spacial dependence of the neutron flux. The flux distribution can be calculated in detail by numerical methods, which describe exactly the geometrical heterogeniety and take into account the neutron flux anisotropy by higher transport theoretical approximations. Starting from the discrete ordinate method an approximation of the neutron transport equation has been developed, allowing for a cylindrical representation of the fuel-elements in a rectangular array of rods. The discretisation of the space variables, is based on the finite-difference approximation, defining a rectangular lattice in a two-dimensional cartesian coordinate system, which can be cut and replaced by circular mesh elements of a partially one-dimensional cylindrical coordinate system at arbitrary space points. To couple the two spacial regions the outer circle line of a cylindrical geometry is approximated in the cartesian system by a polygon with n >= 8. A cylindrical geometry is approximated in the cartesian system by a polygon with n>=8. A cylindrical geometry is thus enclosed by a system of two-dimensional rectangular, triangular and trapezoid mesh elements. The directional distribution of the neutron flux is conserved when switching from the xy-system to the cylindrical coordinate system. The angle discretisation by balanced sets of squares (EQsub(n)) allows a simple definition of transfer-coefficients for the redistribution of the neutron flux due to coordinate transformations. The procedure is verified and tested by selected problems. Possible applications and limits are discussed. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Baker, Randal Scott [Univ. of Arizona, Tucson, AZ (United States)
1990-01-01
The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S_{N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S_{N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S_{N} is well suited for by themselves. The fully coupled Monte Carlo/S_{N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S_{N} calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S_{N} region. The Monte Carlo and S_{N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S_{N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S_{N} code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating S_{N} calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.
International Nuclear Information System (INIS)
Hill, T.R.; Reed, W.H.
1976-01-01
TIMEX solves the time-dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time steps can be taken. Because no iteration is performed the method is exceptionally fast in terms of computing time per time step. Two acceleration methods, exponential extrapolation and rebalance, are utilized to improve the accuracy of the time differencing scheme. Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. The running time for TIMEX is highly problem-dependent, but varies almost linearly with the total number of unknowns and time steps. Provision is made for creation of standard interface output files for angular fluxes and angle-integrated fluxes. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage. 13 tables, 9 figures
Sputtering calculations with the discrete ordinated method
International Nuclear Information System (INIS)
Hoffman, T.J.; Dodds, H.L. Jr.; Robinson, M.T.; Holmes, D.K.
1977-01-01
The purpose of this work is to investigate the applicability of the discrete ordinates (S/sub N/) method to light ion sputtering problems. In particular, the neutral particle discrete ordinates computer code, ANISN, was used to calculate sputtering yields. No modifications to this code were necessary to treat charged particle transport. However, a cross section processing code was written for the generation of multigroup cross sections; these cross sections include a modification to the total macroscopic cross section to account for electronic interactions and small-scattering-angle elastic interactions. The discrete ordinates approach enables calculation of the sputtering yield as functions of incident energy and angle and of many related quantities such as ion reflection coefficients, angular and energy distributions of sputtering particles, the behavior of beams penetrating thin foils, etc. The results of several sputtering problems as calculated with ANISN are presented
Multiband discrete ordinates method: formalism and results
International Nuclear Information System (INIS)
Luneville, L.
1998-06-01
The multigroup discrete ordinates method is a classical way to solve transport equation (Boltzmann) for neutral particles. Self-shielding effects are not correctly treated due to large variations of cross sections in a group (in the resonance range). To treat the resonance domain, the multiband method is introduced. The main idea is to divide the cross section domain into bands. We obtain the multiband parameters using the moment method; the code CALENDF provides probability tables for these parameters. We present our implementation in an existing discrete ordinates code: SN1D. We study deep penetration benchmarks and show the improvement of the method in the treatment of self-shielding effects. (author)
International Nuclear Information System (INIS)
O'Dell, R.D.; Stepanek, J.; Wagner, M.R.
1983-01-01
The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included
Energy Technology Data Exchange (ETDEWEB)
Wilcox, T. P.
1973-09-20
The code ANISN-L solves the one-dimensional, multigroup, time-independent Boltzmann transport equation by the method of discrete ordinates. In problems involving a fissionable system, it can calculate the system multiplication or alpha. In such cases, it is also capable of determining isotopic concentrations, radii, zone widths, or buckling in order to achieve a given multiplication or alpha. The code may also calculate fluxes caused by a specified fixed source. Neutron, gamma, and coupled neutron--gamma problems may be solved in either the forward or adjoint (backward) modes. Cross sections describing upscatter, as well as the usual downscatter, may be employed. This report describes the use of ANISN-L; this is a revised version of ANISN which handles both large and small problems efficiently on CDC-7600 computers. (RWR)
A variational synthesis nodal discrete ordinates method
International Nuclear Information System (INIS)
Favorite, J.A.; Stacey, W.M.
1999-01-01
A self-consistent nodal approximation method for computing discrete ordinates neutron flux distributions has been developed from a variational functional for neutron transport theory. The advantage of the new nodal method formulation is that it is self-consistent in its definition of the homogenized nodal parameters, the construction of the global nodal equations, and the reconstruction of the detailed flux distribution. The efficacy of the method is demonstrated by two-dimensional test problems
SPANDOM - source projection analytic nodal discrete ordinates method
International Nuclear Information System (INIS)
Kim, Tae Hyeong; Cho, Nam Zin
1994-01-01
We describe a new discrete ordinates nodal method for the two-dimensional transport equation. We solve the discrete ordinates equation analytically after the source term is projected and represented in polynomials. The method is applied to two fast reactor benchmark problems and compared with the TWOHEX code. The results indicate that the present method accurately predicts not only multiplication factor but also flux distribution
International Nuclear Information System (INIS)
Prinja, A.K.
1995-08-01
We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S N angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes
International Nuclear Information System (INIS)
Santos, Frederico P.; Xavier, Vinicius S.; Alves Filho, Hermes; Barros, Ricardo C.
2011-01-01
The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)
Energy Technology Data Exchange (ETDEWEB)
Askew, J R; Brissenden, R J [Technical Assessments and Services Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset (United Kingdom)
1963-08-15
This report gives an account of the DSN method for simulating neutron transport, together with methods of solution developed to deal with problems in the physics of thermal reactors, for which previously available computer programmes were unsatisfactory. The methods described are those incorporated in the programmes WINFRITH DSN written in FORTRAN language for the IBM 7090 and STRETCH computers. (author)
International Nuclear Information System (INIS)
Ganapol, B.D.
2015-01-01
Highlights: • Method of doubling solution for the pipe problem. • Uses convergence acceleration. • Fully discretized solution. • Improvement over ADO. - Abstract: We consider transport of light, neutrons, or any uncharged particles in a straight duct of circular cross section. This problem first came to fashion some 30 years ago when Pomraning and Prinja formulated their so called “pipe problem”. In the years to follow, investigators applied essentially every known method of numerical solution, including MMRW’s Wiener–Hopf – except possibly one. This presentation concerns that particular numerical solution, which arguably seems to be the most efficient of all.
Data visualization for ONEDANT and TWODANT discrete ordinates codes
International Nuclear Information System (INIS)
Lee, C.L.
1993-01-01
Effective graphical display of code calculations allow for efficient analysis of results. This is especially true in the case of discrete ordinates transport codes, which can generate thousands of flux or reaction rate data points per calculation. For this reason, a package of portable interface programs called OTTUI (ONEDANT-TWODANT-Tecplot trademark Unix-Based Interface) has been developed at Los Alamos National Laboratory to permit rapid visualization of ONEDANT and TWODANT discrete ordinates results using the graphics package Tecplot. This paper describes the various uses of OTTUI for display of ONEDANT and TWODANT problem geometries and calculational results
Simplified discrete ordinates method in spherical geometry
International Nuclear Information System (INIS)
Elsawi, M.A.; Abdurrahman, N.M.; Yavuz, M.
1999-01-01
The authors extend the method of simplified discrete ordinates (SS N ) to spherical geometry. The motivation for such an extension is that the appearance of the angular derivative (redistribution) term in the spherical geometry transport equation makes it difficult to decide which differencing scheme best approximates this term. In the present method, the angular derivative term is treated implicitly and thus avoids the need for the approximation of such term. This method can be considered to be analytic in nature with the advantage of being free from spatial truncation errors from which most of the existing transport codes suffer. In addition, it treats the angular redistribution term implicitly with the advantage of avoiding approximations to that term. The method also can handle scattering in a very general manner with the advantage of spending almost the same computational effort for all scattering modes. Moreover, the methods can easily be applied to higher-order S N calculations
International Nuclear Information System (INIS)
Longoni, G.; Haghighat, A.; Sjoden, G.
2005-01-01
This paper discusses a new preconditioned Sn algorithm referred to as FAST (Flux Acceleration Sn Transport). This algorithm uses the PENSSn code as the pre-conditioner, and the PENTRANSSn code system as the transport solver. PENSSn is developed based on the even-parity simplified Sn formulation in a parallel environment, and PENTRAN-SSn is a version of PENTRAN that uses PENSSn as the pre-conditioner with the FAST system. The paper briefly discusses the EP-SSn formulation and important numerical features of PENSSn. The FAST algorithm is discussed and tested for the C5G7 MOX eigenvalue benchmark problem. It is demonstrated that FAST leads to significant speedups (∼7) over the standard PENTRAN code. Moreover, FAST shows closer agreement with a reference Monte Carlo simulation. (authors)
Adaptive discrete-ordinates algorithms and strategies
International Nuclear Information System (INIS)
Stone, J.C.; Adams, M.L.
2005-01-01
We present our latest algorithms and strategies for adaptively refined discrete-ordinates quadrature sets. In our basic strategy, which we apply here in two-dimensional Cartesian geometry, the spatial domain is divided into regions. Each region has its own quadrature set, which is adapted to the region's angular flux. Our algorithms add a 'test' direction to the quadrature set if the angular flux calculated at that direction differs by more than a user-specified tolerance from the angular flux interpolated from other directions. Different algorithms have different prescriptions for the method of interpolation and/or choice of test directions and/or prescriptions for quadrature weights. We discuss three different algorithms of different interpolation orders. We demonstrate through numerical results that each algorithm is capable of generating solutions with negligible angular discretization error. This includes elimination of ray effects. We demonstrate that all of our algorithms achieve a given level of error with far fewer unknowns than does a standard quadrature set applied to an entire problem. To address a potential issue with other algorithms, we present one algorithm that retains exact integration of high-order spherical-harmonics functions, no matter how much local refinement takes place. To address another potential issue, we demonstrate that all of our methods conserve partial currents across interfaces where quadrature sets change. We conclude that our approach is extremely promising for solving the long-standing problem of angular discretization error in multidimensional transport problems. (authors)
On the convergence of multigroup discrete-ordinates approximations
International Nuclear Information System (INIS)
Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.
1987-01-01
Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations
Acceleration techniques for the discrete ordinate method
International Nuclear Information System (INIS)
Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego; Trautmann, Thomas
2013-01-01
In this paper we analyze several acceleration techniques for the discrete ordinate method with matrix exponential and the small-angle modification of the radiative transfer equation. These techniques include the left eigenvectors matrix approach for computing the inverse of the right eigenvectors matrix, the telescoping technique, and the method of false discrete ordinate. The numerical simulations have shown that on average, the relative speedup of the left eigenvector matrix approach and the telescoping technique are of about 15% and 30%, respectively. -- Highlights: ► We presented the left eigenvector matrix approach. ► We analyzed the method of false discrete ordinate. ► The telescoping technique is applied for matrix operator method. ► Considered techniques accelerate the computations by 20% in average.
Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem
International Nuclear Information System (INIS)
Wei, J.; Yang, S.
2013-01-01
In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)
DOMINO, Coupling of Discrete Ordinate Program DOT with Monte-Carlo Program MORSE
International Nuclear Information System (INIS)
1974-01-01
1 - Nature of physical problem solved: DOMINO is a general purpose code for coupling discrete ordinates and Monte Carlo radiation transport calculations. 2 - Method of solution: DOMINO transforms the angular flux as a function of energy group, mesh interval and discrete angle into current and subsequently into normalized probability distributions. 3 - Restrictions on the complexity of the problem: The discrete ordinates calculation is limited to an r-z geometry
Energy Technology Data Exchange (ETDEWEB)
Bal, G. [Departement MMN, Service IMA, Direction des Etudes et Recherches, Electricite de France (EDF), 92 - Clamart (France)
1995-10-01
Neutron transport in nuclear reactors is quite well modelled by the linear Boltzmann transport equation. Its solution is relatively easy, but unfortunately too expensive to achieve whole core computations. Thus, we have to simplify it, for example by homogenizing some physical characteristics. However, the solution may then be inaccurate. Moreover, in strongly homogeneous areas, the error may be too big. Then we would like to deal with such an inconvenient by solving the equation accurately on this area, but more coarsely away from it, so that the computation is not too expensive. This problem is the subject of a thesis. We present here some results obtained for slab geometry. The couplings between the fine and coarse discretization regions could be conceived in a number of approaches. Here, we only deal with the coupling at crossing the interface between two sub-domains. In the first section, we present the coupling of discrete ordinate methods for solving the homogeneous, isotropic and mono-kinetic equation. Coupling operators are defined and shown to be optimal. The second and the third sections are devoted to an extension of the previous results when the equation is non-homogeneous, anisotropic and multigroup (under some restrictive assumptions). Some numerical results are given in the case of isotropic and mono-kinetic equations. (author) 15 refs.
Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing
International Nuclear Information System (INIS)
Gerstl, S.A.W.; Zardecki, A.
1985-01-01
Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered
Nuclear data preparation and discrete ordinates calculation
International Nuclear Information System (INIS)
Carmignani, B.
1980-01-01
These lectures deal with the use of the GAM-GATHER and GAM-THERMOS chains for the calculation of lattice cross sections and within use of the discrete ordinates one dimensional ANISN code for the calculation of criticality and flux distribution of the cell and of the whole reactor. As an example the codes are applied to the calculation of a PWR. Results of different approximations are compared. (author)
International Nuclear Information System (INIS)
Engle, W.W. Jr.
1978-01-01
A rather complete description of the derivation of the finite difference form of the transport equation can be found in earlier work; therefore that derivation is discussed here. Attention is focused on the additional equations required to solve the transport equation which are often referred to as flux models and on the iteration process and efforts to accelerate the convergence of the iteration process. All equations discussed here are limited to the one-dimensional, time-independent case, but they may be extended in a straightforward manner to multidimensional, time-dependent geometries
International Nuclear Information System (INIS)
Libotte, Rafael Barbosa; Alves Filho, Hermes; Oliva, Amaury Muñoz
2017-01-01
The physical phenomenon of transport of neutral particles in a host environment is of interest in various scientific applications, e.g., nuclear reactors, shielding calculations, radiological protection, nuclear medicine, agronomy, materials science, oil prospecting, etc. In all these areas there is a need for an accurate description of the transport of the particles in the host medium. In this class of applications are the neutron shielding problems, also referred to as 'fixed-source' problems, where the interaction of the particles with the medium does not produce new neutrons, i.e., non-multiplicative medium. In this context, the development of tools that model these problems is relevant and of a beneficial return to society. In this work, we propose the development of deterministic mathematical and computational modeling of neutron transport using the linearized equation of Boltzmann applied to neutron shielding problems. Here we present also the development of a spectro-nodal method (coarse mesh) considering the scattering phenomenon as being linearly anisotropic. We show the results using a computational application, developed in Java language, version 1.8.0 9 1
International Nuclear Information System (INIS)
Saintagne, P.W.; Azmy, Y.Y.
2005-01-01
A GUI (Graphical User Interface) provides a graphical, interactive and intuitive link between the user and the software. It translates the user'actions into information, e.g; input data that is interpretable by the software. In order to develop an efficient GUI, it is important to master the target computational code. An initial version of a complete GUI for the DOORS and BOT3P packages for solving neutral particle transport problems in 3-dimensional geometry has been completed. This GUI is made of 4 components. The first component GipGui aims at handling cross-sections by mixing microscopic cross-sections from different libraries. The second component TORT-GUI provides the user a simple way to create or modify input files for the TORT codes that is a general purpose neutral transport code able to solve large problems with complex configurations. The third component GGTM-GUI prepares the data describing the problem configuration like the geometrical data, material assignment or key flux positions. The fourth component DTM3-GUI helps the user to visualize TORT results by providing data for a graphics post-processor
MINARET: Towards a time-dependent neutron transport parallel solver
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.; Maday, Y.; Mula, O.
2013-01-01
We present the newly developed time-dependent 3D multigroup discrete ordinates neutron transport solver that has recently been implemented in the MINARET code. The solver is the support for a study about computing acceleration techniques that involve parallel architectures. In this work, we will focus on the parallelization of two of the variables involved in our equation: the angular directions and the time. This last variable has been parallelized by a (time) domain decomposition method called the para-real in time algorithm. (authors)
First and second collision source for mitigating ray effects in discrete ordinate calculations
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Gomes, L.T.; Stevens, P.N.
1991-01-01
This work revisits the problem of ray effects in discrete ordinates calculations that frequently occurs in two- and three-dimensional systems which contain isolated sources within a highly absorbing medium. The effectiveness of using a first collision source or a second collision source are analyzed as possible remedies to mitigate this problem. The first collision and second collision sources are generated by three-dimensional Monte Carlo calculations that enables its application to a variety of source configurations, and the results can be coupled to a two- or three-dimensional discrete ordinates transport code. (author)
Particular solution of the discrete-ordinate method.
Qin, Yi; Box, Michael A; Jupp, David L
2004-06-20
We present two methods that can be used to derive the particular solution of the discrete-ordinate method (DOM) for an arbitrary source in a plane-parallel atmosphere, which allows us to solve the transfer equation 12-18% faster in the case of a single beam source and is even faster for the atmosphere thermal emission source. We also remove the divide by zero problem that occurs when a beam source coincides with a Gaussian quadrature point. In our implementation, solution for multiple sources can be obtained simultaneously. For each extra source, it costs only 1.3-3.6% CPU time required for a full solution. The GDOM code that we developed previously has been revised to integrate with the DOM. Therefore we are now able to compute the Green's function and DOM solutions simultaneously.
A Laplace transform method for energy multigroup hybrid discrete ordinates
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Segatto, C.F.; Vilhena, M.T.; Barros, R.C.
2010-01-01
In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this work we describe a hybrid discrete ordinates (S N) method for energy multigroup slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. The idea is based on the fact that in weakly absorbing media whose physical size is several neutron mean free paths in extent, even the S 2 method (P 1 approximation), leads to an accurate result. We use special fuel-moderator interface conditions and the Laplace transform (LTS N ) analytical numerical method to calculate the two-energy group neutron flux distributions and the thermal disadvantage factor. We present numerical results for a range of typical model problems.
Kylling, A.
1991-01-01
The transfer equations for normal waves in finite, inhomogeneous and plane-parallel magnetoactive media are solved using the discrete ordinate method. The physical process of absorption, emission, and multiple scattering are accounted for, and the medium may be forced both at the top and bottom boundary by anisotropic radiation as well as by internal anisotropic sources. The computational procedure is numerically stable for arbitrarily large optical depths, and the computer time is independent of optical thickness.
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Barichello, L.B.; Siewert, C.E.
1998-01-01
In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given
Method for coupling two-dimensional to three-dimensional discrete ordinates calculations
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Thompson, J.L.; Emmett, M.B.; Rhoades, W.A.; Dodds, H.L. Jr.
1985-01-01
A three-dimensional (3-D) discrete ordinates transport code, TORT, has been developed at the Oak Ridge National Laboratory for radiation penetration studies. It is not feasible to solve some 3-D penetration problems with TORT, such as a building located a large distance from a point source, because (a) the discretized 3-D problem is simply too big to fit on the computer or (b) the computing time (and corresponding cost) is prohibitive. Fortunately, such problems can be solved with a hybrid approach by coupling a two-dimensional (2-D) description of the point source, which is assumed to be azimuthally symmetric, to a 3-D description of the building, the region of interest. The purpose of this paper is to describe this hybrid methodology along with its implementation and evaluation in the DOTTOR (Discrete Ordinates to Three-dimensional Oak Ridge Transport) code
Pin cell discontinuity factors in the transient 3-D discrete ordinates code TORT-TD - 237
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Seubert, A.
2010-01-01
This paper describes the application of generalized equivalence theory to the time-dependent 3-D discrete ordinates neutron transport code TORT-TD. The introduction of pin cell discontinuity factors into the discrete ordinates transport equation is described by assuming a linear dependence of the homogenized neutron angular flux within a pin cell which may be discontinuous at the interfaces to adjacent cells. The homogenized flux discontinuity at cell interfaces is expressed by pin cell discontinuity factors which in turn are determined from fuel assembly lattice calculations using HELIOS. Application of TORT-TD to the all rods in state of the PWR MOX/UO 2 Core Transient Benchmark with pin cell homogenized nuclear cross sections demonstrate the potential of pin cell discontinuity factors to reduce pin cell homogenization errors. (authors)
Li Hong; Lu Ji Dong; Zheng Chu Guan
2003-01-01
In most of the discrete ordinate schemes (DOS) reported in the literature, the discrete directions are fixed, and unable to be arbitrarily adjusted; therefore, it is difficult to employ these schemes to calculate the radiative energy image-formation of pulverized-coal furnaces. On the basis of a new DOS, named the discrete ordinate scheme with (an) infinitely small weight(s), which was recently proposed by the authors, a novel algorithm for computing the pinhole image-formation process is developed in this work. The performance of this algorithm is tested, and is found to be also suitable for parallel computation.
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Li Hongshun; Zhou Huaichun; Lu Jidong; Zheng Chuguang
2003-01-01
In most of the discrete ordinate schemes (DOS) reported in the literature, the discrete directions are fixed, and unable to be arbitrarily adjusted; therefore, it is difficult to employ these schemes to calculate the radiative energy image-formation of pulverized-coal furnaces. On the basis of a new DOS, named the discrete ordinate scheme with (an) infinitely small weight(s), which was recently proposed by the authors, a novel algorithm for computing the pinhole image-formation process is developed in this work. The performance of this algorithm is tested, and is found to be also suitable for parallel computation
Kato, S.; Smith, G. L.; Barker, H. W.
2001-01-01
An algorithm is developed for the gamma-weighted discrete ordinate two-stream approximation that computes profiles of domain-averaged shortwave irradiances for horizontally inhomogeneous cloudy atmospheres. The algorithm assumes that frequency distributions of cloud optical depth at unresolved scales can be represented by a gamma distribution though it neglects net horizontal transport of radiation. This algorithm is an alternative to the one used in earlier studies that adopted the adding method. At present, only overcast cloudy layers are permitted.
International Nuclear Information System (INIS)
Duo, J. I.; Azmy, Y. Y.
2007-01-01
A new method, the Singular Characteristics Tracking algorithm, is developed to account for potential non-smoothness across the singular characteristics in the exact solution of the discrete ordinates approximation of the transport equation. Numerical results show improved rate of convergence of the solution to the discrete ordinates equations in two spatial dimensions with isotropic scattering using the proposed methodology. Unlike the standard Weighted Diamond Difference methods, the new algorithm achieves local convergence in the case of discontinuous angular flux along the singular characteristics. The method also significantly reduces the error for problems where the angular flux presents discontinuous spatial derivatives across these lines. For purposes of verifying the results, the Method of Manufactured Solutions is used to generate analytical reference solutions that permit estimating the local error in the numerical solution. (authors)
Energy Technology Data Exchange (ETDEWEB)
Luneville, L
1998-06-01
The multigroup discrete ordinates method is a classical way to solve transport equation (Boltzmann) for neutral particles. Self-shielding effects are not correctly treated due to large variations of cross sections in a group (in the resonance range). To treat the resonance domain, the multiband method is introduced. The main idea is to divide the cross section domain into bands. We obtain the multiband parameters using the moment method; the code CALENDF provides probability tables for these parameters. We present our implementation in an existing discrete ordinates code: SN1D. We study deep penetration benchmarks and show the improvement of the method in the treatment of self-shielding effects. (author) 15 refs.
CEPXS/ONELD: A one-dimensional coupled electron-photon discrete ordinates code package
International Nuclear Information System (INIS)
Lorence, L.J. Jr.; Morel, J.E.
1992-01-01
CEPXS/ONELD is a discrete ordinates transport code package that can model the electron-photon cascade from 100 MeV to 1 keV. The CEPXS code generates fully-coupled multigroup-Legendre cross section data. This data is used by the general-purpose discrete ordinates code, ONELD, which is derived from the Los Alamos ONEDANT and ONBTRAN codes. Version 1.0 of CEPXS/ONELD was released in 1989 and has been primarily used to analyze the effect of radiation environments on electronics. Version 2.0 is under development and will include user-friendly features such as the automatic selection of group structure, spatial mesh structure, and S N order
International Nuclear Information System (INIS)
Chen, Y.; Fischer, U.
2005-01-01
Shielding calculations of advanced nuclear facilities such as accelerator based neutron sources or fusion devices of the tokamak type are complicated due to their complex geometries and their large dimensions, including bulk shields of several meters thickness. While the complexity of the geometry in the shielding calculation can be hardly handled by the discrete ordinates method, the deep penetration of radiation through bulk shields is a severe challenge for the Monte Carlo particle transport technique. This work proposes a dedicated computational scheme for coupled Monte Carlo-Discrete Ordinates transport calculations to handle this kind of shielding problems. The Monte Carlo technique is used to simulate the particle generation and transport in the target region with both complex geometry and reaction physics, and the discrete ordinates method is used to treat the deep penetration problem in the bulk shield. The coupling scheme has been implemented in a program system by loosely integrating the Monte Carlo transport code MCNP, the three-dimensional discrete ordinates code TORT and a newly developed coupling interface program for mapping process. Test calculations were performed with comparison to MCNP solutions. Satisfactory agreements were obtained between these two approaches. The program system has been chosen to treat the complicated shielding problem of the accelerator-based IFMIF neutron source. The successful application demonstrates that coupling scheme with the program system is a useful computational tool for the shielding analysis of complex and large nuclear facilities. (authors)
Three-dimensional discrete ordinates reactor assembly calculations on GPUs
Energy Technology Data Exchange (ETDEWEB)
Evans, Thomas M [ORNL; Joubert, Wayne [ORNL; Hamilton, Steven P [ORNL; Johnson, Seth R [ORNL; Turner, John A [ORNL; Davidson, Gregory G [ORNL; Pandya, Tara M [ORNL
2015-01-01
In this paper we describe and demonstrate a discrete ordinates sweep algorithm on GPUs. This sweep algorithm is nested within a multilevel comunication-based decomposition based on energy. We demonstrated the effectiveness of this algorithm on detailed three-dimensional critical experiments and PWR lattice problems. For these problems we show improvement factors of 4 6 over conventional communication-based, CPU-only sweeps. These sweep kernel speedups resulted in a factor of 2 total time-to-solution improvement.
A discrete-ordinates solution for a radiation therapy problem
International Nuclear Information System (INIS)
Goldschmidt, Gustavo Brun; Reichert, Janice Teresinha; Barichello, Liliane Basso
2008-01-01
A concise and accurate procedure for evaluating dose distribution, in a radiation therapy planning, is presented. The analytical discrete-ordinates method (ADO method) is used to develop a complete solution for a spectral dependent radiative transfer equation, in a one-dimensional medium, according to a multigroup scheme. Numerical results are presented for test problems, where the Klein-Nishina scattering kernel was used to describe the interaction processes. (author)
On the adequacy of message-passing parallel supercomputers for solving neutron transport problems
International Nuclear Information System (INIS)
Azmy, Y.Y.
1990-01-01
A coarse-grained, static-scheduling parallelization of the standard iterative scheme used for solving the discrete-ordinates approximation of the neutron transport equation is described. The parallel algorithm is based on a decomposition of the angular domain along the discrete ordinates, thus naturally producing a set of completely uncoupled systems of equations in each iteration. Implementation of the parallel code on Intcl's iPSC/2 hypercube, and solutions to test problems are presented as evidence of the high speedup and efficiency of the parallel code. The performance of the parallel code on the iPSC/2 is analyzed, and a model for the CPU time as a function of the problem size (order of angular quadrature) and the number of participating processors is developed and validated against measured CPU times. The performance model is used to speculate on the potential of massively parallel computers for significantly speeding up real-life transport calculations at acceptable efficiencies. We conclude that parallel computers with a few hundred processors are capable of producing large speedups at very high efficiencies in very large three-dimensional problems. 10 refs., 8 figs
Timing comparison of two-dimensional discrete-ordinates codes for criticality calculations
International Nuclear Information System (INIS)
Miller, W.F. Jr.; Alcouffe, R.E.; Bosler, G.E.; Brinkley, F.W. Jr.; O'dell, R.D.
1979-01-01
The authors compare two-dimensional discrete-ordinates neutron transport computer codes to solve reactor criticality problems. The fundamental interest is in determining which code requires the minimum Central Processing Unit (CPU) time for a given numerical model of a reasonably realistic fast reactor core and peripherals. The computer codes considered are the most advanced available and, in three cases, are not officially released. The conclusion, based on the study of four fast reactor core models, is that for this class of problems the diffusion synthetic accelerated version of TWOTRAN, labeled TWOTRAN-DA, is superior to the other codes in terms of CPU requirements
Mining the multigroup-discrete ordinates algorithm for high quality solutions
International Nuclear Information System (INIS)
Ganapol, B.D.; Kornreich, D.E.
2005-01-01
A novel approach to the numerical solution of the neutron transport equation via the discrete ordinates (SN) method is presented. The new technique is referred to as 'mining' low order (SN) numerical solutions to obtain high order accuracy. The new numerical method, called the Multigroup Converged SN (MGCSN) algorithm, is a combination of several sequence accelerators: Romberg and Wynn-epsilon. The extreme accuracy obtained by the method is demonstrated through self consistency and comparison to the independent semi-analytical benchmark BLUE. (authors)
Diffusion-synthetic acceleration methods for discrete-ordinates problems
International Nuclear Information System (INIS)
Larsen, E.W.
1984-01-01
The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas behind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems an the status of current efforts aimed at solving these problems
Massively parallel performance of neutron transport response matrix algorithms
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1993-01-01
Massively parallel red/black response matrix algorithms for the solution of within-group neutron transport problems are implemented on the Connection Machines-2, 200 and 5. The response matrices are dericed from the diamond-differences and linear-linear nodal discrete ordinate and variational nodal P 3 approximations. The unaccelerated performance of the iterative procedure is examined relative to the maximum rated performances of the machines. The effects of processor partitions size, of virtual processor ratio and of problems size are examined in detail. For the red/black algorithm, the ratio of inter-node communication to computing times is found to be quite small, normally of the order of ten percent or less. Performance increases with problems size and with virtual processor ratio, within the memeory per physical processor limitation. Algorithm adaptation to courser grain machines is straight-forward, with total computing time being virtually inversely proportional to the number of physical processors. (orig.)
International Nuclear Information System (INIS)
Coelho, Pedro J.
2014-01-01
Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed
Matrix albedo for discrete ordinates infinite-medium boundary condition
International Nuclear Information System (INIS)
Mathews, K.; Dishaw, J.
2007-01-01
Discrete ordinates problems with an infinite exterior medium (reflector) can be more efficiently computed by eliminating grid cells in the exterior medium and applying a matrix albedo boundary condition. The albedo matrix is a discretized bidirectional reflection distribution function (BRDF) that accounts for the angular quadrature set, spatial quadrature method, and spatial grid that would have been used to model a portion of the exterior medium. The method is exact in slab geometry, and could be used as an approximation in multiple dimensions or curvilinear coordinates. We present an adequate method for computing albedo matrices and demonstrate their use in verifying a discrete ordinates code in slab geometry by comparison with Ganapol's infinite medium semi-analytic TIEL benchmark. With sufficient resolution in the spatial and angular grids and iteration tolerance to yield solutions converged to 6 digits, the conventional (scalar) albedo boundary condition yielded 2-digit accuracy at the boundary, but the matrix albedo solution reproduced the benchmark scalar flux at the boundary to all 6 digits. (authors)
Use of the Streaming Matrix Hybrid Method for discrete-ordinates fusion reactor calculations
International Nuclear Information System (INIS)
Battat, M.E.; Davidson, J.W.; Dudziak, D.J.; Thayer, G.R.
1984-01-01
The use of the discrete-ordinates method for solving two-dimensional, neutral-particle transport in fusion reactor blankets and shields is often limited by inherent inaccuracies due to the ray-effect. This effect presents a particular problem in the case of neutron streaming in the large internal void regions of a fusion reactor. A deterministic streaming technique called the Streaming Matrix Hybrid Method (SMHM) has been incorporated in the two-dimensional discrete-ordinates code TRIDENT-CTR. Calculations have been performed for an actual inertial-confinement fusion (ICF) reactor design using TRIDENT-CTR both with and without the SMHM. Comparisons of the calculated fluxes indicate that substantial mitigation of the ray effect can be achieved with the SMHM. Calculations were performed for the Los Alamos FIRST STEP hybrid ICF reactor designed for tritium production. Conventional 238 U fuel rod assemblies surround the spherical steel target chamber to form an annular cylindrical blanket. An axial fuel region is included to complete the blanket
Extended discrete-ordinate method considering full polarization state
International Nuclear Information System (INIS)
Box, Michael A.; Qin Yi
2006-01-01
This paper presents an extension to the standard discrete-ordinate method (DOM) to consider generalized sources including: beam sources which can be placed at any (vertical) position and illuminate in any direction, thermal emission from the atmosphere and angularly distributed sources which illuminate from a surface as continuous functions of zenith and azimuth angles. As special cases, the thermal emission from the surface and deep space can be implemented as angularly distributed sources. Analytical-particular solutions for all source types are derived using the infinite medium Green's function. Radiation field zenith angle interpolation using source function integration is developed for all source types. The development considers the full state of polarization, including the sources (as applicable) and the (BRDF) surface, but the development can be reduced easily to scalar problems and is ready to be implemented in a single set of code for both scalar and vector radiative transfer computation
Extended discrete-ordinate method considering full polarization state
Energy Technology Data Exchange (ETDEWEB)
Box, Michael A. [School of Physics, University of New South Wales (Australia)]. E-mail: m.box@unsw.edu.au; Qin Yi [School of Physics, University of New South Wales (Australia)]. E-mail: yi.qin@csiro.au
2006-01-15
This paper presents an extension to the standard discrete-ordinate method (DOM) to consider generalized sources including: beam sources which can be placed at any (vertical) position and illuminate in any direction, thermal emission from the atmosphere and angularly distributed sources which illuminate from a surface as continuous functions of zenith and azimuth angles. As special cases, the thermal emission from the surface and deep space can be implemented as angularly distributed sources. Analytical-particular solutions for all source types are derived using the infinite medium Green's function. Radiation field zenith angle interpolation using source function integration is developed for all source types. The development considers the full state of polarization, including the sources (as applicable) and the (BRDF) surface, but the development can be reduced easily to scalar problems and is ready to be implemented in a single set of code for both scalar and vector radiative transfer computation.
Discrete ordinate theory of radiative transfer. 2: Scattering from maritime haze
Kattawar, G. W.; Plass, G. N.; Catchings, F. E.
1971-01-01
Discrete ordinate theory was used to calculate the reflected and transmitted radiance of photons which have interacted with plane parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo were tabulated. The forward peak and other features in the single scattered phase function caused the radiance in many cases to be very different from that for Rayleigh scattering. The variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked, and the relative limb darkening under very thick layers is greater, for haze than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = O is always greater and the cloud albedo is always less for haze than for Rayleigh layers.
The method of lines solution of discrete ordinates method for non-grey media
International Nuclear Information System (INIS)
Cayan, Fatma Nihan; Selcuk, Nevin
2007-01-01
A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for radiative heat transfer in non-grey absorbing-emitting media was developed by incorporation of a gas spectral radiative property model, namely wide band correlated-k (WBCK) model, which is compatible with MOL solution of DOM. Predictive accuracy of the code was evaluated by applying it to 1-D parallel plate and 2-D axisymmetric cylindrical enclosure problems containing absorbing-emitting medium and benchmarking its predictions against line-by-line solutions available in the literature. Comparisons reveal that MOL solution of DOM with WBCK model produces accurate results for radiative heat fluxes and source terms and can be used with confidence in conjunction with computational fluid dynamics codes based on the same approach
Boltzmann-Fokker-Planck calculations using standard discrete-ordinates codes
International Nuclear Information System (INIS)
Morel, J.E.
1987-01-01
The Boltzmann-Fokker-Planck (BFP) equation can be used to describe both neutral and charged-particle transport. Over the past several years, the author and several collaborators have developed methods for representing Fokker-Planck operators with standard multigroup-Legendre cross-section data. When these data are input to a standard S/sub n/ code such as ONETRAN, the code actually solves the Boltzmann-Fokker-Planck equation rather than the Boltzmann equation. This is achieved wihout any modification to the S/sub n/ codes. Because BFP calculations can be more demanding from a numerical viewpoint than standard neutronics calculations, we have found it useful to implement new quadrature methods ad convergence acceleration methods in the standard discrete-ordinates code, ONETRAN. We discuss our BFP cross-section representation techniques, our improved quadrature and acceleration techniques, and present results from BFP coupled electron-photon transport calculations performed with ONETRAN. 19 refs., 7 figs
An analytical nodal method for time-dependent one-dimensional discrete ordinates problems
International Nuclear Information System (INIS)
Barros, R.C. de
1992-01-01
In recent years, relatively little work has been done in developing time-dependent discrete ordinates (S N ) computer codes. Therefore, the topic of time integration methods certainly deserves further attention. In this paper, we describe a new coarse-mesh method for time-dependent monoenergetic S N transport problesm in slab geometry. This numerical method preserves the analytic solution of the transverse-integrated S N nodal equations by constants, so we call our method the analytical constant nodal (ACN) method. For time-independent S N problems in finite slab geometry and for time-dependent infinite-medium S N problems, the ACN method generates numerical solutions that are completely free of truncation errors. Bsed on this positive feature, we expect the ACN method to be more accurate than conventional numerical methods for S N transport calculations on coarse space-time grids
Evaluation of the streaming-matrix method for discrete-ordinates duct-streaming calculations
International Nuclear Information System (INIS)
Clark, B.A.; Urban, W.T.; Dudziak, D.J.
1983-01-01
A new deterministic streaming technique called the Streaming Matrix Hybrid Method (SMHM) is applied to two realistic duct-shielding problems. The results are compared to standard discrete-ordinates and Monte Carlo calculations. The SMHM shows promise as an alternative deterministic streaming method to standard discrete-ordinates
Application of the 2-D discrete-ordinates method to multiple scattering of laser radiation
International Nuclear Information System (INIS)
Zardecki, A.; Gerstl, S.A.W.; Embury, J.F.
1983-01-01
The discrete-ordinates finite-element radiation transport code twotran is applied to describe the multiple scattering of a laser beam from a reflecting target. For a model scenario involving a 99% relative humidity rural aerosol we compute the average intensity of the scattered radiation and correction factors to the Beer-Lambert law arising from multiple scattering. As our results indicate, 2-D x-y and r-z geometry modeling can reliably describe a realistic 3-D scenario. Specific results are presented for the two visual ranges of 1.52 and 0.76 km which show that, for sufficiently high aerosol concentrations (e.g., equivalent to V = 0.76 km), the target signature in a distant detector becomes dominated by multiply scattered radiation from interactions of the laser light with the aerosol environment. The merits of the scaling group and the delta-M approximation for the transfer equation are also explored
High-order solution methods for grey discrete ordinates thermal radiative transfer
Energy Technology Data Exchange (ETDEWEB)
Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)
2016-12-15
This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.
Provably optimal parallel transport sweeps on regular grids
Energy Technology Data Exchange (ETDEWEB)
Adams, M. P.; Adams, M. L.; Hawkins, W. D. [Dept. of Nuclear Engineering, Texas A and M University, 3133 TAMU, College Station, TX 77843-3133 (United States); Smith, T.; Rauchwerger, L.; Amato, N. M. [Dept. of Computer Science and Engineering, Texas A and M University, 3133 TAMU, College Station, TX 77843-3133 (United States); Bailey, T. S.; Falgout, R. D. [Lawrence Livermore National Laboratory (United States)
2013-07-01
We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on regular grids in 3D Cartesian geometry. We describe these algorithms and sketch a 'proof that they always execute the full eight-octant sweep in the minimum possible number of stages for a given P{sub x} x P{sub y} x P{sub z} partitioning. Computational results demonstrate that our optimal scheduling algorithms execute sweeps in the minimum possible stage count. Observed parallel efficiencies agree well with our performance model. An older version of our PDT transport code achieves almost 80% parallel efficiency on 131,072 cores, on a weak-scaling problem with only one energy group, 80 directions, and 4096 cells/core. A newer version is less efficient at present-we are still improving its implementation - but achieves almost 60% parallel efficiency on 393,216 cores. These results conclusively demonstrate that sweeps can perform with high efficiency on core counts approaching 10{sup 6}. (authors)
Provably optimal parallel transport sweeps on regular grids
International Nuclear Information System (INIS)
Adams, M. P.; Adams, M. L.; Hawkins, W. D.; Smith, T.; Rauchwerger, L.; Amato, N. M.; Bailey, T. S.; Falgout, R. D.
2013-01-01
We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on regular grids in 3D Cartesian geometry. We describe these algorithms and sketch a 'proof that they always execute the full eight-octant sweep in the minimum possible number of stages for a given P x x P y x P z partitioning. Computational results demonstrate that our optimal scheduling algorithms execute sweeps in the minimum possible stage count. Observed parallel efficiencies agree well with our performance model. An older version of our PDT transport code achieves almost 80% parallel efficiency on 131,072 cores, on a weak-scaling problem with only one energy group, 80 directions, and 4096 cells/core. A newer version is less efficient at present-we are still improving its implementation - but achieves almost 60% parallel efficiency on 393,216 cores. These results conclusively demonstrate that sweeps can perform with high efficiency on core counts approaching 10 6 . (authors)
Radiative heat transfer in strongly forward scattering media using the discrete ordinates method
Granate, Pedro; Coelho, Pedro J.; Roger, Maxime
2016-03-01
The discrete ordinates method (DOM) is widely used to solve the radiative transfer equation, often yielding satisfactory results. However, in the presence of strongly forward scattering media, this method does not generally conserve the scattering energy and the phase function asymmetry factor. Because of this, the normalization of the phase function has been proposed to guarantee that the scattering energy and the asymmetry factor are conserved. Various authors have used different normalization techniques. Three of these are compared in the present work, along with two other methods, one based on the finite volume method (FVM) and another one based on the spherical harmonics discrete ordinates method (SHDOM). In addition, the approximation of the Henyey-Greenstein phase function by a different one is investigated as an alternative to the phase function normalization. The approximate phase function is given by the sum of a Dirac delta function, which accounts for the forward scattering peak, and a smoother scaled phase function. In this study, these techniques are applied to three scalar radiative transfer test cases, namely a three-dimensional cubic domain with a purely scattering medium, an axisymmetric cylindrical enclosure containing an emitting-absorbing-scattering medium, and a three-dimensional transient problem with collimated irradiation. The present results show that accurate predictions are achieved for strongly forward scattering media when the phase function is normalized in such a way that both the scattered energy and the phase function asymmetry factor are conserved. The normalization of the phase function may be avoided using the FVM or the SHDOM to evaluate the in-scattering term of the radiative transfer equation. Both methods yield results whose accuracy is similar to that obtained using the DOM along with normalization of the phase function. Very satisfactory predictions were also achieved using the delta-M phase function, while the delta
Spatial Treatment of the Slab-geometry Discrete Ordinates Equations Using Artificial Neural Networks
International Nuclear Information System (INIS)
Brantley, P S
2001-01-01
An artificial neural network (ANN) method is developed for treating the spatial variable of the one-group slab-geometry discrete ordinates (S N ) equations in a homogeneous medium with linearly anisotropic scattering. This ANN method takes advantage of the function approximation capability of multilayer ANNs. The discrete ordinates angular flux is approximated by a multilayer ANN with a single input representing the spatial variable x and N outputs representing the angular flux in each of the discrete ordinates angular directions. A global objective function is formulated which measures how accurately the output of the ANN approximates the solution of the discrete ordinates equations and boundary conditions at specified spatial points. Minimization of this objective function determines the appropriate values for the parameters of the ANN. Numerical results are presented demonstrating the accuracy of the method for both fixed source and incident angular flux problems
A novel two-level dynamic parallel data scheme for large 3-D SN calculations
International Nuclear Information System (INIS)
Sjoden, G.E.; Shedlock, D.; Haghighat, A.; Yi, C.
2005-01-01
We introduce a new dynamic parallel memory optimization scheme for executing large scale 3-D discrete ordinates (Sn) simulations on distributed memory parallel computers. In order for parallel transport codes to be truly scalable, they must use parallel data storage, where only the variables that are locally computed are locally stored. Even with parallel data storage for the angular variables, cumulative storage requirements for large discrete ordinates calculations can be prohibitive. To address this problem, Memory Tuning has been implemented into the PENTRAN 3-D parallel discrete ordinates code as an optimized, two-level ('large' array, 'small' array) parallel data storage scheme. Memory Tuning can be described as the process of parallel data memory optimization. Memory Tuning dynamically minimizes the amount of required parallel data in allocated memory on each processor using a statistical sampling algorithm. This algorithm is based on the integral average and standard deviation of the number of fine meshes contained in each coarse mesh in the global problem. Because PENTRAN only stores the locally computed problem phase space, optimal two-level memory assignments can be unique on each node, depending upon the parallel decomposition used (hybrid combinations of angular, energy, or spatial). As demonstrated in the two large discrete ordinates models presented (a storage cask and an OECD MOX Benchmark), Memory Tuning can save a substantial amount of memory per parallel processor, allowing one to accomplish very large scale Sn computations. (authors)
Energy Technology Data Exchange (ETDEWEB)
Azmy, Y.Y. [The Pennsylvania State University, 229 Reber Building, University Park, PA 16802 (United States)]. e-mail: yya3@psu.edu
2004-07-01
Particle transport problems are notorious for their difficulty. This fact requires that production level computer codes designed to address realistic engineering problems possess three important features: (i) high computational efficiency as measured by solution accuracy for a fixed computational cost; (ii) a wide variety of options to enhance robustness of the transport solver; and (iii) a broad collection of support codes that extend the reach of the transport solver to a wide variety of applications. The Discrete Ordinates of Oak Ridge System (DOORS) code package was designed with these features in mind. In this paper, capabilities of member codes in the DOORS package are overviewed with particular emphasis on two newly developed peripheral codes: BOT3P the mesh-generation and visualization code package, and GipGui the graphical user interface for the cross section manipulation code, GIP. Two large applications are used to illustrate the tight coupling between the peripheral codes and the DORT and TORT transport solvers in two and three dimensional geometries, respectively. These are: (i) criticality calculations for the C5G7MOX core benchmark; and (ii) dose distribution calculations for the Target Service Cell (TSC) of the Spallation Neutron Source (SNS). (Author)
International Nuclear Information System (INIS)
Azmy, Y.Y.
2004-01-01
Particle transport problems are notorious for their difficulty. This fact requires that production level computer codes designed to address realistic engineering problems possess three important features: (i) high computational efficiency as measured by solution accuracy for a fixed computational cost; (ii) a wide variety of options to enhance robustness of the transport solver; and (iii) a broad collection of support codes that extend the reach of the transport solver to a wide variety of applications. The Discrete Ordinates of Oak Ridge System (DOORS) code package was designed with these features in mind. In this paper, capabilities of member codes in the DOORS package are overviewed with particular emphasis on two newly developed peripheral codes: BOT3P the mesh-generation and visualization code package, and GipGui the graphical user interface for the cross section manipulation code, GIP. Two large applications are used to illustrate the tight coupling between the peripheral codes and the DORT and TORT transport solvers in two and three dimensional geometries, respectively. These are: (i) criticality calculations for the C5G7MOX core benchmark; and (ii) dose distribution calculations for the Target Service Cell (TSC) of the Spallation Neutron Source (SNS). (Author)
Monte Carlo and discrete-ordinate simulations of irradiances in the coupled atmosphere-ocean system.
Gjerstad, Karl Idar; Stamnes, Jakob J; Hamre, Børge; Lotsberg, Jon K; Yan, Banghua; Stamnes, Knut
2003-05-20
We compare Monte Carlo (MC) and discrete-ordinate radiative-transfer (DISORT) simulations of irradiances in a one-dimensional coupled atmosphere-ocean (CAO) system consisting of horizontal plane-parallel layers. The two models have precisely the same physical basis, including coupling between the atmosphere and the ocean, and we use precisely the same atmospheric and oceanic input parameters for both codes. For a plane atmosphere-ocean interface we find agreement between irradiances obtained with the two codes to within 1%, both in the atmosphere and the ocean. Our tests cover case 1 water, scattering by density fluctuations both in the atmosphere and in the ocean, and scattering by particulate matter represented by a one-parameter Henyey-Greenstein (HG) scattering phase function. The CAO-MC code has an advantage over the CAO-DISORT code in that it can handle surface waves on the atmosphere-ocean interface, but the CAO-DISORT code is computationally much faster. Therefore we use CAO-MC simulations to study the influence of ocean surface waves and propose a way to correct the results of the CAO-DISORT code so as to obtain fast and accurate underwater irradiances in the presence of surface waves.
Effect of flux discontinuity on spatial approximations for discrete ordinates methods
International Nuclear Information System (INIS)
Duo, J.I.; Azmy, Y.Y.
2005-01-01
This work presents advances on error analysis of the spatial approximation of the discrete ordinates method for solving the neutron transport equation. Error norms for different non-collided flux problems over a two dimensional pure absorber medium are evaluated using three numerical methods. The problems are characterized by the incoming flux boundary conditions to obtain solutions with different level of differentiability. The three methods considered are the Diamond Difference (DD) method, the Arbitrarily High Order Transport method of the Nodal type (AHOT-N), and of the Characteristic type (AHOT-C). The last two methods are employed in constant, linear and quadratic orders of spatial approximation. The cell-wise error is computed as the difference between the cell-averaged flux computed by each method and the exact value, then the L 1 , L 2 , and L ∞ error norms are calculated. The results of this study demonstrate that the level of differentiability of the exact solution profoundly affects the rate of convergence of the numerical methods' solutions. Furthermore, in the case of discontinuous exact flux the methods fail to converge in the maximum error norm, or in the pointwise sense, in accordance with previous local error analysis. (authors)
International Nuclear Information System (INIS)
Rosa, M.; Warsa, J. S.; Chang, J. H.
2006-01-01
A Fourier analysis is conducted for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. Both 'traditional' TSA (TTSA) and a 'modified' TSA (MTSA), in which only the scattering in the low order equations is reduced by some non-negative factor β and < 1, are considered. The results for the un-accelerated algorithm show that convergence of the PBJ algorithm can degrade. The PBJ algorithm with TTSA can be effective provided the β parameter is properly tuned for a given scattering ratio c, but is potentially unstable. Compared to TTSA, MTSA is less sensitive to the choice of β, more effective for the same computational effort (c'), and it is unconditionally stable. (authors)
International Nuclear Information System (INIS)
Han Jingru; Chen Yixue; Yuan Longjun
2013-01-01
The Monte Carlo (MC) and discrete ordinates (SN) are the commonly used methods in the design of radiation shielding. Monte Carlo method is able to treat the geometry exactly, but time-consuming in dealing with the deep penetration problem. The discrete ordinate method has great computational efficiency, but it is quite costly in computer memory and it suffers from ray effect. Single discrete ordinates method or single Monte Carlo method has limitation in shielding calculation for large complex nuclear facilities. In order to solve the problem, the Monte Carlo and discrete ordinates bidirectional coupling method is developed. The bidirectional coupling method is implemented in the interface program to transfer the particle probability distribution of MC and angular flux of discrete ordinates. The coupling method combines the advantages of MC and SN. The test problems of cartesian and cylindrical coordinate have been calculated by the coupling methods. The calculation results are performed with comparison to MCNP and TORT and satisfactory agreements are obtained. The correctness of the program is proved. (authors)
On the adequacy of Cartesian geometry discrete ordinates solutions for assembly calculations
International Nuclear Information System (INIS)
Schunert, S.; Azmy, Y. Y.
2009-01-01
The current generation of lattice codes employs the method of Collision Probabilities (CP), the Method of Characteristics (MOC) or methods derived thereof to solve the two-dimensional multigroup transport equation on the assembly level. We compare the attainable solution accuracy of the lattice code DRAGON to the accuracy of the Discrete Ordinates (DO) code DORT on the basis of the two-dimensional GE-13 assembly in order to determine if the DO on Cartesian meshes is suitable as flux solver in future lattice codes. If DO exhibits high accuracy for assembly configurations, the next question is at what computational expense compared to traditional assembly codes. For this purpose DORT and DRAGON are required to converge to a reference solution, obtained by a multigroup MCNP calculation, with increasing angular quadrature order and decreasing spatial cell size; additionally for DRAGON the reference solution must be approached with increasing tracking density. The convergence of the two codes is judged via the multiplication factor, the pin wise relative error in the fission production rate, it's RMS and the maximum of it's absolute value over all pins. Additionally the computational cost of the obtained solutions is judged via the user CPU time. Although the multiplication factor computed by both codes converges with refinement of the employed meshes, the maximum deviation error of the fission production rate in the central region of the assembly remains unsatisfactorily high for CP and MOC. (authors)
Parallel FE Electron-Photon Transport Analysis on 2-D Unstructured Mesh
International Nuclear Information System (INIS)
Drumm, C.R.; Lorenz, J.
1999-01-01
A novel solution method has been developed to solve the coupled electron-photon transport problem on an unstructured triangular mesh. Instead of tackling the first-order form of the linear Boltzmann equation, this approach is based on the second-order form in conjunction with the conventional multi-group discrete-ordinates approximation. The highly forward-peaked electron scattering is modeled with a multigroup Legendre expansion derived from the Goudsmit-Saunderson theory. The finite element method is used to treat the spatial dependence. The solution method is unique in that the space-direction dependence is solved simultaneously, eliminating the need for the conventional inner iterations, a method that is well suited for massively parallel computers
International Nuclear Information System (INIS)
McGhee, J.M.; Roberts, R.M.; Morel, J.E.
1997-01-01
A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner for scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated
Benchmarking of EPRI-cell epithermal methods with the point-energy discrete-ordinates code (OZMA)
International Nuclear Information System (INIS)
Williams, M.L.; Wright, R.Q.; Barhen, J.; Rothenstein, W.
1982-01-01
The purpose of the present study is to benchmark E-C resonance-shielding and cell-averaging methods against a rigorous deterministic solution on a fine-group level (approx. 30 groups between 1 eV and 5.5 keV). The benchmark code used is OZMA, which solves the space-dependent slowing-down equations using continuous-energy discrete ordinates or integral transport theory to produce fine-group cross sections. Results are given for three water-moderated lattices - a mixed oxide, a uranium method, and a tight-pitch high-conversion uranium oxide configuration. The latter two lattices were chosen because of the strong self shielding of the 238 U resonances
Pin cell discontinuity factors in the transient 3-D discrete ordinates code TORT-TD
International Nuclear Information System (INIS)
Seubert, A.
2010-01-01
Even with the rapid increase of computing power, whole core transient and accident analyses based on the direct solution of the 3-D neutron transport equation with a large number of energy groups and a detailed heterogeneous description of the core still remain computationally challenging. Current industrial methods for reactor core calculations therefore involve a two step approach in which lattice (assembly) depletion transport methods are used to prepare energy collapsed and fuel assembly or pin cell homogenized cross sections for subsequent whole core transport calculations. Spatial homogenization, in principal, requires the knowledge of both the actual boundary condition (local core environment) of the fuel assembly and the exact heterogeneous flux distribution (reference solution) of the whole core problem within that fuel assembly. Since, in particular, the latter is not known a priori, an infinite medium (zero net current) condition is used in the lattice calculations. It is well known that this approximation may lead to undesirable errors in cores in which large flux gradients are present across the fuel assemblies. This is the case in cores that have high heterogeneity and/or strong local absorbers, e.g. PWRs with partial MOX loading and inserted control rod clusters. There are two major approaches to mitigate spatial homogenization errors, superhomogenization (SPH) factors, and discontinuity factors within the scope of equivalence theory (ET) and generalized equivalence theory (GET). Although discontinuity factors are usually applied at the level of fuel assembly node size (assembly discontinuity factors, ADF), the methodology can be extended to pin cell homogenized whole core calculations involving pin cell discontinuity factors (PDF). There are also further developments for both the diffusion and the simplified transport (SP3) equation. In this paper, PDFs are introduced into the time-dependent 3-D discrete ordinates code TORT-TD in order to reduce the
Derivation of new 3D discrete ordinate equations
International Nuclear Information System (INIS)
Ahrens, C. D.
2012-01-01
The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way. (authors)
International Nuclear Information System (INIS)
Rosa, M.; Warsa, J. S.; Chang, J. H.
2007-01-01
A Fourier analysis is conducted in two-dimensional (2D) Cartesian geometry for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. The results for the un-accelerated algorithm show that convergence of PBJ can degrade, leading in particular to stagnation of GMRES(m) in problems containing optically thin sub-domains. The results for the accelerated algorithm indicate that TSA can be used to efficiently precondition an iterative method in the optically thin case when implemented in the 'modified' version MTSA, in which only the scattering in the low order equations is reduced by some non-negative factor β<1. (authors)
International Nuclear Information System (INIS)
Barros, R.C. de; Larsen, E.W.
1991-01-01
A generalization of the one-group Spectral Green's Function (SGF) method is developed for multigroup, slab-geometry discrete ordinates (S N ) problems. The multigroup SGF method is free from spatial truncation errors; it generated numerical values for the cell-edge and cell-average angular fluxes that agree with the analytic solution of the multigroup S N equations. Numerical results are given to illustrate the method's accuracy
International Nuclear Information System (INIS)
Ben Jaffel, L.; Vidal-Madjar, A.
1989-01-01
The discrete ordinate method for the resolution of the radiative transfer equation is developed. We show that the construction of a quasi-analytical solution to the corresponding matrix diagonalization problem reduces the time calculation and allows the use of more dense discrete frequency and angle grids. Comparison with previous work is made, showing that the present method reduces by more than a factor of ten the computational time, and is more appropriate in all cases
International Nuclear Information System (INIS)
Voloschenko, A.M.; Gukov, S.V.; Kryuchkov, V.P.; Dubinin, A.A.; Sumaneev, O.V.
2005-01-01
The CNCSN package is composed of the following codes: -) KATRIN-2.0: a three-dimensional neutral and charged particle transport code; -) KASKAD-S-2.5: a two-dimensional neutral and charged particle transport code; -) ROZ-6.6: a one-dimensional neutral and charged particle transport code; -) ARVES-2.5: a preprocessor for the working macroscopic cross-section format FMAC-M for transport calculations; -) MIXERM: a utility code for preparing mixtures on the base of multigroup cross-section libraries in ANISN format; -) CEPXS-BFP: a version of the Sandia National Lab. multigroup coupled electron-photon cross-section generating code CEPXS, adapted for solving the charged particles transport in the Boltzmann-Fokker-Planck formulation with the use of discrete ordinate method; -) SADCO-2.4: Institute for High-Energy Physics modular system for generating coupled nuclear data libraries to provide high-energy particles transport calculations by multigroup method; -) KATRIF: the post-processor for the KATRIN code; -) KASF: the post-processor for the KASKAD-S code; and ROZ6F: the post-processor for the ROZ-6 code. The coding language is Fortran-90
Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method
International Nuclear Information System (INIS)
Norris, Edward T.; Liu, Xin; Hsieh, Jiang
2015-01-01
Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently. Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. The CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods. Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors’ study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer
Directory of Open Access Journals (Sweden)
JONG WOON KIM
2014-04-01
In this paper, we introduce a modified scattering kernel approach to avoid the unnecessarily repeated calculations involved with the scattering source calculation, and used it with parallel computing to effectively reduce the computation time. Its computational efficiency was tested for three-dimensional full-coupled photon-electron transport problems using our computer program which solves the multi-group discrete ordinates transport equation by using the discontinuous finite element method with unstructured tetrahedral meshes for complicated geometrical problems. The numerical tests show that we can improve speed up to 17∼42 times for the elapsed time per iteration using the modified scattering kernel, not only in the single CPU calculation but also in the parallel computing with several CPUs.
Energy Technology Data Exchange (ETDEWEB)
Azmy, Yousry
2014-06-10
We employ the Integral Transport Matrix Method (ITMM) as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells' fluxes and between the cells' and boundary surfaces' fluxes. The main goals of this work are to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and parallel performance of the developed methods with increasing number of processes, P. The fastest observed parallel solution method, Parallel Gauss-Seidel (PGS), was used in a weak scaling comparison with the PARTISN transport code, which uses the source iteration (SI) scheme parallelized with the Koch-baker-Alcouffe (KBA) method. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method- even without acceleration/preconditioning-is completitive for optically thick problems as P is increased to the tens of thousands range. For the most optically thick cells tested, PGS reduced execution time by an approximate factor of three for problems with more than 130 million computational cells on P = 32,768. Moreover, the SI-DSA execution times's trend rises generally more steeply with increasing P than the PGS trend. Furthermore, the PGS method outperforms SI for the periodic heterogeneous layers (PHL) configuration problems. The PGS method outperforms SI and SI-DSA on as few as P = 16 for PHL problems and reduces execution time by a factor of ten or more for all problems considered with more than 2 million computational cells on P = 4.096.
Energy Technology Data Exchange (ETDEWEB)
Silva, Davi J.M.; Nunes, Carlos E.A.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: ceanunes@yahoo.com.br, E-mail: rcbarros@pq.cnpq.br [Secretaria Municipal de Educacao de Itaborai, RJ (Brazil); Universidade Estacio de Sa (UNESA), Rio de Janeiro, RJ (Brazil); Universidade do Estado do Rio de Janeiro (UERJ), Novra Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional
2017-11-01
Discussed here is the accuracy of approximate albedo boundary conditions for energy multigroup discrete ordinates (S{sub N}) eigenvalue problems in two-dimensional rectangular geometry for criticality calculations in neutron fission reacting systems, such as nuclear reactors. The multigroup (S{sub N}) albedo matrix substitutes approximately the non-multiplying media around the core, e.g., baffle and reflector, as we neglect the transverse leakage terms within these non-multiplying regions. Numerical results to a typical model problem are given to illustrate the accuracy versus the computer running time. (author)
Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case
International Nuclear Information System (INIS)
Doicu, A.; Trautmann, T.
2009-01-01
We present a discrete-ordinate algorithm using the matrix-exponential solution for pseudo-spherical radiative transfer. Following the finite-element technique we introduce the concept of layer equation and formulate the discrete radiative transfer problem in terms of the level values of the radiance. The layer quantities are expressed by means of matrix exponentials, which are computed by using the matrix eigenvalue method and the Pade approximation. These solution methods lead to a compact and versatile formulation of the radiative transfer. Simulated nadir and limb radiances for an aerosol-loaded atmosphere and a cloudy atmosphere are presented along with a discussion of the model intercomparisons and timings
Diffusion-synthetic acceleration methods for the discrete-ordinates equations
International Nuclear Information System (INIS)
Larsen, E.W.
1983-01-01
The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas beind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems and the status of current efforts aimed at solving these problems
Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system.
Hestenes, Kjersti; Nielsen, Kristian P; Zhao, Lu; Stamnes, Jakob J; Stamnes, Knut
2007-04-20
We perform a detailed comparison study of Monte Carlo (MC) simulations and discrete-ordinate radiative-transfer (DISORT) calculations of spectral radiances in a 1D coupled air-tissue (CAT) system consisting of horizontal plane-parallel layers. The MC and DISORT models have the same physical basis, including coupling between the air and the tissue, and we use the same air and tissue input parameters for both codes. We find excellent agreement between radiances obtained with the two codes, both above and in the tissue. Our tests cover typical optical properties of skin tissue at the 280, 540, and 650 nm wavelengths. The normalized volume scattering function for internal structures in the skin is represented by the one-parameter Henyey-Greenstein function for large particles and the Rayleigh scattering function for small particles. The CAT-DISORT code is found to be approximately 1000 times faster than the CAT-MC code. We also show that the spectral radiance field is strongly dependent on the inherent optical properties of the skin tissue.
International Nuclear Information System (INIS)
Seubert, A.; Velkov, K.; Langenbuch, S.
2008-01-01
This paper describes the time-dependent 3D discrete ordinates transport code TORT-TD. Thermal-hydraulic feedback is considered by coupling TORT-TD with the thermal-hydraulics system code ATHLET. The coupled code TORT-TD/ATHLET allows 3D pin-by-pin analyses of transients in few energy groups and anisotropic scattering by solving the time-dependent transport equation using the unconditionally stable implicit method. The nuclear cross sections are interpolated between pre-calculated table values of fuel temperature, moderator density and boron concentration. For verification of the implementation, selected test cases have been calculated by TORT-TD/ATHLET. They include a control rod ejection transient in a small PWR fuel assembly arrangement and a local boron concentration change in a single PWR fuel assembly. In the latter, special attention has been paid to study the influence of the thermal-hydraulic feedback modelling in ATHLET. The results obtained for a control rod ejection accident in a PWR quarter core demonstrate the applicability of TORT-TD/ATHLET. (authors)
Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.
2012-01-01
A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.
International Nuclear Information System (INIS)
Kim, Jong Woon; Lee, Young Ouk
2016-01-01
When we use MCNP code for a deep shielding problem, we prefer to use variance reduction technique such as geometry splitting, or weight window, or source biasing to have relative error within reliable confidence interval. To generate importance map for geometry splitting in MCNP calculation, we should know the track entering number and previous importance on each cells since a new importance is calculated based on these information. If a problem is deep shielding problem such that we have zero tracks entering on a cell, we cannot generate new importance map. In this case, discrete ordinates code can provide information to generate importance map easily. In this paper, we use AETIUS code as a discrete ordinates code. Importance map for MCNP is generated based on a zone average flux of AETIUS calculation. The discretization of space, angle, and energy is not necessary for MCNP calculation. This is the big merit of MCNP code compared to the deterministic code. However, deterministic code (i.e., AETIUS) can provide a rough estimate of the flux throughout a problem relatively quickly. This can help MCNP by providing variance reduction parameters. Recently, ADVANTG code is released. This is an automated tool for generating variance reduction parameters for fixed-source continuous-energy Monte Carlo simulations with MCNP5 v1.60
Owens, A. R.; Kópházi, J.; Welch, J. A.; Eaton, M. D.
2017-04-01
In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates (SN) equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the "exact" adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem.
International Nuclear Information System (INIS)
Kodeli, I.; Tanner, R.
2005-01-01
In the scope of QUADOS, a Concerted Action of the European Commission, eight calculational problems were prepared in order to evaluate the use of computational codes for dosimetry in radiation protection and medical physics, and to disseminate 'good practice' throughout the radiation dosimetry community. This paper focuses on the analysis of the P4 problem on the 'TLD-albedo dosemeter: neutron and/or photon response of a four-element TL-dosemeter mounted on a standard ISO slab phantom'. Altogether 17 solutions were received from the participants, 14 of those transported neutrons and 15 photons. Most participants (16 out of 17) used Monte Carlo methods. These calculations are time-consuming, requiring several days of CPU time to perform the whole set of calculations and achieve good statistical precision. The possibility of using deterministic discrete ordinates codes as an alternative to Monte Carlo was therefore investigated and is presented here. In particular the capacity of the adjoint mode calculations is shown. (authors)
International Nuclear Information System (INIS)
Cramer, S.N.; Slater, C.O.
1990-01-01
A general adjoint Monte Carlo-forward discrete ordinates radiation transport calculational scheme has been created to study the effects of the radiation environment in Hiroshima and Nagasaki due to the bombing of these two cities. Various such studies for comparison with physical data have progressed since the end of World War II with advancements in computing machinery and computational methods. These efforts have intensified in the last several years with the U.S.-Japan joint reassessment of nuclear weapons dosimetry in Hiroshima and Nagasaki. Three principal areas of investigation are: (1) to determine by experiment and calculation the neutron and gamma-ray energy and angular spectra and total yield of the two weapons; (2) using these weapons descriptions as source terms, to compute radiation effects at several locations in the two cities for comparison with experimental data collected at various times after the bombings and thus validate the source terms; and (3) to compute radiation fields at the known locations of fatalities and surviving individuals at the time of the bombings and thus establish an absolute cause-and-effect relationship between the radiation received and the resulting injuries to these individuals and any of their descendants as indicated by their medical records. It is in connection with the second and third items, the determination of the radiation effects and the dose received by individuals, that the current study is concerned
Advanced quadratures and periodic boundary conditions in parallel 3D Sn transport
International Nuclear Information System (INIS)
Manalo, K.; Yi, C.; Huang, M.; Sjoden, G.
2013-01-01
Significant updates in numerical quadratures have warranted investigation with 3D Sn discrete ordinates transport. We show new applications of quadrature departing from level symmetric ( 2 o) and Pn-Tn (>S 2 o). investigating 3 recently developed quadratures: Even-Odd (EO), Linear-Discontinuous Finite Element - Surface Area (LDFE-SA), and the non-symmetric Icosahedral Quadrature (IC). We discuss implementation changes to 3D Sn codes (applied to Hybrid MOC-Sn TITAN and 3D parallel PENTRAN) that can be performed to accommodate Icosahedral Quadrature, as this quadrature is not 90-degree rotation invariant. In particular, as demonstrated using PENTRAN, the properties of Icosahedral Quadrature are suitable for trivial application using periodic BCs versus that of reflective BCs. In addition to implementing periodic BCs for 3D Sn PENTRAN, we implemented a technique termed 'angular re-sweep' which properly conditions periodic BCs for outer eigenvalue iterative loop convergence. As demonstrated by two simple transport problems (3-group fixed source and 3-group reflected/periodic eigenvalue pin cell), we remark that all of the quadratures we investigated are generally superior to level symmetric quadrature, with Icosahedral Quadrature performing the most efficiently for problems tested. (authors)
Energy Technology Data Exchange (ETDEWEB)
Libotte, Rafael Barbosa; Alves Filho, Hermes; Oliva, Amaury Muñoz, E-mail: rafaellibotte@hotmail.com, E-mail: halves@iprj.uerj.br, E-mail: aoliva@iprj.uerj.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional
2017-07-01
The physical phenomenon of transport of neutral particles in a host environment is of interest in various scientific applications, e.g., nuclear reactors, shielding calculations, radiological protection, nuclear medicine, agronomy, materials science, oil prospecting, etc. In all these areas there is a need for an accurate description of the transport of the particles in the host medium. In this class of applications are the neutron shielding problems, also referred to as 'fixed-source' problems, where the interaction of the particles with the medium does not produce new neutrons, i.e., non-multiplicative medium. In this context, the development of tools that model these problems is relevant and of a beneficial return to society. In this work, we propose the development of deterministic mathematical and computational modeling of neutron transport using the linearized equation of Boltzmann applied to neutron shielding problems. Here we present also the development of a spectro-nodal method (coarse mesh) considering the scattering phenomenon as being linearly anisotropic. We show the results using a computational application, developed in Java language, version 1.8.0{sub 9}1.
Reactor Dosimetry Applications Using RAPTOR-M3G:. a New Parallel 3-D Radiation Transport Code
Longoni, Gianluca; Anderson, Stanwood L.
2009-08-01
The numerical solution of the Linearized Boltzmann Equation (LBE) via the Discrete Ordinates method (SN) requires extensive computational resources for large 3-D neutron and gamma transport applications due to the concurrent discretization of the angular, spatial, and energy domains. This paper will discuss the development RAPTOR-M3G (RApid Parallel Transport Of Radiation - Multiple 3D Geometries), a new 3-D parallel radiation transport code, and its application to the calculation of ex-vessel neutron dosimetry responses in the cavity of a commercial 2-loop Pressurized Water Reactor (PWR). RAPTOR-M3G is based domain decomposition algorithms, where the spatial and angular domains are allocated and processed on multi-processor computer architectures. As compared to traditional single-processor applications, this approach reduces the computational load as well as the memory requirement per processor, yielding an efficient solution methodology for large 3-D problems. Measured neutron dosimetry responses in the reactor cavity air gap will be compared to the RAPTOR-M3G predictions. This paper is organized as follows: Section 1 discusses the RAPTOR-M3G methodology; Section 2 describes the 2-loop PWR model and the numerical results obtained. Section 3 addresses the parallel performance of the code, and Section 4 concludes this paper with final remarks and future work.
The numerical parallel computing of photon transport
International Nuclear Information System (INIS)
Huang Qingnan; Liang Xiaoguang; Zhang Lifa
1998-12-01
The parallel computing of photon transport is investigated, the parallel algorithm and the parallelization of programs on parallel computers both with shared memory and with distributed memory are discussed. By analyzing the inherent law of the mathematics and physics model of photon transport according to the structure feature of parallel computers, using the strategy of 'to divide and conquer', adjusting the algorithm structure of the program, dissolving the data relationship, finding parallel liable ingredients and creating large grain parallel subtasks, the sequential computing of photon transport into is efficiently transformed into parallel and vector computing. The program was run on various HP parallel computers such as the HY-1 (PVP), the Challenge (SMP) and the YH-3 (MPP) and very good parallel speedup has been gotten
Los Alamos neutral particle transport codes: New and enhanced capabilities
International Nuclear Information System (INIS)
Alcouffe, R.E.; Baker, R.S.; Brinkley, F.W.; Clark, B.A.; Koch, K.R.; Marr, D.R.
1992-01-01
We present new developments in Los Alamos discrete-ordinates transport codes and introduce THREEDANT, the latest in the series of Los Alamos discrete ordinates transport codes. THREEDANT solves the multigroup, neutral-particle transport equation in X-Y-Z and R-Θ-Z geometries. THREEDANT uses computationally efficient algorithms: Diffusion Synthetic Acceleration (DSA) is used to accelerate the convergence of transport iterations, the DSA solution is accelerated using the multigrid technique. THREEDANT runs on a wide range of computers, from scientific workstations to CRAY supercomputers. The algorithms are highly vectorized on CRAY computers. Recently, the THREEDANT transport algorithm was implemented on the massively parallel CM-2 computer, with performance that is comparable to a single-processor CRAY-YMP We present the results of THREEDANT analysis of test problems
Energy Technology Data Exchange (ETDEWEB)
Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)
2017-04-01
The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.
The response matrix discrete ordinates solution to the 1D radiative transfer equation
International Nuclear Information System (INIS)
Ganapol, Barry D.
2015-01-01
The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and computational techniques have become more powerful and efficient. Here, we again consider the analytical solution to the discrete radiative transfer equation in a homogeneous medium by proposing a new, and consistent, form of solution that improves upon previous forms. Aided by a Wynn-epsilon convergence acceleration, its numerical evaluation can achieve extreme precision as demonstrated by comparison with published benchmarks. Finally, we readily extend the solution to a heterogeneous medium through the star product formulation producing a novel benchmark for closed form Henyey–Greenstein scattering as an example. - Highlights: • Presents a new solution to the RTE called the response matrix DOM (RM/DOM). • Solution representations avoid the instability common in exponential solutions. • Explicit form in terms of matrix hyperbolic functions. • Extreme accuracy through Wynn-epsilon acceleration checked by published benchmarks. • Provides a more transparent numerical evaluation than found previously
International Nuclear Information System (INIS)
Larsen, E.W.; Alcouffe, R.E.
1981-01-01
In this article a new linear characteristic (LC) spatial differencing scheme for the discrete ordinates equations in (x,y)-geometry is described and numerical comparisons are given with the diamond difference (DD) method. The LC method is more stable with mesh size and is generally much more accurate than the DD method on both fine and coarse meshes, for eigenvalue and deep penetration problems. The LC method is based on computations involving the exact solution of a cell problem which has spatially linear boundary conditions and interior source. The LC method is coupled to the diffusion synthetic acceleration (DSA) algorithm in that the linear variations of the source are determined in part by the results of the DSA calculation from the previous inner iteration. An inexpensive negative-flux fixup is used which has very little effect on the accuracy of the solution. The storage requirements for LC are essentially the same as that for DD, while the computational times for LC are generally less than twice the DD computational times for the same mesh. This increase in computational cost is offset if one computes LC solutions on somewhat coarser meshes than DD; the resulting LC solutions are still generally much more accurate than the DD solutions. (orig.) [de
On radiative transfer in water spray curtains using the discrete ordinates method
Energy Technology Data Exchange (ETDEWEB)
Collin, A. [Laboratoire d' Energetique et de Mecanique Theorique and Appliquee (LEMTA), CNRS UMR 7563, Faculte des Sciences et Techniques BP 239 - 54506 VANDOEUVRE Cedex (France); Boulet, P. [Laboratoire d' Energetique et de Mecanique Theorique and Appliquee (LEMTA), CNRS UMR 7563, Faculte des Sciences et Techniques BP 239 - 54506 VANDOEUVRE Cedex (France)]. E-mail: Pascal.Boulet@lemta.uhp-nancy.fr; Lacroix, D. [Laboratoire d' Energetique et de Mecanique Theorique and Appliquee (LEMTA), CNRS UMR 7563, Faculte des Sciences et Techniques BP 239 - 54506 VANDOEUVRE Cedex (France); Jeandel, G. [Laboratoire d' Energetique et de Mecanique Theorique and Appliquee (LEMTA), CNRS UMR 7563, Faculte des Sciences et Techniques BP 239 - 54506 VANDOEUVRE Cedex (France)
2005-04-15
Radiative transfer through water spray curtains has been presently addressed in conditions similar to devices used in fire protection systems. The radiation propagation from the heat source through the medium is simulated using a 2D Discrete Ordinates Method. The curtain is treated as an absorbing and anisotropically scattering medium, made of droplets injected in a mixing of air, water vapor and carbon dioxide. Such a participating medium requires a careful treatment of its spectral response in order to model the radiative transfer accurately. This particular problem is dealt with using a correlated-K method. Radiative properties for the droplets are calculated applying the Mie theory. Transmissivities under realistic conditions are then simulated after a validation thanks to comparisons with some experimental data available in the literature. Owing to promising results which are already observed in this case of uncoupled radiative problem, next step will be to combine the present study with a companion work dedicated to the careful treatment of the spray dynamics and of the induced heat transfer phenomena.
Ray effects in the discrete-ordinate solution for surface radiation exchange
Energy Technology Data Exchange (ETDEWEB)
Liou, B T [Dept. of Mechanical Engineering, National Cheng Kung Univ., Tainan (Taiwan, Province of China); Wu, C Y [Dept. of Mechanical Engineering, National Cheng Kung Univ., Tainan (Taiwan, Province of China)
1997-04-01
A study of the application of the discrete-ordinate method (DOM) with remedy for the ray effects to the solution of surface radiation exchange is presented in this paper. The remedy for the ray effects is achieved by dividing the radiative intensity into the attenuated incident and the medium emitting components. To demonstrate the application of the technique, this work considers radiative heat transfer in a two-dimensional cylindrical enclosure filled with a nearly transparent medium. The results obtained by the present DOM are in excellent agreement with those by the radiosity/irradiation method. (orig.). With 4 figs., 3 tabs. [Deutsch] In der Arbeit wird ein Weg aufgezeigt, wie die Stoerstrahlungseffekte bei Anwendung der Methode der diskreten Ordinaten auf die Berechnung des Energietausches zwischen Oberflaechenstrahlern vermieden werden koennen. Dies laesst sich durch Aufspaltung der Strahlungsintensitaet in die abgeschwaechte einfallende und die vom Medium emittierte Komponente erreichen. Als Beispiel fuer die Anwendung dieses Verfahrens dient der Waermeaustausch durch Strahlung in einem zweidimensionalen zylindrischen Behaeltnis, das mit einem nahezu transparenten Medium befuellt ist. Die mit der modifizierten Methode erhaltenen Ergebnisse stimmen ausgezeichnet mit jenen nach dem klassischen Brutto-Verfahren ueberein. (orig.)
International Nuclear Information System (INIS)
Abreu, M.P. de
1994-01-01
The use of exact albedo boundary conditions in numerical methods applied to one-dimensional one-speed discrete ordinates (S n ) eigenvalue problems for nuclear reactor global calculations is described. An albedo operator that treats the reflector region around a nuclear reactor core implicitly is described and exactly was derived. To illustrate the method's efficiency and accuracy, it was used conventional linear diamond method with the albedo option to solve typical model problems. (author)
Parallel thermal radiation transport in two dimensions
International Nuclear Information System (INIS)
Smedley-Stevenson, R.P.; Ball, S.R.
2003-01-01
This paper describes the distributed memory parallel implementation of a deterministic thermal radiation transport algorithm in a 2-dimensional ALE hydrodynamics code. The parallel algorithm consists of a variety of components which are combined in order to produce a state of the art computational capability, capable of solving large thermal radiation transport problems using Blue-Oak, the 3 Tera-Flop MPP (massive parallel processors) computing facility at AWE (United Kingdom). Particular aspects of the parallel algorithm are described together with examples of the performance on some challenging applications. (author)
Parallel thermal radiation transport in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Smedley-Stevenson, R.P.; Ball, S.R. [AWE Aldermaston (United Kingdom)
2003-07-01
This paper describes the distributed memory parallel implementation of a deterministic thermal radiation transport algorithm in a 2-dimensional ALE hydrodynamics code. The parallel algorithm consists of a variety of components which are combined in order to produce a state of the art computational capability, capable of solving large thermal radiation transport problems using Blue-Oak, the 3 Tera-Flop MPP (massive parallel processors) computing facility at AWE (United Kingdom). Particular aspects of the parallel algorithm are described together with examples of the performance on some challenging applications. (author)
1993-06-01
1•) + ) •,(v)(•,L) = ()(Q)+ sEXT (F). (4) The scalar flux, 0, is related to the angular flux, W, by (F)= f (dQ Vh) (5) and the particle current, J...J," v,p’) u +at(U, v) w(u, U, p’)= as(u, v) O(u, v) + SEXT (uv)] (92) 0 Ul,(V) I Assuming the area of the triangle is sufficiently small that cross...M + SEXT () (98) Wvn and WoUT are angular flux averages along the input and output edges, respectively, and are defined by WD Iv = f- ds. V(s.v) (99
Energy Technology Data Exchange (ETDEWEB)
Mansur, Ralph S.; Moura, Carlos A., E-mail: ralph@ime.uerj.br, E-mail: demoura@ime.uerj.br [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil). Departamento de Engenharia Mecanica; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional
2017-07-01
Presented here is an application of the Response Matrix (RM) method for adjoint discrete ordinates (S{sub N}) problems in slab geometry applied to energy-dependent source-detector problems. The adjoint RM method is free from spatial truncation errors, as it generates numerical results for the adjoint angular fluxes in multilayer slabs that agree with the numerical values obtained from the analytical solution of the energy multigroup adjoint SN equations. Numerical results are given for two typical source-detector problems to illustrate the accuracy and the efficiency of the offered RM computer code. (author)
International Nuclear Information System (INIS)
Godoy, William F.; DesJardin, Paul E.
2010-01-01
The application of flux limiters to the discrete ordinates method (DOM), S N , for radiative transfer calculations is discussed and analyzed for 3D enclosures for cases in which the intensities are strongly coupled to each other such as: radiative equilibrium and scattering media. A Newton-Krylov iterative method (GMRES) solves the final systems of linear equations along with a domain decomposition strategy for parallel computation using message passing libraries in a distributed memory system. Ray effects due to angular discretization and errors due to domain decomposition are minimized until small variations are introduced by these effects in order to focus on the influence of flux limiters on errors due to spatial discretization, known as numerical diffusion, smearing or false scattering. Results are presented for the DOM-integrated quantities such as heat flux, irradiation and emission. A variety of flux limiters are compared to 'exact' solutions available in the literature, such as the integral solution of the RTE for pure absorbing-emitting media and isotropic scattering cases and a Monte Carlo solution for a forward scattering case. Additionally, a non-homogeneous 3D enclosure is included to extend the use of flux limiters to more practical cases. The overall balance of convergence, accuracy, speed and stability using flux limiters is shown to be superior compared to step schemes for any test case.
Energy Technology Data Exchange (ETDEWEB)
Watanabe, Hideo; Kawai, Wataru; Nemoto, Toshiyuki [Fujitsu Ltd., Tokyo (Japan); and others
1997-12-01
Several computer codes in the nuclear field have been vectorized, parallelized and transported on the FUJITSU VPP500 system at Center for Promotion of Computational Science and Engineering in Japan Atomic Energy Research Institute. These results are reported in 3 parts, i.e., the vectorization part, the parallelization part and the porting part. In this report, we describe the parallelization. In this parallelization part, the parallelization of 2-Dimensional relativistic electromagnetic particle code EM2D, Cylindrical Direct Numerical Simulation code CYLDNS and molecular dynamics code for simulating radiation damages in diamond crystals DGR are described. In the vectorization part, the vectorization of two and three dimensional discrete ordinates simulation code DORT-TORT, gas dynamics analysis code FLOWGR and relativistic Boltzmann-Uehling-Uhlenbeck simulation code RBUU are described. And then, in the porting part, the porting of reactor safety analysis code RELAP5/MOD3.2 and RELAP5/MOD3.2.1.2, nuclear data processing system NJOY and 2-D multigroup discrete ordinate transport code TWOTRAN-II are described. And also, a survey for the porting of command-driven interactive data analysis plotting program IPLOT are described. (author)
International Nuclear Information System (INIS)
Santos, Frederico P.; Alves Filho, Hermes; Barros, Ricardo C.; Xavier, Vinicius S.
2011-01-01
The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)
International Nuclear Information System (INIS)
Lydia, Emilio J.; Barros, Ricardo C.
2011-01-01
In this paper we describe a response matrix method for one-speed slab-geometry discrete ordinates (SN) neutral particle transport problems that is completely free from spatial truncation errors. The unknowns in the method are the cell-edge angular fluxes of particles. The numerical results generated for these quantities are exactly those obtained from the analytic solution of the SN problem apart from finite arithmetic considerations. Our method is based on a spectral analysis that we perform in the SN equations with scattering inside a discretization cell of the spatial grid set up on the slab. As a result of this spectral analysis, we are able to obtain an expression for the local general solution of the SN equations. With this local general solution, we determine the response matrix and use the prescribed boundary conditions and continuity conditions to sweep across the discretization cells from left to right and from right to left across the slab, until a prescribed convergence criterion is satisfied. (author)
International Nuclear Information System (INIS)
Kitsos, S.; Assad, A.; Diop, C.M.; Nimal, J.C.
1994-01-01
Exposure and energy absorption buildup factors for aluminum, iron, lead, and water are calculated by the SNID discrete ordinates code for an isotropic point source in a homogeneous medium. The calculation of the buildup factors takes into account the effects of both bound-electron Compton (incoherent) and coherent (Rayleigh) scattering. A comparison with buildup factors from the literature shows that these two effects greatly increase the buildup factors for energies below a few hundred kilo-electron-volts, and thus the new results are improved relative to the experiment. This greater accuracy is due to the increase in the linear attenuation coefficient, which leads to the calculation of the buildup factors for a mean free path with a smaller shield thickness. On the other hand, for the same shield thickness, exposure increases when only incoherent scattering is included and decreases when only coherent scattering is included, so that the exposure finally decreases when both effects are included. Great care must also be taken when checking the approximations for gamma-ray deep-penetration transport calculations, as well as for the cross-section treatment and origin
Energy Technology Data Exchange (ETDEWEB)
Vaillon, R; Lallemand, M; Lemonnier, D [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France)
1997-12-31
The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.
Energy Technology Data Exchange (ETDEWEB)
Vaillon, R.; Lallemand, M.; Lemonnier, D. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France)
1996-12-31
The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.
Tsay, Si-Chee; Stamnes, Knut; Wiscombe, Warren; Laszlo, Istvan; Einaudi, Franco (Technical Monitor)
2000-01-01
This update reports a state-of-the-art discrete ordinate algorithm for monochromatic unpolarized radiative transfer in non-isothermal, vertically inhomogeneous, but horizontally homogeneous media. The physical processes included are Planckian thermal emission, scattering with arbitrary phase function, absorption, and surface bidirectional reflection. The system may be driven by parallel or isotropic diffuse radiation incident at the top boundary, as well as by internal thermal sources and thermal emission from the boundaries. Radiances, fluxes, and mean intensities are returned at user-specified angles and levels. DISORT has enjoyed considerable popularity in the atmospheric science and other communities since its introduction in 1988. Several new DISORT features are described in this update: intensity correction algorithms designed to compensate for the 8-M forward-peak scaling and obtain accurate intensities even in low orders of approximation; a more general surface bidirectional reflection option; and an exponential-linear approximation of the Planck function allowing more accurate solutions in the presence of large temperature gradients. DISORT has been designed to be an exemplar of good scientific software as well as a program of intrinsic utility. An extraordinary effort has been made to make it numerically well-conditioned, error-resistant, and user-friendly, and to take advantage of robust existing software tools. A thorough test suite is provided to verify the program both against published results, and for consistency where there are no published results. This careful attention to software design has been just as important in DISORT's popularity as its powerful algorithmic content.
A spectral nodal method for discrete ordinates problems in x,y geometry
International Nuclear Information System (INIS)
Barros, R.C. de; Larsen, E.W.
1991-06-01
A new nodal method is proposed for the solution of S N problems in x- y-geometry. This method uses the Spectral Green's Function (SGF) scheme for solving the one-dimensional transverse-integrated nodal transport equations with no spatial truncation error. Thus, the only approximations in the x, y-geometry nodal method occur in the transverse leakage terms, as in diffusion theory. We approximate these leakage terms using a flat or constant approximation, and we refer to the resulting method as the SGF-Constant Nodal (SGF-CN) method. We show in numerical calculations that the SGF-CN method is much more accurate than other well-known transport nodal methods for coarse-mesh deep-penetration S N problems, even though the transverse leakage terms are approximated rather simply. (author)
Cohen, D; Stamnes, S; Tanikawa, T; Sommersten, E R; Stamnes, J J; Lotsberg, J K; Stamnes, K
2013-04-22
A comparison is presented of two different methods for polarized radiative transfer in coupled media consisting of two adjacent slabs with different refractive indices, each slab being a stratified medium with no change in optical properties except in the direction of stratification. One of the methods is based on solving the integro-differential radiative transfer equation for the two coupled slabs using the discrete ordinate approximation. The other method is based on probabilistic and statistical concepts and simulates the propagation of polarized light using the Monte Carlo approach. The emphasis is on non-Rayleigh scattering for particles in the Mie regime. Comparisons with benchmark results available for a slab with constant refractive index show that both methods reproduce these benchmark results when the refractive index is set to be the same in the two slabs. Computed results for test cases with coupling (different refractive indices in the two slabs) show that the two methods produce essentially identical results for identical input in terms of absorption and scattering coefficients and scattering phase matrices.
International Nuclear Information System (INIS)
Youssef, M.Z.; Feder, R.; Davis, I.
2007-01-01
The ITER IT has adopted the newly developed FEM, 3-D, and CAD-based Discrete Ordinates code, ATTILA for the neutronics studies contingent on its success in predicting key neutronics parameters and nuclear field according to the stringent QA requirements set forth by the Management and Quality Program (MQP). ATTILA has the advantage of providing a full flux and response functions mapping everywhere in one run where components subjected to excessive radiation level and strong streaming paths can be identified. The ITER neutronics community had agreed to use a standard CAD model of ITER (40 degree sector, denoted ''Benchmark CAD Model'') to compare results for several responses selected for calculation benchmarking purposes to test the efficiency and accuracy of the CAD-MCNP approach developed by each party. Since ATTILA seems to lend itself as a powerful design tool with minimal turnaround time, it was decided to benchmark this model with ATTILA as well and compare the results to those obtained with the CAD MCNP calculations. In this paper we report such comparison for five responses, namely: (1) Neutron wall load on the surface of the 18 shield blanket module (SBM), (2) Neutron flux and nuclear heating rate in the divertor cassette, (3) nuclear heating rate in the winding pack of the inner leg of the TF coil, (4) Radial flux profile across dummy port plug and shield plug placed in the equatorial port, and (5) Flux at seven point locations situated behind the equatorial port plug. (orig.)
International Nuclear Information System (INIS)
Rozanov, Vladimir V.; Vountas, Marco
2014-01-01
Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes–Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently. -- Highlights: • We derived the radiative transfer equation accounting for rotational Raman scattering. • Different approximate radiative transfer approaches with first order scattering were used. • Rigorous and approximate approaches are shown to derive particular integrals. • An alternative forward-adjoint technique is suggested as well. • An additional spectral binning scheme which speeds up the calculations is presented
International Nuclear Information System (INIS)
Nunes, Carlos Eduardo de Araujo
2011-01-01
As neutron fission events do not take place in the non-multiplying regions of nuclear reactors, e.g., moderator, reflector, and structural core, these regions do not generate power and the computational efficiency of nuclear reactor global calculations can hence be improved by eliminating the explicit numerical calculations within the non-multiplying regions around the active domain. Discussed here is the computational efficiency of approximate discrete ordinates (SN) albedo boundary conditions for two-energy group eigenvalue problems in X, Y geometry. Albedo, the Latin word for w hiteness , was originally defined as the fraction of incident light reflected diffusely by a surface. This Latin word has remained the usual scientific term in astronomy and in this dissertation this concept is extended for the reflection of neutrons. The non-standard SN albedo substitutes approximately the reflector region around the active domain, as we neglect the transverse leakage terms within the non-multiplying reflector. Should the problem have no transverse leakage terms, i.e., one dimensional slab geometry, then the offered albedo boundary conditions are exact. By computational efficiency we mean analyzing the accuracy of the numerical results versus the CPU execution time of each run for a given model problem. Numerical results to two 1/4 symmetric test problems are shown to illustrate this efficiency analysis. (author)
International Nuclear Information System (INIS)
Wagner, J.C.; Haghighat, A.
1998-01-01
Although the Monte Carlo method is considered to be the most accurate method available for solving radiation transport problems, its applicability is limited by its computational expense. Thus, biasing techniques, which require intuition, guesswork, and iterations involving manual adjustments, are employed to make reactor shielding calculations feasible. To overcome this difficulty, the authors have developed a method for using the S N adjoint function for automated variance reduction of Monte Carlo calculations through source biasing and consistent transport biasing with the weight window technique. They describe the implementation of this method into the standard production Monte Carlo code MCNP and its application to a realistic calculation, namely, the reactor cavity dosimetry calculation. The computational effectiveness of the method, as demonstrated through the increase in calculational efficiency, is demonstrated and quantified. Important issues associated with this method and its efficient use are addressed and analyzed. Additional benefits in terms of the reduction in time and effort required of the user are difficult to quantify but are possibly as important as the computational efficiency. In general, the automated variance reduction method presented is capable of increases in computational performance on the order of thousands, while at the same time significantly reducing the current requirements for user experience, time, and effort. Therefore, this method can substantially increase the applicability and reliability of Monte Carlo for large, real-world shielding applications
International Nuclear Information System (INIS)
Oliveira, J.V.P. de; Cardona, A.V.; Vilhena, M.T.M.B. de
2002-01-01
In this work, we present a new approach to solve the one-dimensional time-dependent discrete ordinates problem (S N problem) in a slab. The main idea is based upon the application of the spectral method to the set of S N time-dependent differential equations and solution of the resulting coupling equations by the LTS N method. We report numerical simulations
International Nuclear Information System (INIS)
Muresan, Cristian; Vaillon, Rodolphe; Menezo, Christophe; Morlot, Rodolphe
2004-01-01
The coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation is solved. The collimated and diffuse components problems are treated separately. The solution for diffuse radiation is obtained by using a composite discrete ordinates method and includes the development of adaptive directional quadratures to overcome the difficulties usually encountered at the interfaces. The complete radiation numerical model is validated against the predictions obtained by using the Monte Carlo method
Energy Technology Data Exchange (ETDEWEB)
Nemoto, Toshiyuki; Kawai, Wataru [Fujitsu Ltd., Tokyo (Japan); Kawasaki, Nobuo [and others
1997-12-01
Several computer codes in the nuclear field have been vectorized, parallelized and transported on the FUJITSU VPP500 system at Center for Promotion of Computational Science and Engineering in Japan Atomic Energy Research Institute. These results are reported in 3 parts, i.e., the vectorization part, the parallelization part and the porting part. In this report, we describe the vectorization. In this vectorization part, the vectorization of two and three dimensional discrete ordinates simulation code DORT-TORT, gas dynamics analysis code FLOWGR and relativistic Boltzmann-Uehling-Uhlenbeck simulation code RBUU are described. In the parallelization part, the parallelization of 2-Dimensional relativistic electromagnetic particle code EM2D, Cylindrical Direct Numerical Simulation code CYLDNS and molecular dynamics code for simulating radiation damages in diamond crystals DGR are described. And then, in the porting part, the porting of reactor safety analysis code RELAP5/MOD3.2 and RELAP5/MOD3.2.1.2, nuclear data processing system NJOY and 2-D multigroup discrete ordinate transport code TWOTRAN-II are described. And also, a survey for the porting of command-driven interactive data analysis plotting program IPLOT are described. (author)
Energy Technology Data Exchange (ETDEWEB)
Nemoto, Toshiyuki [Fujitsu Ltd., Tokyo (Japan); Kawasaki, Nobuo; Tanabe, Hidenobu [and others
1998-01-01
Several computer codes in the nuclear field have been vectorized, parallelized and transported on the FUJITSU VPP500 system at Center for Promotion of Computational Science and Engineering in Japan Atomic Energy Research Institute. These results are reported in 3 parts, i.e., the vectorization part, the parallelization part and the porting part. In this report, we describe the porting. In this porting part, the porting of reactor safety analysis code RELAP5/MOD3.2 and RELAP5/MOD3.2.1.2, nuclear data processing system NJOY and 2-D multigroup discrete ordinate transport code TWOTRAN-II are described. And also, a survey for the porting of command-driven interactive data analysis plotting program IPLOT are described. In the parallelization part, the parallelization of 2-Dimensional relativistic electromagnetic particle code EM2D, Cylindrical Direct Numerical Simulation code CYLDNS and molecular dynamics code for simulating radiation damages in diamond crystals DGR are described. And then, in the vectorization part, the vectorization of two and three dimensional discrete ordinates simulation code DORT-TORT, gas dynamics analysis code FLOWGR and relativistic Boltzmann-Uehling-Uhlenbeck simulation code RBUU are described. (author)
Acceleration of Multidimensional Discrete Ordinates Methods Via Adjacent-Cell Preconditioners
International Nuclear Information System (INIS)
Azmy, Y.Y.
2000-01-01
The adjacent-cell preconditioner (AP) formalism originally derived in slab geometry is extended to multidimensional Cartesian geometry for generic fixed-weight, weighted diamond difference neutron transport methods. This is accomplished for the thick-cell regime (KAP) and thin-cell regime (NAP). A spectral analysis of the resulting acceleration schemes demonstrates their excellent spectral properties for model problem configurations, characterized by a uniform mesh of infinite extent and homogeneous material composition, each in its own cell-size regime. Thus, the spectral radius of KAP vanishes as the computational cell size approaches infinity, but it exceeds unity for very thin cells, thereby implying instability. In contrast, NAP is stable and robust for all cell sizes, but its spectral radius vanishes more slowly as the cell size increases. For this reason, and to avoid potential complication in the case of cells that are thin in one dimension and thick in another, NAP is adopted in the remainder of this work. The most important feature of AP for practical implementation in production level codes is that it is cell centered, reducing the size of the algebraic system comprising the acceleration stage compared to face-centered schemes. Boundary conditions for finite extent problems and a mixing formula across material and cell-size discontinuity are derived and used to implement NAP in a test code, AHOT, and a production code, TORT. Numerical testing for algebraically linear iterative schemes for the cases embodied in Burre's Suite of Test Problems demonstrates the high efficiency of the new method in reducing the number of iterations required to achieve convergence, especially for optically thick cells where acceleration is most needed. Also, for algebraically nonlinear (adaptive) methods, AP generally performs better than the partial current rebalance method in TORT and the diffusion synthetic acceleration method in TWODANT. Finally, application of the AP
Parallel S/sub n/ iteration schemes
International Nuclear Information System (INIS)
Wienke, B.R.; Hiromoto, R.E.
1986-01-01
The iterative, multigroup, discrete ordinates (S/sub n/) technique for solving the linear transport equation enjoys widespread usage and appeal. Serial iteration schemes and numerical algorithms developed over the years provide a timely framework for parallel extension. On the Denelcor HEP, the authors investigate three parallel iteration schemes for solving the one-dimensional S/sub n/ transport equation. The multigroup representation and serial iteration methods are also reviewed. This analysis represents a first attempt to extend serial S/sub n/ algorithms to parallel environments and provides good baseline estimates on ease of parallel implementation, relative algorithm efficiency, comparative speedup, and some future directions. The authors examine ordered and chaotic versions of these strategies, with and without concurrent rebalance and diffusion acceleration. Two strategies efficiently support high degrees of parallelization and appear to be robust parallel iteration techniques. The third strategy is a weaker parallel algorithm. Chaotic iteration, difficult to simulate on serial machines, holds promise and converges faster than ordered versions of the schemes. Actual parallel speedup and efficiency are high and payoff appears substantial
Combined spatial/angular domain decomposition SN algorithms for shared memory parallel machines
International Nuclear Information System (INIS)
Hunter, M.A.; Haghighat, A.
1993-01-01
Several parallel processing algorithms on the basis of spatial and angular domain decomposition methods are developed and incorporated into a two-dimensional discrete ordinates transport theory code. These algorithms divide the spatial and angular domains into independent subdomains so that the flux calculations within each subdomain can be processed simultaneously. Two spatial parallel algorithms (Block-Jacobi, red-black), one angular parallel algorithm (η-level), and their combinations are implemented on an eight processor CRAY Y-MP. Parallel performances of the algorithms are measured using a series of fixed source RZ geometry problems. Some of the results are also compared with those executed on an IBM 3090/600J machine. (orig.)
Weng, Fuzhong
1992-01-01
A theory is developed for discretizing the vector integro-differential radiative transfer equation including both solar and thermal radiation. A complete solution and boundary equations are obtained using the discrete-ordinate method. An efficient numerical procedure is presented for calculating the phase matrix and achieving computational stability. With natural light used as a beam source, the Stokes parameters from the model proposed here are compared with the analytical solutions of Chandrasekhar (1960) for a Rayleigh scattering atmosphere. The model is then applied to microwave frequencies with a thermal source, and the brightness temperatures are compared with those from Stamnes'(1988) radiative transfer model.
DOT-IV two-dimensional discrete ordinates transport code with space-dependent mesh and quadrature
International Nuclear Information System (INIS)
Rhoades, W.A.; Simpson, D.B.; Childs, R.L.; Engle, W.W. Jr.
1979-01-01
DOT IV is designed to allow very large problems to be solved on a wide range of computers and memory arrangements. New flexibility in both space-mesh and directional-quadrature specification is allowed. For example, the radial mesh in an R-Z problem can vary with axial position. The directional quadrature can vary with both space and energy group. Several features improve performance on both deep penetration and criticality problems. The program has been checked and used extensively on several types of computers. All of the features have been insured operable except the following two, which must not be used: criticality searches and P/sub L/ variable by group or material. Diffusion theory problems must not use internal or external boundary sources, variable mesh, or variable quadrature. A diffusion iteration cannot produce internal boundary source output or ''angular flux tape.'' The P 1 module is very limited. The special geometries, INGEOM greater than or equal to 10, have not been completely checked and are not guaranteed. 7 figures, 1 table
Parallel processing Monte Carlo radiation transport codes
International Nuclear Information System (INIS)
McKinney, G.W.
1994-01-01
Issues related to distributed-memory multiprocessing as applied to Monte Carlo radiation transport are discussed. Measurements of communication overhead are presented for the radiation transport code MCNP which employs the communication software package PVM, and average efficiency curves are provided for a homogeneous virtual machine
Parallel SN transport calculations on a transputer network
International Nuclear Information System (INIS)
Kim, Yong Hee; Cho, Nam Zin
1994-01-01
A parallel computing algorithm for the neutron transport problems has been implemented on a transputer network and two reactor benchmark problems (a fixed-source problem and an eigenvalue problem) are solved. We have shown that the parallel calculations provided significant reduction in execution time over the sequential calculations
Gauge field governing parallel transport along mixed states
International Nuclear Information System (INIS)
Uhlmann, A.
1990-01-01
At first a short account is given of some basic notations and results on parallel transport along mixed states. A new connection form (gauge field) is introduced to give a geometric meaning to the concept of parallelity in the theory of density operators. (Author) 11 refs
Performance of a neutron transport code with full phase space decomposition on the Cray Research T3D
International Nuclear Information System (INIS)
Dorr, M.R.; Salo, E.M.
1995-01-01
We present performance results obtained on a 128-node Cray Research T3D computer by a neutron transport code implementing a standard mtiltigroup, discrete ordinates algorithm on a three-dimensional Cartesian grid. After summarizing the implementation strategy used to obtain a full decomposition of phase space (i.e., simultaneous parallelization of the neutron energy, directional and spatial variables), we investigate the scalability of the fundamental source iteration step with respect to each phase space variable. We also describe enhancements that have enabled performance rates approaching 10 gigaflops on the full 128-node machine
Angular parallelization of a curvilinear Sn transport theory method
International Nuclear Information System (INIS)
Haghighat, A.
1991-01-01
In this paper a parallel algorithm for angular domain decomposition (or parallelization) of an r-dependent spherical S n transport theory method is derived. The parallel formulation is incorporated into TWOTRAN-II using the IBM Parallel Fortran compiler and implemented on an IBM 3090/400 (with four processors). The behavior of the parallel algorithm for different physical problems is studied, and it is concluded that the parallel algorithm behaves differently in the presence of a fission source as opposed to the absence of a fission source; this is attributed to the relative contributions of the source and the angular redistribution terms in the S s algorithm. Further, the parallel performance of the algorithm is measured for various problem sizes and different combinations of angular subdomains or processors. Poor parallel efficiencies between ∼35 and 50% are achieved in situations where the relative difference of parallel to serial iterations is ∼50%. High parallel efficiencies between ∼60% and 90% are obtained in situations where the relative difference of parallel to serial iterations is <35%
Energy Technology Data Exchange (ETDEWEB)
Le Dez, V; Lallemand, M [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M; Charette, A [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees
1997-12-31
The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.
Energy Technology Data Exchange (ETDEWEB)
Le Dez, V.; Lallemand, M. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M.; Charette, A. [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees
1996-12-31
The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.
International Nuclear Information System (INIS)
Hennart, J.P.; Valle, E. del.
1995-01-01
A generalized nodal finite element formalism is presented, which covers virtually all known finit difference approximation to the discrete ordinates equations in slab geometry. This paper (Part 1) presents the theory of the so called open-quotes continuous moment methodsclose quotes, which include such well-known methods as the open-quotes diamond differenceclose quotes and the open-quotes characteristicclose quotes schemes. In a second paper (hereafter referred to as Part II), the authors will present the theory of the open-quotes discontinuous moment methodsclose quotes, consisting in particular of the open-quotes linear discontinuousclose quotes scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III). 12 refs
da Silva, Anabela; Elias, Mady; Andraud, Christine; Lafait, Jacques
2003-12-01
Two methods for solving the radiative transfer equation are compared with the aim of computing the angular distribution of the light scattered by a heterogeneous scattering medium composed of a single flat layer or a multilayer. The first method [auxiliary function method (AFM)], recently developed, uses an auxiliary function and leads to an exact solution; the second [discrete-ordinate method (DOM)] is based on the channel concept and needs an angular discretization. The comparison is applied to two different media presenting two typical and extreme scattering behaviors: Rayleigh and Mie scattering with smooth or very anisotropic phase functions, respectively. A very good agreement between the predictions of the two methods is observed in both cases. The larger the number of channels used in the DOM, the better the agreement. The principal advantages and limitations of each method are also listed.
Parallel heat transport in integrable and chaotic magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Castillo-Negrete, D. del; Chacon, L. [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-8071 (United States)
2012-05-15
The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly challenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), {chi}{sub ||} , and the perpendicular, {chi}{sub Up-Tack }, conductivities ({chi}{sub ||} /{chi}{sub Up-Tack} may exceed 10{sup 10} in fusion plasmas); (ii) Nonlocal parallel transport in the limit of small collisionality; and (iii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates. Motivated by these issues, we present a Lagrangian Green's function method to solve the local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geometry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island), weakly chaotic (Devil's staircase), and fully chaotic magnetic field configurations. For the latter, numerical solutions of the parallel heat transport equation show that the effective radial transport, with local and non-local parallel closures, is non-diffusive, thus casting doubts on the applicability of quasilinear diffusion descriptions. General conditions for the existence of non-diffusive, multivalued flux-gradient relations in the temperature evolution are derived.
Load Balancing of Parallel Monte Carlo Transport Calculations
International Nuclear Information System (INIS)
Procassini, R J; O'Brien, M J; Taylor, J M
2005-01-01
The performance of parallel Monte Carlo transport calculations which use both spatial and particle parallelism is increased by dynamically assigning processors to the most worked domains. Since he particle work load varies over the course of the simulation, this algorithm determines each cycle if dynamic load balancing would speed up the calculation. If load balancing is required, a small number of particle communications are initiated in order to achieve load balance. This method has decreased the parallel run time by more than a factor of three for certain criticality calculations
Dynamic Load Balancing of Parallel Monte Carlo Transport Calculations
International Nuclear Information System (INIS)
O'Brien, M; Taylor, J; Procassini, R
2004-01-01
The performance of parallel Monte Carlo transport calculations which use both spatial and particle parallelism is increased by dynamically assigning processors to the most worked domains. Since the particle work load varies over the course of the simulation, this algorithm determines each cycle if dynamic load balancing would speed up the calculation. If load balancing is required, a small number of particle communications are initiated in order to achieve load balance. This method has decreased the parallel run time by more than a factor of three for certain criticality calculations
Local and Nonlocal Parallel Heat Transport in General Magnetic Fields
International Nuclear Information System (INIS)
Castillo-Negrete, D. del; Chacon, L.
2011-01-01
A novel approach for the study of parallel transport in magnetized plasmas is presented. The method avoids numerical pollution issues of grid-based formulations and applies to integrable and chaotic magnetic fields with local or nonlocal parallel closures. In weakly chaotic fields, the method gives the fractal structure of the devil's staircase radial temperature profile. In fully chaotic fields, the temperature exhibits self-similar spatiotemporal evolution with a stretched-exponential scaling function for local closures and an algebraically decaying one for nonlocal closures. It is shown that, for both closures, the effective radial heat transport is incompatible with the quasilinear diffusion model.
Parallel processing of neutron transport in fuel assembly calculation
International Nuclear Information System (INIS)
Song, Jae Seung
1992-02-01
Group constants, which are used for reactor analyses by nodal method, are generated by fuel assembly calculations based on the neutron transport theory, since one or a quarter of the fuel assembly corresponds to a unit mesh in the current nodal calculation. The group constant calculation for a fuel assembly is performed through spectrum calculations, a two-dimensional fuel assembly calculation, and depletion calculations. The purpose of this study is to develop a parallel algorithm to be used in a parallel processor for the fuel assembly calculation and the depletion calculations of the group constant generation. A serial program, which solves the neutron integral transport equation using the transmission probability method and the linear depletion equation, was prepared and verified by a benchmark calculation. Small changes from the serial program was enough to parallelize the depletion calculation which has inherent parallel characteristics. In the fuel assembly calculation, however, efficient parallelization is not simple and easy because of the many coupling parameters in the calculation and data communications among CPU's. In this study, the group distribution method is introduced for the parallel processing of the fuel assembly calculation to minimize the data communications. The parallel processing was performed on Quadputer with 4 CPU's operating in NURAD Lab. at KAIST. Efficiencies of 54.3 % and 78.0 % were obtained in the fuel assembly calculation and depletion calculation, respectively, which lead to the overall speedup of about 2.5. As a result, it is concluded that the computing time consumed for the group constant generation can be easily reduced by parallel processing on the parallel computer with small size CPU's
Parallelization of a spherical Sn transport theory algorithm
International Nuclear Information System (INIS)
Haghighat, A.
1989-01-01
The work described in this paper derives a parallel algorithm for an R-dependent spherical S N transport theory algorithm and studies its performance by testing different sample problems. The S N transport method is one of the most accurate techniques used to solve the linear Boltzmann equation. Several studies have been done on the vectorization of the S N algorithms; however, very few studies have been performed on the parallelization of this algorithm. Weinke and Hommoto have looked at the parallel processing of the different energy groups, and Azmy recently studied the parallel processing of the inner iterations of an X-Y S N nodal transport theory method. Both studies have reported very encouraging results, which have prompted us to look at the parallel processing of an R-dependent S N spherical geometry algorithm. This geometry was chosen because, in spite of its simplicity, it contains the complications of the curvilinear geometries (i.e., redistribution of neutrons over the discretized angular bins)
Parallelization of a Monte Carlo particle transport simulation code
Hadjidoukas, P.; Bousis, C.; Emfietzoglou, D.
2010-05-01
We have developed a high performance version of the Monte Carlo particle transport simulation code MC4. The original application code, developed in Visual Basic for Applications (VBA) for Microsoft Excel, was first rewritten in the C programming language for improving code portability. Several pseudo-random number generators have been also integrated and studied. The new MC4 version was then parallelized for shared and distributed-memory multiprocessor systems using the Message Passing Interface. Two parallel pseudo-random number generator libraries (SPRNG and DCMT) have been seamlessly integrated. The performance speedup of parallel MC4 has been studied on a variety of parallel computing architectures including an Intel Xeon server with 4 dual-core processors, a Sun cluster consisting of 16 nodes of 2 dual-core AMD Opteron processors and a 200 dual-processor HP cluster. For large problem size, which is limited only by the physical memory of the multiprocessor server, the speedup results are almost linear on all systems. We have validated the parallel implementation against the serial VBA and C implementations using the same random number generator. Our experimental results on the transport and energy loss of electrons in a water medium show that the serial and parallel codes are equivalent in accuracy. The present improvements allow for studying of higher particle energies with the use of more accurate physical models, and improve statistics as more particles tracks can be simulated in low response time.
Inter-dot coupling effects on transport through correlated parallel
Indian Academy of Sciences (India)
Transport through symmetric parallel coupled quantum dot system has been studied, using non-equilibrium Green function formalism. The inter-dot tunnelling with on-dot and inter-dot Coulomb repulsion is included. The transmission coefficient and Landaur–Buttiker like current formula are shown in terms of internal states ...
International Nuclear Information System (INIS)
Kosako, K.; Yamano, N.; Fukahori, T.; Shibata, K.; Hasegawa, A.
2006-01-01
1 - Description of program or function: JENDL-3.3 based, 175 neutron-42 photon groups (VITAMIN-J) MATXS library for discrete ordinates multi-group transport codes. Format: MATXS. Number of groups: 175 neutron, 42 gamma-ray. Nuclides: 337 nuclides contained in JENDL-3.3: H-1, H-2, He-3, He-4, Li-6, Li-7, Be-9, B-10, B-11, C-Nat, N-14, N-15, O-16, F-19, Na-23, Mg-24, Mg-25, Mg-26, Al-27, Si-28, Si-29, Si-30, P-31, S-32, S-33, S-34, S-36, Cl-35, Cl-37, Ar-40, K-39, K-40, K-41, Ca-40, Ca-42, Ca-43, Ca-44, Ca-46, Ca-48, Sc-45, Ti-46, Ti-47, Ti-48, Ti-49, Ti-50, V-Nat, Cr-50, Cr-52, Cr-53, Cr-54, Mn-55, Fe-54, Fe-56, Fe-57, Fe-58, Co-59, Ni-58, Ni-60, Ni-61, Ni-62, Ni-64, Cu-63, Cu-65, Ga-69, Ga-71, Ge-70, Ge-72, Ge-73, Ge-74, Ge-76, As-75, Se-74, Se-76, Se-77, Se-78, Se-79, Se-80, Se-82, Br-79, Br-81, Kr-78, Kr-80, Kr-82, Kr-83, Kr-84, Kr-85, Kr-86, Rb-85, Rb-87, Sr-86, Sr-87, Sr-88, Sr-89, Sr-90, Y-89, Y-91, Zr-90, Zr-91, Zr-92, Zr-93, Zr-94, Zr-95, Zr-96, Nb-93, Nb-94, Nb-95, Mo-92, Mo-94, Mo-95, Mo-96, Mo-97, Mo-98, Mo-99, Mo-100, Tc-99, Ru-96, Ru-98, Ru-99, Ru-100, Ru-101, Ru-102, Ru-103, Ru-104, Ru-106, Rh-103, Rh-105, Pd-102, Pd-104, Pd-105, Pd-106, Pd-107, Pd-108, Pd-110, Ag-107, Ag-109, Ag-110m, Cd-106, Cd-108, Cd-110, Cd-111, Cd-112, Cd-113, Cd-114, Cd-116, In-113, In-115, Sn-112, Sn-114, Sn-115, Sn-116, Sn-117, Sn-118, Sn-119, Sn-120, Sn-122, Sn-123, Sn-124, Sn-126, Sb-121, Sb-123, Sb-124, Sb-125, Te-120, Te-122, Te-123, Te-124, Te-125, Te-126, Te-127m, Te-128, Te-129m, Te-130, I-127, I-129, I-131, Xe-124, Xe-126, Xe-128, Xe-129, Xe-130, Xe-131, Xe-132, Xe-133, Xe-134, Xe-135, Xe-136, Cs-133, Cs-134, Cs-135, Cs-136, Cs-137, Ba-130, Ba-132, Ba-134, Ba-135, Ba-136, Ba-137, Ba-138, Ba-140, La-138, La-139, Ce-140, Ce-141, Ce-142, Ce-144, Pr-141, Pr-143, Nd-142, Nd-143, Nd-144, Nd-145, Nd-146, Nd-147, Nd-148, Nd-150, Pm-147, Pm-148, Pm-148m, Pm-149, Sm-144, Sm-147, Sm-148, Sm-149, Sm-150, Sm-151, Sm-152, Sm-153, Sm-154, Eu-151, Eu-152, Eu-153, Eu-154, Eu-155, Eu
Stamnes, Knut; Tsay, S.-CHEE; Jayaweera, Kolf; Wiscombe, Warren
1988-01-01
The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.
Parallel processing of two-dimensional Sn transport calculations
International Nuclear Information System (INIS)
Uematsu, M.
1997-01-01
A parallel processing method for the two-dimensional S n transport code DOT3.5 has been developed to achieve a drastic reduction in computation time. In the proposed method, parallelization is achieved with angular domain decomposition and/or space domain decomposition. The calculational speed of parallel processing by angular domain decomposition is largely influenced by frequent communications between processing elements. To assess parallelization efficiency, sample problems with up to 32 x 32 spatial meshes were solved with a Sun workstation using the PVM message-passing library. As a result, parallel calculation using 16 processing elements, for example, was found to be nine times as fast as that with one processing element. As for parallel processing by geometry segmentation, the influence of processing element communications on computation time is small; however, discontinuity at the segment boundary degrades convergence speed. To accelerate the convergence, an alternate sweep of angular flux in conjunction with space domain decomposition and a two-step rescaling method consisting of segmentwise rescaling and ordinary pointwise rescaling have been developed. By applying the developed method, the number of iterations needed to obtain a converged flux solution was reduced by a factor of 2. As a result, parallel calculation using 16 processing elements was found to be 5.98 times as fast as the original DOT3.5 calculation
Minaret, a deterministic neutron transport solver for nuclear core calculations
International Nuclear Information System (INIS)
Moller, J-Y.; Lautard, J-J.
2011-01-01
We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared. (author)
Minaret, a deterministic neutron transport solver for nuclear core calculations
Energy Technology Data Exchange (ETDEWEB)
Moller, J-Y.; Lautard, J-J., E-mail: jean-yves.moller@cea.fr, E-mail: jean-jacques.lautard@cea.fr [CEA - Centre de Saclay , Gif sur Yvette (France)
2011-07-01
We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared. (author)
Parallel computing solution of Boltzmann neutron transport equation
International Nuclear Information System (INIS)
Ansah-Narh, T.
2010-01-01
The focus of the research was on developing parallel computing algorithm for solving Eigen-values of the Boltzmam Neutron Transport Equation (BNTE) in a slab geometry using multi-grid approach. In response to the problem of slow execution of serial computing when solving large problems, such as BNTE, the study was focused on the design of parallel computing systems which was an evolution of serial computing that used multiple processing elements simultaneously to solve complex physical and mathematical problems. Finite element method (FEM) was used for the spatial discretization scheme, while angular discretization was accomplished by expanding the angular dependence in terms of Legendre polynomials. The eigenvalues representing the multiplication factors in the BNTE were determined by the power method. MATLAB Compiler Version 4.1 (R2009a) was used to compile the MATLAB codes of BNTE. The implemented parallel algorithms were enabled with matlabpool, a Parallel Computing Toolbox function. The option UseParallel was set to 'always' and the default value of the option was 'never'. When those conditions held, the solvers computed estimated gradients in parallel. The parallel computing system was used to handle all the bottlenecks in the matrix generated from the finite element scheme and each domain of the power method generated. The parallel algorithm was implemented on a Symmetric Multi Processor (SMP) cluster machine, which had Intel 32 bit quad-core x 86 processors. Convergence rates and timings for the algorithm on the SMP cluster machine were obtained. Numerical experiments indicated the designed parallel algorithm could reach perfect speedup and had good stability and scalability. (au)
Simulation of neutron transport equation using parallel Monte Carlo for deep penetration problems
International Nuclear Information System (INIS)
Bekar, K. K.; Tombakoglu, M.; Soekmen, C. N.
2001-01-01
Neutron transport equation is simulated using parallel Monte Carlo method for deep penetration neutron transport problem. Monte Carlo simulation is parallelized by using three different techniques; direct parallelization, domain decomposition and domain decomposition with load balancing, which are used with PVM (Parallel Virtual Machine) software on LAN (Local Area Network). The results of parallel simulation are given for various model problems. The performances of the parallelization techniques are compared with each other. Moreover, the effects of variance reduction techniques on parallelization are discussed
International Nuclear Information System (INIS)
Voloschenko, A. M.; Gukov, S. V.; Russkov, A. A.; Gurevich, M. I.; Shkarovsky, D. A.; Kryuchkov, V. P.; Sumaneev, O. V.; Dubinin, A. A.
2009-01-01
KATRIN, KASKAD-Sand ROZ-6 codes solve the multigroup transport equation for neutrons, photons and charged particles in 3D. BOT3P-5., ConDat can be used as preprocessor. ARVES-2.5, a cross-section preprocessor (the package of utilities for operating with the cross section file in FMAC-M format) is included. Auxiliary codes MIXERM, CEPXS-BFP, CEPXS-BFP, SADCO-2.4 and CNCSN-2 are used
Energy Technology Data Exchange (ETDEWEB)
Slater, C.O.
1990-07-01
Results are reported for two-dimensional discrete ordinates, X-Y geometry calculations performed for seven Halden Heavy Boiling Water Reactor core configurations. The calculations were performed in support of an effort to reassess the neutron fluence received by the reactor vessel. Nickel foil measurement data indicated considerable underprediction of fluences by the previously used multigroup removal- diffusion method. Therefore, calculations by a more accurate method were deemed appropriate. For each core configuration, data are presented for (1) integral fluxes in the core and near the vessel wall, (2) neutron spectra at selected locations, (3) isoflux contours superimposed on the geometry models, (4) plots of the geometry models, and (5) input for the calculations. The initial calculations were performed with several mesh sizes. Comparisons of the results from these calculations indicated that the uncertainty in the calculated fluxes should be less than 10%. However, three-dimensional effects (such as axial asymmetry in the fuel loading) could contribute to much greater uncertainty in the calculated neutron fluxes. 7 refs., 22 figs., 11 tabs.
Sn transport calculations on vector and parallel processors
International Nuclear Information System (INIS)
Rhoades, W.A.; Childs, R.L.
1987-01-01
The transport of radiation from the source to the location of people or equipment gives rise to some of the most challenging of calculations. A problem may involve as many as a billion unknowns, each evaluated several times to resolve interdependence. Such calculations run many hours on a Cray computer, and a typical study involves many such calculations. This paper will discuss the steps taken to vectorize the DOT code, which solves transport problems in two space dimensions (2-D); the extension of this code to 3-D; and the plans for extension to parallel processors
Parallel computing for homogeneous diffusion and transport equations in neutronics
International Nuclear Information System (INIS)
Pinchedez, K.
1999-06-01
Parallel computing meets the ever-increasing requirements for neutronic computer code speed and accuracy. In this work, two different approaches have been considered. We first parallelized the sequential algorithm used by the neutronics code CRONOS developed at the French Atomic Energy Commission. The algorithm computes the dominant eigenvalue associated with PN simplified transport equations by a mixed finite element method. Several parallel algorithms have been developed on distributed memory machines. The performances of the parallel algorithms have been studied experimentally by implementation on a T3D Cray and theoretically by complexity models. A comparison of various parallel algorithms has confirmed the chosen implementations. We next applied a domain sub-division technique to the two-group diffusion Eigen problem. In the modal synthesis-based method, the global spectrum is determined from the partial spectra associated with sub-domains. Then the Eigen problem is expanded on a family composed, on the one hand, from eigenfunctions associated with the sub-domains and, on the other hand, from functions corresponding to the contribution from the interface between the sub-domains. For a 2-D homogeneous core, this modal method has been validated and its accuracy has been measured. (author)
Directory of Open Access Journals (Sweden)
KIM Jong Woon
2017-01-01
In this paper, we describe a brief overview of AETIUS and provide numerical results from both AETIUS and a Monte Carlo code, MCNP5, in a deep penetration problem with small detection volumes. The results demonstrate the effectiveness and efficiency of AETIUS for such calculations.
Parallel MCNP Monte Carlo transport calculations with MPI
International Nuclear Information System (INIS)
Wagner, J.C.; Haghighat, A.
1996-01-01
The steady increase in computational performance has made Monte Carlo calculations for large/complex systems possible. However, in order to make these calculations practical, order of magnitude increases in performance are necessary. The Monte Carlo method is inherently parallel (particles are simulated independently) and thus has the potential for near-linear speedup with respect to the number of processors. Further, the ever-increasing accessibility of parallel computers, such as workstation clusters, facilitates the practical use of parallel Monte Carlo. Recognizing the nature of the Monte Carlo method and the trends in available computing, the code developers at Los Alamos National Laboratory implemented the message-passing general-purpose Monte Carlo radiation transport code MCNP (version 4A). The PVM package was chosen by the MCNP code developers because it supports a variety of communication networks, several UNIX platforms, and heterogeneous computer systems. This PVM version of MCNP has been shown to produce speedups that approach the number of processors and thus, is a very useful tool for transport analysis. Due to software incompatibilities on the local IBM SP2, PVM has not been available, and thus it is not possible to take advantage of this useful tool. Hence, it became necessary to implement an alternative message-passing library package into MCNP. Because the message-passing interface (MPI) is supported on the local system, takes advantage of the high-speed communication switches in the SP2, and is considered to be the emerging standard, it was selected
Novel Parallel Numerical Methods for Radiation and Neutron Transport
International Nuclear Information System (INIS)
Brown, P N
2001-01-01
In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both
Pthreads vs MPI Parallel Performance of Angular-Domain Decomposed S
International Nuclear Information System (INIS)
Azmy, Y.Y.; Barnett, D.A.
2000-01-01
Two programming models for parallelizing the Angular Domain Decomposition (ADD) of the discrete ordinates (S n ) approximation of the neutron transport equation are examined. These are the shared memory model based on the POSIX threads (Pthreads) standard, and the message passing model based on the Message Passing Interface (MPI) standard. These standard libraries are available on most multiprocessor platforms thus making the resulting parallel codes widely portable. The question is: on a fixed platform, and for a particular code solving a given test problem, which of the two programming models delivers better parallel performance? Such comparison is possible on Symmetric Multi-Processors (SMP) architectures in which several CPUs physically share a common memory, and in addition are capable of emulating message passing functionality. Implementation of the two-dimensional,(S n ), Arbitrarily High Order Transport (AHOT) code for solving neutron transport problems using these two parallelization models is described. Measured parallel performance of each model on the COMPAQ AlphaServer 8400 and the SGI Origin 2000 platforms is described, and comparison of the observed speedup for the two programming models is reported. For the case presented in this paper it appears that the MPI implementation scales better than the Pthreads implementation on both platforms
Time-dependent deterministic transport on parallel architectures using PARTISN
International Nuclear Information System (INIS)
Alcouffe, R.E.; Baker, R.S.
1998-01-01
In addition to the ability to solve the static transport equation, the authors have also incorporated time dependence into the parallel S N code PARTISN. Using a semi-implicit scheme, PARTISN is capable of performing time-dependent calculations for both fissioning and pure source driven problems. They have applied this to various types of problems such as shielding and prompt fission experiments. This paper describes the form of the time-dependent equations implemented, their solution strategies in PARTISN including iteration acceleration, and the strategies used for time-step control. Results are presented for a iron-water shielding calculation and a criticality excursion in a uranium solution configuration
New adaptive differencing strategy in the PENTRAN 3-d parallel Sn code
International Nuclear Information System (INIS)
Sjoden, G.E.; Haghighat, A.
1996-01-01
It is known that three-dimensional (3-D) discrete ordinates (S n ) transport problems require an immense amount of storage and computational effort to solve. For this reason, parallel codes that offer a capability to completely decompose the angular, energy, and spatial domains among a distributed network of processors are required. One such code recently developed is PENTRAN, which iteratively solves 3-D multi-group, anisotropic S n problems on distributed-memory platforms, such as the IBM-SP2. Because large problems typically contain several different material zones with various properties, available differencing schemes should automatically adapt to the transport physics in each material zone. To minimize the memory and message-passing overhead required for massively parallel S n applications, available differencing schemes in an adaptive strategy should also offer reasonable accuracy and positivity, yet require only the zeroth spatial moment of the transport equation; differencing schemes based on higher spatial moments, in spite of their greater accuracy, require at least twice the amount of storage and communication cost for implementation in a massively parallel transport code. This paper discusses a new adaptive differencing strategy that uses increasingly accurate schemes with low parallel memory and communication overhead. This strategy, implemented in PENTRAN, includes a new scheme, exponential directional averaged (EDA) differencing
Multitasking TORT Under UNICOS: Parallel Performance Models and Measurements
International Nuclear Information System (INIS)
Azmy, Y.Y.; Barnett, D.A.
1999-01-01
The existing parallel algorithms in the TORT discrete ordinates were updated to function in a UNI-COS environment. A performance model for the parallel overhead was derived for the existing algorithms. The largest contributors to the parallel overhead were identified and a new algorithm was developed. A parallel overhead model was also derived for the new algorithm. The results of the comparison of parallel performance models were compared to applications of the code to two TORT standard test problems and a large production problem. The parallel performance models agree well with the measured parallel overhead
Multitasking TORT under UNICOS: Parallel performance models and measurements
International Nuclear Information System (INIS)
Barnett, A.; Azmy, Y.Y.
1999-01-01
The existing parallel algorithms in the TORT discrete ordinates code were updated to function in a UNICOS environment. A performance model for the parallel overhead was derived for the existing algorithms. The largest contributors to the parallel overhead were identified and a new algorithm was developed. A parallel overhead model was also derived for the new algorithm. The results of the comparison of parallel performance models were compared to applications of the code to two TORT standard test problems and a large production problem. The parallel performance models agree well with the measured parallel overhead
Improved parallel solution techniques for the integral transport matrix method
Energy Technology Data Exchange (ETDEWEB)
Zerr, R. Joseph, E-mail: rjz116@psu.edu [Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA (United States); Azmy, Yousry Y., E-mail: yyazmy@ncsu.edu [Department of Nuclear Engineering, North Carolina State University, Burlington Engineering Laboratories, Raleigh, NC (United States)
2011-07-01
Alternative solution strategies to the parallel block Jacobi (PBJ) method for the solution of the global problem with the integral transport matrix method operators have been designed and tested. The most straightforward improvement to the Jacobi iterative method is the Gauss-Seidel alternative. The parallel red-black Gauss-Seidel (PGS) algorithm can improve on the number of iterations and reduce work per iteration by applying an alternating red-black color-set to the subdomains and assigning multiple sub-domains per processor. A parallel GMRES(m) method was implemented as an alternative to stationary iterations. Computational results show that the PGS method can improve on the PBJ method execution time by up to 10´ when eight sub-domains per processor are used. However, compared to traditional source iterations with diffusion synthetic acceleration, it is still approximately an order of magnitude slower. The best-performing cases are optically thick because sub-domains decouple, yielding faster convergence. Further tests revealed that 64 sub-domains per processor was the best performing level of sub-domain division. An acceleration technique that improves the convergence rate would greatly improve the ITMM. The GMRES(m) method with a diagonal block pre conditioner consumes approximately the same time as the PBJ solver but could be improved by an as yet undeveloped, more efficient pre conditioner. (author)
Improved parallel solution techniques for the integral transport matrix method
International Nuclear Information System (INIS)
Zerr, R. Joseph; Azmy, Yousry Y.
2011-01-01
Alternative solution strategies to the parallel block Jacobi (PBJ) method for the solution of the global problem with the integral transport matrix method operators have been designed and tested. The most straightforward improvement to the Jacobi iterative method is the Gauss-Seidel alternative. The parallel red-black Gauss-Seidel (PGS) algorithm can improve on the number of iterations and reduce work per iteration by applying an alternating red-black color-set to the subdomains and assigning multiple sub-domains per processor. A parallel GMRES(m) method was implemented as an alternative to stationary iterations. Computational results show that the PGS method can improve on the PBJ method execution time by up to 10´ when eight sub-domains per processor are used. However, compared to traditional source iterations with diffusion synthetic acceleration, it is still approximately an order of magnitude slower. The best-performing cases are optically thick because sub-domains decouple, yielding faster convergence. Further tests revealed that 64 sub-domains per processor was the best performing level of sub-domain division. An acceleration technique that improves the convergence rate would greatly improve the ITMM. The GMRES(m) method with a diagonal block pre conditioner consumes approximately the same time as the PBJ solver but could be improved by an as yet undeveloped, more efficient pre conditioner. (author)
Energy Technology Data Exchange (ETDEWEB)
Lasuik, J.; Shalchi, A., E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)
2017-09-20
Recently, a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other nonlinear theories the new approach has the advantage that it provides a full time-dependent description of the transport. Furthermore, a diffusion approximation is no longer part of that theory. The purpose of this paper is to combine this new approach with a time-dependent model for parallel transport and different turbulence configurations in order to explore the parameter regimes for which we get ballistic transport, compound subdiffusion, and normal Markovian diffusion.
International Nuclear Information System (INIS)
Deng Li; Xie Zhongsheng
1999-01-01
The coupled neutron and photon transport Monte Carlo code MCNP (version 3B) has been parallelized in parallel virtual machine (PVM) and message passing interface (MPI) by modifying a previous serial code. The new code has been verified by solving sample problems. The speedup increases linearly with the number of processors and the average efficiency is up to 99% for 12-processor. (author)
Bao, Jian; Lau, Calvin; Kuley, Animesh; Lin, Zhihong; Fulton, Daniel; Tajima, Toshiki; Tri Alpha Energy, Inc. Team
2017-10-01
Collisional and turbulent transport in a field reversed configuration (FRC) is studied in global particle simulation by using GTC (gyrokinetic toroidal code). The global FRC geometry is incorporated in GTC by using a field-aligned mesh in cylindrical coordinates, which enables global simulation coupling core and scrape-off layer (SOL) across the separatrix. Furthermore, fully kinetic ions are implemented in GTC to treat magnetic-null point in FRC core. Both global simulation coupling core and SOL regions and independent SOL region simulation have been carried out to study turbulence. In this work, the ``logical sheath boundary condition'' is implemented to study parallel transport in the SOL. This method helps to relax time and spatial steps without resolving electron plasma frequency and Debye length, which enables turbulent transports simulation with sheath effects. We will study collisional and turbulent SOL parallel transport with mirror geometry and sheath boundary condition in C2-W divertor.
Resolution of the neutron transport equation by massively parallel computer in the Cronos code
International Nuclear Information System (INIS)
Zardini, D.M.
1996-01-01
The feasibility of neutron transport problems parallel resolution by CRONOS code's SN module is here studied. In this report we give the first data about the parallel resolution by angular variable decomposition of the transport equation. Problems about parallel resolution by spatial variable decomposition and memory stage limits are also explained here. (author)
Parallel Transport Quantum Logic Gates with Trapped Ions.
de Clercq, Ludwig E; Lo, Hsiang-Yu; Marinelli, Matteo; Nadlinger, David; Oswald, Robin; Negnevitsky, Vlad; Kienzler, Daniel; Keitch, Ben; Home, Jonathan P
2016-02-26
We demonstrate single-qubit operations by transporting a beryllium ion with a controlled velocity through a stationary laser beam. We use these to perform coherent sequences of quantum operations, and to perform parallel quantum logic gates on two ions in different processing zones of a multiplexed ion trap chip using a single recycled laser beam. For the latter, we demonstrate individually addressed single-qubit gates by local control of the speed of each ion. The fidelities we observe are consistent with operations performed using standard methods involving static ions and pulsed laser fields. This work therefore provides a path to scalable ion trap quantum computing with reduced requirements on the optical control complexity.
Non-Almost Periodicity of Parallel Transports for Homogeneous Connections
International Nuclear Information System (INIS)
Brunnemann, Johannes; Fleischhack, Christian
2012-01-01
Let A be the affine space of all connections in an SU(2) principal fibre bundle over ℝ 3 . The set of homogeneous isotropic connections forms a line l in A. We prove that the parallel transports for general, non-straight paths in the base manifold do not depend almost periodically on l. Consequently, the embedding l ↪ A does not continuously extend to an embedding l-bar ↪ A-bar of the respective compactifications. Here, the Bohr compactification l-bar corresponds to the configuration space of homogeneous isotropic loop quantum cosmology and A-bar to that of loop quantum gravity. Analogous results are given for the anisotropic case.
Neutron transport solver parallelization using a Domain Decomposition method
International Nuclear Information System (INIS)
Van Criekingen, S.; Nataf, F.; Have, P.
2008-01-01
A domain decomposition (DD) method is investigated for the parallel solution of the second-order even-parity form of the time-independent Boltzmann transport equation. The spatial discretization is performed using finite elements, and the angular discretization using spherical harmonic expansions (P N method). The main idea developed here is due to P.L. Lions. It consists in having sub-domains exchanging not only interface point flux values, but also interface flux 'derivative' values. (The word 'derivative' is here used with quotes, because in the case considered here, it in fact consists in the Ω.∇ operator, with Ω the angular variable vector and ∇ the spatial gradient operator.) A parameter α is introduced, as proportionality coefficient between point flux and 'derivative' values. This parameter can be tuned - so far heuristically - to optimize the method. (authors)
Plane parallel radiance transport for global illumination in vegetation
Energy Technology Data Exchange (ETDEWEB)
Max, N.; Mobley, C.; Keating, B.; Wu, E.H.
1997-01-05
This paper applies plane parallel radiance transport techniques to scattering from vegetation. The leaves, stems, and branches are represented as a volume density of scattering surfaces, depending only on height and the vertical component of the surface normal. Ordinary differential equations are written for the multiply scattered radiance as a function of the height above the ground, with the sky radiance and ground reflectance as boundary conditions. They are solved using a two-pass integration scheme to unify the two-point boundary conditions, and Fourier series for the dependence on the azimuthal angle. The resulting radiance distribution is used to precompute diffuse and specular `ambient` shading tables, as a function of height and surface normal, to be used in rendering, together with a z-buffer shadow algorithm for direct solar illumination.
Discrete elements method of neutron transport
International Nuclear Information System (INIS)
Mathews, K.A.
1988-01-01
In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution
Study on MPI/OpenMP hybrid parallelism for Monte Carlo neutron transport code
International Nuclear Information System (INIS)
Liang Jingang; Xu Qi; Wang Kan; Liu Shiwen
2013-01-01
Parallel programming with mixed mode of messages-passing and shared-memory has several advantages when used in Monte Carlo neutron transport code, such as fitting hardware of distributed-shared clusters, economizing memory demand of Monte Carlo transport, improving parallel performance, and so on. MPI/OpenMP hybrid parallelism was implemented based on a one dimension Monte Carlo neutron transport code. Some critical factors affecting the parallel performance were analyzed and solutions were proposed for several problems such as contention access, lock contention and false sharing. After optimization the code was tested finally. It is shown that the hybrid parallel code can reach good performance just as pure MPI parallel program, while it saves a lot of memory usage at the same time. Therefore hybrid parallel is efficient for achieving large-scale parallel of Monte Carlo neutron transport. (authors)
Radiation-magnetohydrodynamics of fusion plasmas on parallel supercomputers
International Nuclear Information System (INIS)
Yasar, O.; Moses, G.A.; Tautges, T.J.
1993-01-01
A parallel computational model to simulate fusion plasmas in the radiation-magnetohydrodynamics (R-MHD) framework is presented. Plasmas are often treated in a fluid dynamics context (magnetohydrodynamics, MHD), but when the flow field is coupled with the radiation field it falls into a more complex category, radiation magnetohydrodynamics (R-MHD), where the interaction between the flow field and the radiation field is nonlinear. The solution for the radiation field usually dominates the R-MHD computation. To solve for the radiation field, one usually chooses the S N discrete ordinates method (a deterministic method) rather than the Monte Carlo method if the geometry is not complex. The discrete ordinates method on a massively parallel processor (Intel iPSC/860) is implemented. The speedup is 14 for a run on 16 processors and the performance is 3.7 times better than a single CRAY YMP processor implementation. (orig./DG)
Parallel processing of Monte Carlo code MCNP for particle transport problem
Energy Technology Data Exchange (ETDEWEB)
Higuchi, Kenji; Kawasaki, Takuji
1996-06-01
It is possible to vectorize or parallelize Monte Carlo codes (MC code) for photon and neutron transport problem, making use of independency of the calculation for each particle. Applicability of existing MC code to parallel processing is mentioned. As for parallel computer, we have used both vector-parallel processor and scalar-parallel processor in performance evaluation. We have made (i) vector-parallel processing of MCNP code on Monte Carlo machine Monte-4 with four vector processors, (ii) parallel processing on Paragon XP/S with 256 processors. In this report we describe the methodology and results for parallel processing on two types of parallel or distributed memory computers. In addition, we mention the evaluation of parallel programming environments for parallel computers used in the present work as a part of the work developing STA (Seamless Thinking Aid) Basic Software. (author)
Energy Technology Data Exchange (ETDEWEB)
Joseph, D.
2004-04-01
The prediction of pollutant species such as soots and NO{sub x} emissions and lifetime of the walls in a combustion chamber is strongly dependant on heat transfer by radiation at high temperatures. This work deals with the development of a code based on the Discrete Ordinates Method (DOM) aiming at providing radiative source terms and wall fluxes with a good compromise between cpu time and accuracy. Radiative heat transfers are calculated using the unstructured grids defined by the Computational Fluid Dynamics (CFD) codes. The spectral properties of the combustion gases are taken into account by a statistical narrow bands correlated-k model (SNB-ck). Various types of angular quadrature are tested and three different spatial differencing schemes were integrated and compared. The validation tests show the limit at strong optical thicknesses of the finite volume approximation used the Discrete Ordinates Method. The first calculations performed on LES solutions are presented, it provides instantaneous radiative source terms and wall heat fluxes. Those results represent a first step towards radiation/combustion coupling. (author)
Li, Jiuyi; Busscher, Henk J.; Norde, Willem; Sjollema, Jelmer
2011-01-01
In order to investigate bacterium-substratum interactions, understanding of bacterial mass transport is necessary. Comparisons of experimentally observed initial deposition rates with mass transport rates in parallel-plate-flow-chambers (PPFC) predicted by convective-diffusion yielded deposition
International Nuclear Information System (INIS)
Johnson, Jeffrey O.; Gallmeier, Franz X.; Popova, Irina
2002-01-01
Determining the bulk shielding requirements for accelerator environments is generally an easy task compared to analyzing the radiation transport through the complex shield configurations and penetrations typically associated with the detailed Title II design efforts of a facility. Shielding calculations for penetrations in the SNS accelerator environment are presented based on hybrid Monte Carlo and discrete ordinates particle transport methods. This methodology relies on coupling tools that map boundary surface leakage information from the Monte Carlo calculations to boundary sources for one-, two-, and three-dimensional discrete ordinates calculations. The paper will briefly introduce the coupling tools for coupling MCNPX to the one-, two-, and three-dimensional discrete ordinates codes in the DOORS code suite. The paper will briefly present typical applications of these tools in the design of complex shield configurations and penetrations in the SNS proton beam transport system
International Nuclear Information System (INIS)
Plimpton, Steven J.; Hendrickson, Bruce; Burns, Shawn P.; McLendon, William III; Rauchwerger, Lawrence
2005-01-01
The method of discrete ordinates is commonly used to solve the Boltzmann transport equation. The solution in each ordinate direction is most efficiently computed by sweeping the radiation flux across the computational grid. For unstructured grids this poses many challenges, particularly when implemented on distributed-memory parallel machines where the grid geometry is spread across processors. We present several algorithms relevant to this approach: (a) an asynchronous message-passing algorithm that performs sweeps simultaneously in multiple ordinate directions, (b) a simple geometric heuristic to prioritize the computational tasks that a processor works on, (c) a partitioning algorithm that creates columnar-style decompositions for unstructured grids, and (d) an algorithm for detecting and eliminating cycles that sometimes exist in unstructured grids and can prevent sweeps from successfully completing. Algorithms (a) and (d) are fully parallel; algorithms (b) and (c) can be used in conjunction with (a) to achieve higher parallel efficiencies. We describe our message-passing implementations of these algorithms within a radiation transport package. Performance and scalability results are given for unstructured grids with up to 3 million elements (500 million unknowns) running on thousands of processors of Sandia National Laboratories' Intel Tflops machine and DEC-Alpha CPlant cluster
The effect of plasma fluctuations on parallel transport parameters in the SOL
DEFF Research Database (Denmark)
Havlíčková, E.; Fundamenski, W.; Naulin, Volker
2011-01-01
The effect of plasma fluctuations due to turbulence at the outboard midplane on parallel transport properties is investigated. Time-dependent fluctuating signals at different radial locations are used to study the effect of signal statistics. Further, a computational analysis of parallel transport...... to a comparison of steady-state and time-dependent modelling....
International Nuclear Information System (INIS)
Masukawa, Fumihiro; Takano, Makoto; Naito, Yoshitaka; Yamazaki, Takao; Fujisaki, Masahide; Suzuki, Koichiro; Okuda, Motoi.
1993-11-01
In order to improve the accuracy and calculating speed of shielding analyses, MCNP 4, a Monte Carlo neutron and photon transport code system, has been parallelized and measured of its efficiency in the highly parallel distributed memory type computer, AP1000. The code has been analyzed statically and dynamically, then the suitable algorithm for parallelization has been determined for the shielding analysis functions of MCNP 4. This includes a strategy where a new history is assigned to the idling processor element dynamically during the execution. Furthermore, to avoid the congestion of communicative processing, the batch concept, processing multi-histories by a unit, has been introduced. By analyzing a sample cask problem with 2,000,000 histories by the AP1000 with 512 processor elements, the 82 % of parallelization efficiency is achieved, and the calculational speed has been estimated to be around 50 times as fast as that of FACOM M-780. (author)
Parallel transport in ideal magnetohydrodynamics and applications to resistive wall modes
International Nuclear Information System (INIS)
Finn, J.M.; Gerwin, R.A.
1996-01-01
It is shown that in magnetohydrodynamics (MHD) with an ideal Ohm close-quote s law, in the presence of parallel heat flux, density gradient, temperature gradient, and parallel compression, but in the absence of perpendicular compressibility, there is an exact cancellation of the parallel transport terms. This cancellation is due to the fact that magnetic flux is advected in the presence of an ideal Ohm close-quote s law, and therefore parallel transport of temperature and density gives the same result as perpendicular advection of the same quantities. Discussions are also presented regarding parallel viscosity and parallel velocity shear, and the generalization to toroidal geometry. These results suggest that a correct generalization of the Hammett endash Perkins fluid operator [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)] to simulate Landau damping for electromagnetic modes must give an operator that acts on the dynamics parallel to the perturbed magnetic field lines. copyright 1996 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Muller, J [IRSID, Institut de Recherches Siderurgie, 57 - Maizieres-les-Metz (France)
1997-12-31
Radiant heat transfer is the main solution retained in many iron and steel metallurgy installations (re-heating and annealing furnaces etc..). Today, it has become important to dispose of performing radiant heat transfer models in heat transfer and fluid mechanics simulation softwares, and well adapted to multidimensional industrial problems. This work presents the discrete ordinate radiant heat transfer model developed at the IRSID (the French institute of research in iron and steel metallurgy) and coupled with the PHOENICS heat transfer-fluid mechanics software. Three modeling approaches are presented concerning the radiative properties of gases (H{sub 2}O-CO{sub 2}). A ``weighted grey gases sum`` model gives satisfactory results for several 1-D validation cases. (J.S.) 20 refs.
Energy Technology Data Exchange (ETDEWEB)
Muller, J. [IRSID, Institut de Recherches Siderurgie, 57 - Maizieres-les-Metz (France)
1996-12-31
Radiant heat transfer is the main solution retained in many iron and steel metallurgy installations (re-heating and annealing furnaces etc..). Today, it has become important to dispose of performing radiant heat transfer models in heat transfer and fluid mechanics simulation softwares, and well adapted to multidimensional industrial problems. This work presents the discrete ordinate radiant heat transfer model developed at the IRSID (the French institute of research in iron and steel metallurgy) and coupled with the PHOENICS heat transfer-fluid mechanics software. Three modeling approaches are presented concerning the radiative properties of gases (H{sub 2}O-CO{sub 2}). A ``weighted grey gases sum`` model gives satisfactory results for several 1-D validation cases. (J.S.) 20 refs.
Collection of problems in transport theory
International Nuclear Information System (INIS)
Kaper, H.G.
1975-01-01
Problems presented are: (1) definition of transport operators; (2) relation between the integro-differential and integral form of the transport equation; (3) asymptotic behavior of the scalar density near curved boundaries and interfaces; (4) singularities at a corner; (5) regularity of the solution of the transport equation; (7) transport equations on a manifold; (8) numerical analysis; (9) cubature; (10) point spectrum of the transport operator; (11) convergence of the multigroup approximation; (12) convergence of discrete ordinates approximations; (13) the finite double-norm property; (14) convergence of discrete ordinates approximation. The presentation of the problems is intended to direct attention to gaps in the existing knowledge of transport theory and to stimulate research into new areas of transport theory
Finite element method for solving neutron transport problems
International Nuclear Information System (INIS)
Ferguson, J.M.; Greenbaum, A.
1984-01-01
A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems
Application of the three-dimensional Oak Ridge transport code
International Nuclear Information System (INIS)
Rhoades, W.A.; Childs, R.L.; Emmett, M.B.; Cramer, S.N.
1984-01-01
TORT, a 3-d extension of the DOT discrete ordinates transport code is now in production use for studies of radiation penetration into large concrete and masonry structures. This paper discusses certain features of the new code and shows representative results, including comparisons with Monte Carlo calculations
Effects of parallel electron dynamics on plasma blob transport
Energy Technology Data Exchange (ETDEWEB)
Angus, Justin R.; Krasheninnikov, Sergei I. [University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093 (United States); Umansky, Maxim V. [Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550 (United States)
2012-08-15
The 3D effects on sheath connected plasma blobs that result from parallel electron dynamics are studied by allowing for the variation of blob density and potential along the magnetic field line and using collisional Ohm's law to model the parallel current density. The parallel current density from linear sheath theory, typically used in the 2D model, is implemented as parallel boundary conditions. This model includes electrostatic 3D effects, such as resistive drift waves and blob spinning, while retaining all of the fundamental 2D physics of sheath connected plasma blobs. If the growth time of unstable drift waves is comparable to the 2D advection time scale of the blob, then the blob's density gradient will be depleted resulting in a much more diffusive blob with little radial motion. Furthermore, blob profiles that are initially varying along the field line drive the potential to a Boltzmann relation that spins the blob and thereby acts as an addition sink of the 2D potential. Basic dimensionless parameters are presented to estimate the relative importance of these two 3D effects. The deviation of blob dynamics from that predicted by 2D theory in the appropriate limits of these parameters is demonstrated by a direct comparison of 2D and 3D seeded blob simulations.
Energy Technology Data Exchange (ETDEWEB)
Bernal, A.; Abarca, A.; Barrachina, T.; Miro, R.; Verdu, G.
2013-07-01
The resolution of the neutron transport equation in steady state in pool-type nuclear reactors, is normally achieved through 2 different numerical methods: Monte Carlo (stochastic) and discrete ordinates (deterministic). The discrete ordinates method solves the neutron transport equation for a set of specific addresses, obtaining a set of equations and solutions for each direction, where the solution for each direction is the angular flux. With the aim of treating energy dependence, used energy multigroup approximation, thus obtaining a set of equations that depends on the number of energy groups considered.
Implementation of a parallel algorithm for spherical SN calculations on the IBM 3090
International Nuclear Information System (INIS)
Haghighat, A.; Lawrence, R.D.
1989-01-01
Parallel S N algorithms based on domain decomposition in angle are straightforward to develop in Cartesian geometry because the computation of the angular fluxes for a specific discrete ordinate can be performed independently of all other angles. This is not the case for curvilinear geometries, where the angular redistribution component of the discretized streaming operator results in coupling between angular fluxes along adjacent discrete ordinates. Previously, the authors developed a parallel algorithm for S N calculations in spherical geometry and examined its iterative convergence for criticality and detector problems with differing scattering/absorption ratios. In this paper, the authors describe the implementation of the algorithm on an IBM 3090 Model 400 (four processors) and present computational results illustrating the efficiency of the algorithm relative to serial execution
A portable, parallel, object-oriented Monte Carlo neutron transport code in C++
International Nuclear Information System (INIS)
Lee, S.R.; Cummings, J.C.; Nolen, S.D.
1997-01-01
We have developed a multi-group Monte Carlo neutron transport code using C++ and the Parallel Object-Oriented Methods and Applications (POOMA) class library. This transport code, called MC++, currently computes k and α-eigenvalues and is portable to and runs parallel on a wide variety of platforms, including MPPs, clustered SMPs, and individual workstations. It contains appropriate classes and abstractions for particle transport and, through the use of POOMA, for portable parallelism. Current capabilities of MC++ are discussed, along with physics and performance results on a variety of hardware, including all Accelerated Strategic Computing Initiative (ASCI) hardware. Current parallel performance indicates the ability to compute α-eigenvalues in seconds to minutes rather than hours to days. Future plans and the implementation of a general transport physics framework are also discussed
International Nuclear Information System (INIS)
Helander, P.; Hazeltine, R.D.; Catto, P.J.
1996-01-01
The orderings in the kinetic equations commonly used to study the plasma core of a tokamak do not allow a balance between parallel ion streaming and radial diffusion, and are, therefore, inappropriate in the plasma edge. Different orderings are required in the edge region where radial transport across the steep gradients associated with the scrape-off layer is large enough to balance the rapid parallel flow caused by conditions close to collecting surfaces (such as the Bohm sheath condition). In the present work, we derive and solve novel kinetic equations, allowing for such a balance, and construct distinctive transport laws for impure, collisional, edge plasmas in which the perpendicular transport is (i) due to Coulomb collisions of ions with heavy impurities, or (ii) governed by anomalous diffusion driven by electrostatic turbulence. In both the collisional and anomalous radial transport cases, we find that one single diffusion coefficient determines the radial transport of particles, momentum and heat. The parallel transport laws and parallel thermal force in the scrape-off layer assume an unconventional form, in which the relative ion-impurity flow is driven by a combination of the conventional parallel gradients, and new (i) collisional or (ii) anomalous terms involving products of radial derivatives of the temperature and density with the radial shear of the parallel velocity. Thus, in the presence of anomalous radial diffusion, the parallel ion transport cannot be entirely classical, as usually assumed in numerical edge computations. The underlying physical reason is the appearance of a novel type of parallel thermal force resulting from the combined action of anomalous diffusion and radial temperature and velocity gradients. In highly sheared flows the new terms can modify impurity penetration into the core plasma
Parallelizing an electron transport Monte Carlo simulator (MOCASIN 2.0)
International Nuclear Information System (INIS)
Schwetman, H.; Burdick, S.
1988-01-01
Electron transport simulators are tools for studying electrical properties of semiconducting materials and devices. As demands for modeling more complex devices and new materials have emerged, so have demands for more processing power. This paper documents a project to convert an electron transport simulator (MOCASIN 2.0) to a parallel processing environment. In addition to describing the conversion, the paper presents PPL, a parallel programming version of C running on a Sequent multiprocessor system. In timing tests, models that simulated the movement of 2,000 particles for 100 time steps were executed on ten processors, with a parallel efficiency of over 97%
Momentum-energy transport from turbulence driven by parallel flow shear
International Nuclear Information System (INIS)
Dong, J.Q.; Horton, W.; Bengtson, R.D.; Li, G.X.
1994-04-01
The low frequency E x B turbulence driven by the shear in the mass flow velocity parallel to the magnetic field is studied using the fluid theory in a slab configuration with magnetic shear. Ion temperature gradient effects are taken into account. The eigenfunctions of the linear instability are asymmetric about the mode rational surfaces. Quasilinear Reynolds stress induced by such asymmetric fluctuations produces momentum and energy transport across the magnetic field. Analytic formulas for the parallel and perpendicular Reynolds stress, viscosity and energy transport coefficients are given. Experimental observations of the parallel and poloidal plasma flows on TEXT-U are presented and compared with the theoretical models
MC++: A parallel, portable, Monte Carlo neutron transport code in C++
International Nuclear Information System (INIS)
Lee, S.R.; Cummings, J.C.; Nolen, S.D.
1997-01-01
MC++ is an implicit multi-group Monte Carlo neutron transport code written in C++ and based on the Parallel Object-Oriented Methods and Applications (POOMA) class library. MC++ runs in parallel on and is portable to a wide variety of platforms, including MPPs, SMPs, and clusters of UNIX workstations. MC++ is being developed to provide transport capabilities to the Accelerated Strategic Computing Initiative (ASCI). It is also intended to form the basis of the first transport physics framework (TPF), which is a C++ class library containing appropriate abstractions, objects, and methods for the particle transport problem. The transport problem is briefly described, as well as the current status and algorithms in MC++ for solving the transport equation. The alpha version of the POOMA class library is also discussed, along with the implementation of the transport solution algorithms using POOMA. Finally, a simple test problem is defined and performance and physics results from this problem are discussed on a variety of platforms
Application of Raptor-M3G to reactor dosimetry problems on massively parallel architectures - 026
International Nuclear Information System (INIS)
Longoni, G.
2010-01-01
The solution of complex 3-D radiation transport problems requires significant resources both in terms of computation time and memory availability. Therefore, parallel algorithms and multi-processor architectures are required to solve efficiently large 3-D radiation transport problems. This paper presents the application of RAPTOR-M3G (Rapid Parallel Transport Of Radiation - Multiple 3D Geometries) to reactor dosimetry problems. RAPTOR-M3G is a newly developed parallel computer code designed to solve the discrete ordinates (SN) equations on multi-processor computer architectures. This paper presents the results for a reactor dosimetry problem using a 3-D model of a commercial 2-loop pressurized water reactor (PWR). The accuracy and performance of RAPTOR-M3G will be analyzed and the numerical results obtained from the calculation will be compared directly to measurements of the neutron field in the reactor cavity air gap. The parallel performance of RAPTOR-M3G on massively parallel architectures, where the number of computing nodes is in the order of hundreds, will be analyzed up to four hundred processors. The performance results will be presented based on two supercomputing architectures: the POPLE supercomputer operated by the Pittsburgh Supercomputing Center and the Westinghouse computer cluster. The Westinghouse computer cluster is equipped with a standard Ethernet network connection and an InfiniBand R interconnects capable of a bandwidth in excess of 20 GBit/sec. Therefore, the impact of the network architecture on RAPTOR-M3G performance will be analyzed as well. (authors)
Energy Technology Data Exchange (ETDEWEB)
Pinchedez, K
1999-06-01
Parallel computing meets the ever-increasing requirements for neutronic computer code speed and accuracy. In this work, two different approaches have been considered. We first parallelized the sequential algorithm used by the neutronics code CRONOS developed at the French Atomic Energy Commission. The algorithm computes the dominant eigenvalue associated with PN simplified transport equations by a mixed finite element method. Several parallel algorithms have been developed on distributed memory machines. The performances of the parallel algorithms have been studied experimentally by implementation on a T3D Cray and theoretically by complexity models. A comparison of various parallel algorithms has confirmed the chosen implementations. We next applied a domain sub-division technique to the two-group diffusion Eigen problem. In the modal synthesis-based method, the global spectrum is determined from the partial spectra associated with sub-domains. Then the Eigen problem is expanded on a family composed, on the one hand, from eigenfunctions associated with the sub-domains and, on the other hand, from functions corresponding to the contribution from the interface between the sub-domains. For a 2-D homogeneous core, this modal method has been validated and its accuracy has been measured. (author)
International Nuclear Information System (INIS)
Apisit, Patchimpattapong; Alireza, Haghighat; Shedlock, D.
2003-01-01
An expert system for generating an effective mesh distribution for the SN particle transport simulation has been developed. This expert system consists of two main parts: 1) an algorithm for generating an effective mesh distribution in a serial environment, and 2) an algorithm for inference of an effective domain decomposition strategy for parallel computing. For the first part, the algorithm prepares an effective mesh distribution considering problem physics and the spatial differencing scheme. For the second part, the algorithm determines a parallel-performance-index (PPI), which is defined as the ratio of the granularity to the degree-of-coupling. The parallel-performance-index provides expected performance of an algorithm depending on computing environment and resources. A large index indicates a high granularity algorithm with relatively low coupling among processors. This expert system has been successfully tested within the PENTRAN (Parallel Environment Neutral-Particle Transport) code system for simulating real-life shielding problems. (authors)
Energy Technology Data Exchange (ETDEWEB)
Apisit, Patchimpattapong [Electricity Generating Authority of Thailand, Office of Corporate Planning, Bangkruai, Nonthaburi (Thailand); Alireza, Haghighat; Shedlock, D. [Florida Univ., Department of Nuclear and Radiological Engineering, Gainesville, FL (United States)
2003-07-01
An expert system for generating an effective mesh distribution for the SN particle transport simulation has been developed. This expert system consists of two main parts: 1) an algorithm for generating an effective mesh distribution in a serial environment, and 2) an algorithm for inference of an effective domain decomposition strategy for parallel computing. For the first part, the algorithm prepares an effective mesh distribution considering problem physics and the spatial differencing scheme. For the second part, the algorithm determines a parallel-performance-index (PPI), which is defined as the ratio of the granularity to the degree-of-coupling. The parallel-performance-index provides expected performance of an algorithm depending on computing environment and resources. A large index indicates a high granularity algorithm with relatively low coupling among processors. This expert system has been successfully tested within the PENTRAN (Parallel Environment Neutral-Particle Transport) code system for simulating real-life shielding problems. (authors)
The discontinuous finite element method for solving Eigenvalue problems of transport equations
International Nuclear Information System (INIS)
Yang, Shulin; Wang, Ruihong
2011-01-01
In this paper, the multigroup transport equations for solving the eigenvalues λ and K_e_f_f under two dimensional cylindrical coordinate are discussed. Aimed at the equations, the discretizing way combining discontinuous finite element method (DFE) with discrete ordinate method (SN) is developed, and the iterative algorithms and steps are studied. The numerical results show that the algorithms are efficient. (author)
To the development of numerical methods in problems of radiation transport
International Nuclear Information System (INIS)
Germogenova, T.A.
1990-01-01
Review of studies on the development of numerical methods and the discrete ordinate method in particular, used for solution of radiation protection physics problems is given. Consideration is given to the problems, which arise when calculating fields of penetrating radiation and when studying processes of charged-particle transport and cascade processes, generated by high-energy primary radiation
International Nuclear Information System (INIS)
Clancy, B.E.
1982-05-01
ANAUSN is a general purpose, one-dimensional discrete ordinate transport theory program which has access to AUS datapools. Fixed source, reactivity and a variety of criticality search calculations can be performed. The program can be operated as a module in the AUS scheme or as a stand-alone program
A parallel version of a multigrid algorithm for isotropic transport equations
International Nuclear Information System (INIS)
Manteuffel, T.; McCormick, S.; Yang, G.; Morel, J.; Oliveira, S.
1994-01-01
The focus of this paper is on a parallel algorithm for solving the transport equations in a slab geometry using multigrid. The spatial discretization scheme used is a finite element method called the modified linear discontinuous (MLD) scheme. The MLD scheme represents a lumped version of the standard linear discontinuous (LD) scheme. The parallel algorithm was implemented on the Connection Machine 2 (CM2). Convergence rates and timings for this algorithm on the CM2 and Cray-YMP are shown
Parallel processing implementation for the coupled transport of photons and electrons using OpenMP
Doerner, Edgardo
2016-05-01
In this work the use of OpenMP to implement the parallel processing of the Monte Carlo (MC) simulation of the coupled transport for photons and electrons is presented. This implementation was carried out using a modified EGSnrc platform which enables the use of the Microsoft Visual Studio 2013 (VS2013) environment, together with the developing tools available in the Intel Parallel Studio XE 2015 (XE2015). The performance study of this new implementation was carried out in a desktop PC with a multi-core CPU, taking as a reference the performance of the original platform. The results were satisfactory, both in terms of scalability as parallelization efficiency.
International Nuclear Information System (INIS)
Mo Zeyao
2004-11-01
Multiphysics parallel numerical simulations are usually essential to simplify researches on complex physical phenomena in which several physics are tightly coupled. It is very important on how to concatenate those coupled physics for fully scalable parallel simulation. Meanwhile, three objectives should be balanced, the first is efficient data transfer among simulations, the second and the third are efficient parallel executions and simultaneously developments of those simulation codes. Two concatenating algorithms for multiphysics parallel numerical simulations coupling radiation hydrodynamics with neutron transport on unstructured grid are presented. The first algorithm, Fully Loosely Concatenation (FLC), focuses on the independence of code development and the independence running with optimal performance of code. The second algorithm. Two Level Tightly Concatenation (TLTC), focuses on the optimal tradeoffs among above three objectives. Theoretical analyses for communicational complexity and parallel numerical experiments on hundreds of processors on two parallel machines have showed that these two algorithms are efficient and can be generalized to other multiphysics parallel numerical simulations. In especial, algorithm TLTC is linearly scalable and has achieved the optimal parallel performance. (authors)
Application of the three-dimensional transport code to analysis of the neutron streaming experiment
International Nuclear Information System (INIS)
Chatani, K.; Slater, C.O.
1990-01-01
The neutron streaming through an experimental mock-up of a Clinch River Breeder Reactor (CRBR) prototypic coolant pipe chaseway was recalculated with a three-dimensional discrete ordinates code. The experiment was conducted at the Tower Shielding Facility at Oak Ridge National Laboratory in 1976 and 1977. The measurement of the neutron flux, using Bonner ball detectors, indicated nine orders of attenuation in the empty pipeway, which contained two 90-deg bends and was surrounded by concrete walls. The measurement data were originally analyzed using the DOT3.5 two-dimensional discrete ordinates radiation transport code. However, the results did not agree with measurement data at the bend because of the difficulties in modeling the three-dimensional configurations using two-dimensional methods. The two-dimensional calculations used a three-step procedure in which each of the three legs making the two 90-deg bends was a separate calculation. The experiment was recently analyzed with the TORT three-dimensional discrete ordinates radiation transport code, not only to compare the calculational results with the experimental results, but also to compare with results obtained from analyses in Japan using DOT3.5, MORSE, and ENSEMBLE, which is a three-dimensional discrete ordinates radiation transport code developed in Japan
International Nuclear Information System (INIS)
Miller, T.M.; Pevey, R.E.; Lillie, R.A.; Johnson, J.O.
2000-01-01
A detailed radiation transport analysis of the Spallation Neutron Source (SNS) shutters is important for the construction of the SNS because of its impact on conventional facility design, normal operation of the facility, and maintenance operations. Thus far the analysis of the SNS shutter travel gaps has been completed. This analysis was performed using coupled Monte Carlo and multi-dimensional discrete ordinates calculations
penORNL: a parallel Monte Carlo photon and electron transport package using PENELOPE
International Nuclear Information System (INIS)
Bekar, Kursat B.; Miller, Thomas Martin; Patton, Bruce W.; Weber, Charles F.
2015-01-01
The parallel Monte Carlo photon and electron transport code package penORNL was developed at Oak Ridge National Laboratory to enable advanced scanning electron microscope (SEM) simulations on high-performance computing systems. This paper discusses the implementations, capabilities and parallel performance of the new code package. penORNL uses PENELOPE for its physics calculations and provides all available PENELOPE features to the users, as well as some new features including source definitions specifically developed for SEM simulations, a pulse-height tally capability for detailed simulations of gamma and x-ray detectors, and a modified interaction forcing mechanism to enable accurate energy deposition calculations. The parallel performance of penORNL was extensively tested with several model problems, and very good linear parallel scaling was observed with up to 512 processors. penORNL, along with its new features, will be available for SEM simulations upon completion of the new pulse-height tally implementation.
Parallel/vector algorithms for the spherical SN transport theory method
International Nuclear Information System (INIS)
Haghighat, A.; Mattis, R.E.
1990-01-01
This paper discusses vector and parallel processing of a 1-D curvilinear (i.e. spherical) S N transport theory algorithm on the Cornell National SuperComputer Facility (CNSF) IBM 3090/600E. Two different vector algorithms were developed and parallelized based on angular decomposition. It is shown that significant speedups are attainable. For example, for problems with large granularity, using 4 processors, the parallel/vector algorithm achieves speedups (for wall-clock time) of more than 4.5 relative to the old serial/scalar algorithm. Furthermore, this work has demonstrated the existing potential for the development of faster processing vector and parallel algorithms for multidimensional curvilinear geometries. (author)
International Nuclear Information System (INIS)
Youssef, M. Z.
2007-01-01
Attila is a newly developed finite element code based on Sn neutron, gamma, and charged particle transport in 3-D geometry in which unstructured tetrahedral meshes are generated to describe complex geometry that is based on CAD input (Solid Works, Pro/Engineer, etc). In the present work we benchmark its calculation accuracy by comparing its prediction to the measured data inside two experimental mock-ups bombarded with 14 MeV neutrons. The results are also compared to those based on MCNP calculations. The experimental mock-ups simulate parts of the International Thermonuclear Experimental Reactor (ITER) in-vessel components, namely: (1) the Tungsten mockup configuration (54.3 cm x 46.8 cm x 45 cm), and (2) the ITER shielding blanket followed by the SCM region (simulated by alternating layers of SS316 and copper). In the latter configuration, a high aspect ratio rectangular streaming channel was introduced (to simulate steaming paths between ITER blanket modules) which ends with a rectangular cavity. The experiments on these two fusion-oriented integral experiments were performed at the Fusion Neutron Generator (FNG) facility, Frascati, Italy. In addition, the nuclear performance of the ITER MCNP 'Benchmark' CAD model has been performed with Attila to compare its results to those obtained with CAD-based MCNP approach developed by several ITER participants. The objective of this paper is to compare results based on two distinctive 3-D calculation tools using the same nuclear data, FENDL2.1, and the same response functions of several reaction rates measured in ITER mock-ups and to enhance confidence from the international neutronics community in the Attila code and how it can precisely quantify the nuclear field in large and complex systems, such as ITER. Attila has the advantage of providing a full flux mapping visualization everywhere in one run where components subjected to excessive radiation level and strong streaming paths can be identified. In addition, the
Parallelization of a three-dimensional whole core transport code DeCART
Energy Technology Data Exchange (ETDEWEB)
Jin Young, Cho; Han Gyu, Joo; Ha Yong, Kim; Moon-Hee, Chang [Korea Atomic Energy Research Institute, Yuseong-gu, Daejon (Korea, Republic of)
2003-07-01
Parallelization of the DeCART (deterministic core analysis based on ray tracing) code is presented that reduces the computational burden of the tremendous computing time and memory required in three-dimensional whole core transport calculations. The parallelization employs the concept of MPI grouping and the MPI/OpenMP mixed scheme as well. Since most of the computing time and memory are used in MOC (method of characteristics) and the multi-group CMFD (coarse mesh finite difference) calculation in DeCART, variables and subroutines related to these two modules are the primary targets for parallelization. Specifically, the ray tracing module was parallelized using a planar domain decomposition scheme and an angular domain decomposition scheme. The parallel performance of the DeCART code is evaluated by solving a rodded variation of the C5G7MOX three dimensional benchmark problem and a simplified three-dimensional SMART PWR core problem. In C5G7MOX problem with 24 CPUs, a speedup of maximum 21 is obtained on an IBM Regatta machine and 22 on a LINUX Cluster in the MOC kernel, which indicates good parallel performance of the DeCART code. In the simplified SMART problem, the memory requirement of about 11 GBytes in the single processor cases reduces to 940 Mbytes with 24 processors, which means that the DeCART code can now solve large core problems with affordable LINUX clusters. (authors)
Computational methods of electron/photon transport
International Nuclear Information System (INIS)
Mack, J.M.
1983-01-01
A review of computational methods simulating the non-plasma transport of electrons and their attendant cascades is presented. Remarks are mainly restricted to linearized formalisms at electron energies above 1 keV. The effectiveness of various metods is discussed including moments, point-kernel, invariant imbedding, discrete-ordinates, and Monte Carlo. Future research directions and the potential impact on various aspects of science and engineering are indicated
Monte Carlo photon transport on shared memory and distributed memory parallel processors
International Nuclear Information System (INIS)
Martin, W.R.; Wan, T.C.; Abdel-Rahman, T.S.; Mudge, T.N.; Miura, K.
1987-01-01
Parallelized Monte Carlo algorithms for analyzing photon transport in an inertially confined fusion (ICF) plasma are considered. Algorithms were developed for shared memory (vector and scalar) and distributed memory (scalar) parallel processors. The shared memory algorithm was implemented on the IBM 3090/400, and timing results are presented for dedicated runs with two, three, and four processors. Two alternative distributed memory algorithms (replication and dispatching) were implemented on a hypercube parallel processor (1 through 64 nodes). The replication algorithm yields essentially full efficiency for all cube sizes; with the 64-node configuration, the absolute performance is nearly the same as with the CRAY X-MP. The dispatching algorithm also yields efficiencies above 80% in a large simulation for the 64-processor configuration
Vlasov modelling of parallel transport in a tokamak scrape-off layer
International Nuclear Information System (INIS)
Manfredi, G; Hirstoaga, S; Devaux, S
2011-01-01
A one-dimensional Vlasov-Poisson model is used to describe the parallel transport in a tokamak scrape-off layer. Thanks to a recently developed 'asymptotic-preserving' numerical scheme, it is possible to lift numerical constraints on the time step and grid spacing, which are no longer limited by, respectively, the electron plasma period and Debye length. The Vlasov approach provides a good velocity-space resolution even in regions of low density. The model is applied to the study of parallel transport during edge-localized modes, with particular emphasis on the particles and energy fluxes on the divertor plates. The numerical results are compared with analytical estimates based on a free-streaming model, with good general agreement. An interesting feature is the observation of an early electron energy flux, due to suprathermal electrons escaping the ions' attraction. In contrast, the long-time evolution is essentially quasi-neutral and dominated by the ion dynamics.
International Nuclear Information System (INIS)
Pandya, Tara M.; Johnson, Seth R.; Evans, Thomas M.; Davidson, Gregory G.; Hamilton, Steven P.; Godfrey, Andrew T.
2015-01-01
This paper discusses the implementation, capabilities, and validation of Shift, a massively parallel Monte Carlo radiation transport package developed and maintained at Oak Ridge National Laboratory. It has been developed to scale well from laptop to small computing clusters to advanced supercomputers. Special features of Shift include hybrid capabilities for variance reduction such as CADIS and FW-CADIS, and advanced parallel decomposition and tally methods optimized for scalability on supercomputing architectures. Shift has been validated and verified against various reactor physics benchmarks and compares well to other state-of-the-art Monte Carlo radiation transport codes such as MCNP5, CE KENO-VI, and OpenMC. Some specific benchmarks used for verification and validation include the CASL VERA criticality test suite and several Westinghouse AP1000 ® problems. These benchmark and scaling studies show promising results
Load balancing in highly parallel processing of Monte Carlo code for particle transport
International Nuclear Information System (INIS)
Higuchi, Kenji; Takemiya, Hiroshi; Kawasaki, Takuji
1998-01-01
In parallel processing of Monte Carlo (MC) codes for neutron, photon and electron transport problems, particle histories are assigned to processors making use of independency of the calculation for each particle. Although we can easily parallelize main part of a MC code by this method, it is necessary and practically difficult to optimize the code concerning load balancing in order to attain high speedup ratio in highly parallel processing. In fact, the speedup ratio in the case of 128 processors remains in nearly one hundred times when using the test bed for the performance evaluation. Through the parallel processing of the MCNP code, which is widely used in the nuclear field, it is shown that it is difficult to attain high performance by static load balancing in especially neutron transport problems, and a load balancing method, which dynamically changes the number of assigned particles minimizing the sum of the computational and communication costs, overcomes the difficulty, resulting in nearly fifteen percentage of reduction for execution time. (author)
Directional Transport of a Liquid Drop between Parallel-Nonparallel Combinative Plates.
Huang, Yao; Hu, Liang; Chen, Wenyu; Fu, Xin; Ruan, Xiaodong; Xie, Haibo
2018-04-17
Liquids confined between two parallel plates can perform the function of transmission, support, or lubrication in many practical applications, due to which to maintain liquids stable within their working area is very important. However, instabilities may lead to the formation of leaking drops outside the bulk liquid, thus it is necessary to transport the detached drops back without overstepping the working area and causing destructive leakage to the system. In this study, we report a novel and facile method to solve this problem by introducing the wedgelike geometry into the parallel gap to form a parallel-nonparallel combinative construction. Transport performances of this structure were investigated. The criterion for self-propelled motion was established, which seemed more difficult to meet than that in the nonparallel gap. Then, we performed a more detailed investigation into the drop dynamics under squeezing and relaxing modes because the drops can surely return in hydrophilic combinative gaps, whereas uncertainties arose in gaps with a weak hydrophobic character. Therefore, through exploration of the transition mechanism of the drop motion state, a crucial factor named turning point was discovered and supposed to be directly related to the final state of the drops. On the basis of the theoretical model of turning point, the criterion to identify whether a liquid drop returns to the parallel part under squeezing and relaxing modes was achieved. These criteria can provide guidance on parameter selection and structural optimization for the combinative gap, so that the destructive leakage in practical productions can be avoided.
3-D neutron transport benchmarks
International Nuclear Information System (INIS)
Takeda, T.; Ikeda, H.
1991-03-01
A set of 3-D neutron transport benchmark problems proposed by the Osaka University to NEACRP in 1988 has been calculated by many participants and the corresponding results are summarized in this report. The results of K eff , control rod worth and region-averaged fluxes for the four proposed core models, calculated by using various 3-D transport codes are compared and discussed. The calculational methods used were: Monte Carlo, Discrete Ordinates (Sn), Spherical Harmonics (Pn), Nodal Transport and others. The solutions of the four core models are quite useful as benchmarks for checking the validity of 3-D neutron transport codes
Discrete elements method of neutral particle transport
International Nuclear Information System (INIS)
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
International Nuclear Information System (INIS)
Zawaideh, E.S.
1985-01-01
A new set of two-fluid equations which are valid from collisional to weakly collisional limits are derived. Starting from gyrokinetic equations in flux coordinates with no zeroth order drifts, a set of moment equations describing plasma transport along the field lines of a space and time dependent magnetic field are derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii while in the weakly collisional limit, they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations. The new transport equations are used to study the effects of collisionality, magnetic field structure, and plasma anisotropy on plasma parallel transport. Numerical examples comparing these equations with conventional transport equations show that the conventional equations may contain large errors near the sound speed (M approx. = 1). It is also found that plasma anisotropy, which is not included in the conventional equations, is a critical parameter in determining plasma transport in varying magnetic field. The new transport equations are also used to study axial confinement in multiple mirror devices from the strongly to weakly collisional regime. A new ion conduction model was worked out to extend the regime of validity of the transport equations to the low density multiple mirror regime
Parallel transport of long mean-free-path plasma along open magnetic field lines: Parallel heat flux
International Nuclear Information System (INIS)
Guo Zehua; Tang Xianzhu
2012-01-01
In a long mean-free-path plasma where temperature anisotropy can be sustained, the parallel heat flux has two components with one associated with the parallel thermal energy and the other the perpendicular thermal energy. Due to the large deviation of the distribution function from local Maxwellian in an open field line plasma with low collisionality, the conventional perturbative calculation of the parallel heat flux closure in its local or non-local form is no longer applicable. Here, a non-perturbative calculation is presented for a collisionless plasma in a two-dimensional flux expander bounded by absorbing walls. Specifically, closures of previously unfamiliar form are obtained for ions and electrons, which relate two distinct components of the species parallel heat flux to the lower order fluid moments such as density, parallel flow, parallel and perpendicular temperatures, and the field quantities such as the magnetic field strength and the electrostatic potential. The plasma source and boundary condition at the absorbing wall enter explicitly in the closure calculation. Although the closure calculation does not take into account wave-particle interactions, the results based on passing orbits from steady-state collisionless drift-kinetic equation show remarkable agreement with fully kinetic-Maxwell simulations. As an example of the physical implications of the theory, the parallel heat flux closures are found to predict a surprising observation in the kinetic-Maxwell simulation of the 2D magnetic flux expander problem, where the parallel heat flux of the parallel thermal energy flows from low to high parallel temperature region.
Hybrid shared/distributed parallelism for 3D characteristics transport solvers
International Nuclear Information System (INIS)
Dahmani, M.; Roy, R.
2005-01-01
In this paper, we will present a new hybrid parallel model for solving large-scale 3-dimensional neutron transport problems used in nuclear reactor simulations. Large heterogeneous reactor problems, like the ones that occurs when simulating Candu cores, have remained computationally intensive and impractical for routine applications on single-node or even vector computers. Based on the characteristics method, this new model is designed to solve the transport equation after distributing the calculation load on a network of shared memory multi-processors. The tracks are either generated on the fly at each characteristics sweep or stored in sequential files. The load balancing is taken into account by estimating the calculation load of tracks and by distributing batches of uniform load on each node of the network. Moreover, the communication overhead can be predicted after benchmarking the latency and bandwidth using appropriate network test suite. These models are useful for predicting the performance of the parallel applications and to analyze the scalability of the parallel systems. (authors)
Development Of A Parallel Performance Model For The THOR Neutral Particle Transport Code
Energy Technology Data Exchange (ETDEWEB)
Yessayan, Raffi; Azmy, Yousry; Schunert, Sebastian
2017-02-01
The THOR neutral particle transport code enables simulation of complex geometries for various problems from reactor simulations to nuclear non-proliferation. It is undergoing a thorough V&V requiring computational efficiency. This has motivated various improvements including angular parallelization, outer iteration acceleration, and development of peripheral tools. For guiding future improvements to the code’s efficiency, better characterization of its parallel performance is useful. A parallel performance model (PPM) can be used to evaluate the benefits of modifications and to identify performance bottlenecks. Using INL’s Falcon HPC, the PPM development incorporates an evaluation of network communication behavior over heterogeneous links and a functional characterization of the per-cell/angle/group runtime of each major code component. After evaluating several possible sources of variability, this resulted in a communication model and a parallel portion model. The former’s accuracy is bounded by the variability of communication on Falcon while the latter has an error on the order of 1%.
A non overlapping parallel domain decomposition method applied to the simplified transport equations
International Nuclear Information System (INIS)
Lathuiliere, B.; Barrault, M.; Ramet, P.; Roman, J.
2009-01-01
A reactivity computation requires to compute the highest eigenvalue of a generalized eigenvalue problem. An inverse power algorithm is used commonly. Very fine modelizations are difficult to tackle for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time. So, we propose a non-overlapping domain decomposition method for the approximate resolution of the linear system to solve at each inverse power iteration. Our method brings to a low development effort as the inner multigroup solver can be re-use without modification, and allows us to adapt locally the numerical resolution (mesh, finite element order). Numerical results are obtained by a parallel implementation of the method on two different cases with a pin by pin discretization. This results are analyzed in terms of memory consumption and parallel efficiency. (authors)
Yu, Leiming; Nina-Paravecino, Fanny; Kaeli, David; Fang, Qianqian
2018-01-01
We present a highly scalable Monte Carlo (MC) three-dimensional photon transport simulation platform designed for heterogeneous computing systems. Through the development of a massively parallel MC algorithm using the Open Computing Language framework, this research extends our existing graphics processing unit (GPU)-accelerated MC technique to a highly scalable vendor-independent heterogeneous computing environment, achieving significantly improved performance and software portability. A number of parallel computing techniques are investigated to achieve portable performance over a wide range of computing hardware. Furthermore, multiple thread-level and device-level load-balancing strategies are developed to obtain efficient simulations using multiple central processing units and GPUs. (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).
Energy Technology Data Exchange (ETDEWEB)
Moryakov, A. V., E-mail: sailor@orc.ru [National Research Centre Kurchatov Institute (Russian Federation)
2016-12-15
An algorithm for solving the time-dependent transport equation in the P{sub m}S{sub n} group approximation with the use of parallel computations is presented. The algorithm is implemented in the LUCKY-TD code for supercomputers employing the MPI standard for the data exchange between parallel processes.
Gudmundsson, Vidar; Abdullah, Nzar Rauf; Sitek, Anna; Goan, Hsi-Sheng; Tang, Chi-Shung; Manolescu, Andrei
2018-06-01
We calculate the current correlations for the steady-state electron transport through multi-level parallel quantum dots embedded in a short quantum wire, that is placed in a non-perfect photon cavity. We account for the electron-electron Coulomb interaction, and the para- and diamagnetic electron-photon interactions with a stepwise scheme of configuration interactions and truncation of the many-body Fock spaces. In the spectral density of the temporal current-current correlations we identify all the transitions, radiative and non-radiative, active in the system in order to maintain the steady state. We observe strong signs of two types of Rabi oscillations.
Vectorization and parallelization of Monte-Carlo programs for calculation of radiation transport
International Nuclear Information System (INIS)
Seidel, R.
1995-01-01
The versatile MCNP-3B Monte-Carlo code written in FORTRAN77, for simulation of the radiation transport of neutral particles, has been subjected to vectorization and parallelization of essential parts, without touching its versatility. Vectorization is not dependent on a specific computer. Several sample tasks have been selected in order to test the vectorized MCNP-3B code in comparison to the scalar MNCP-3B code. The samples are a representative example of the 3-D calculations to be performed for simulation of radiation transport in neutron and reactor physics. (1) 4πneutron detector. (2) High-energy calorimeter. (3) PROTEUS benchmark (conversion rates and neutron multiplication factors for the HCLWR (High Conversion Light Water Reactor)). (orig./HP) [de
Global restructuring of the CPM-2 transport algorithm for vector and parallel processing
International Nuclear Information System (INIS)
Vujic, J.L.; Martin, W.R.
1989-01-01
The CPM-2 code is an assembly transport code based on the collision probability (CP) method. It can in principle be applied to global reactor problems, but its excessive computational demands prevent this application. Therefore, a new transport algorithm for CPM-2 has been developed for vector-parallel architectures, which has resulted in an overall factor of 20 speedup (wall clock) on the IBM 3090-600E. This paper presents the detailed results of this effort as well as a brief description of ongoing effort to remove some of the modeling limitations in CPM-2 that inhibit its use for global applications, such as the use of the pure CP treatment and the assumption of isotropic scattering
International Nuclear Information System (INIS)
Satake, Shinsuke; Okamoto, Masao; Nakajima, Noriyoshi; Takamaru, Hisanori
2005-11-01
A neoclassical transport simulation code (FORTEC-3D) applicable to three-dimensional configurations has been developed using High Performance Fortran (HPF). Adoption of computing techniques for parallelization and a hybrid simulation model to the δf Monte-Carlo method transport simulation, including non-local transport effects in three-dimensional configurations, makes it possible to simulate the dynamism of global, non-local transport phenomena with a self-consistent radial electric field within a reasonable computation time. In this paper, development of the transport code using HPF is reported. Optimization techniques in order to achieve both high vectorization and parallelization efficiency, adoption of a parallel random number generator, and also benchmark results, are shown. (author)
The transport of neutrons and gamma-rays in the air
International Nuclear Information System (INIS)
Adamski, J.
1980-01-01
The transport of neutrons and gamma rays in the infinite homogeneous air has been investigated. For the calculations has been used the Multigroup One Dimensional Discrete Ordinates Transport Code ANISN-W. The calculations have been performed for three types of neutron sources. The neutrons and gamma ray doses in the air have been analyzed, and comparison to the other authors' results has been given. (author)
Vlasov modelling of parallel transport in a tokamak scrape-off layer
Energy Technology Data Exchange (ETDEWEB)
Manfredi, G [Institut de Physique et Chimie des Materiaux, CNRS and Universite de Strasbourg, BP 43, F-67034 Strasbourg (France); Hirstoaga, S [INRIA Nancy Grand-Est and Institut de Recherche en Mathematiques Avancees, 7 rue Rene Descartes, F-67084 Strasbourg (France); Devaux, S, E-mail: Giovanni.Manfredi@ipcms.u-strasbg.f, E-mail: hirstoaga@math.unistra.f, E-mail: Stephane.Devaux@ccfe.ac.u [JET-EFDA, Culham Science Centre, Abingdon, OX14 3DB (United Kingdom)
2011-01-15
A one-dimensional Vlasov-Poisson model is used to describe the parallel transport in a tokamak scrape-off layer. Thanks to a recently developed 'asymptotic-preserving' numerical scheme, it is possible to lift numerical constraints on the time step and grid spacing, which are no longer limited by, respectively, the electron plasma period and Debye length. The Vlasov approach provides a good velocity-space resolution even in regions of low density. The model is applied to the study of parallel transport during edge-localized modes, with particular emphasis on the particles and energy fluxes on the divertor plates. The numerical results are compared with analytical estimates based on a free-streaming model, with good general agreement. An interesting feature is the observation of an early electron energy flux, due to suprathermal electrons escaping the ions' attraction. In contrast, the long-time evolution is essentially quasi-neutral and dominated by the ion dynamics.
International Nuclear Information System (INIS)
Brown, P.; Chang, B.
1998-01-01
The linear Boltzmann transport equation (BTE) is an integro-differential equation arising in deterministic models of neutral and charged particle transport. In slab (one-dimensional Cartesian) geometry and certain higher-dimensional cases, Diffusion Synthetic Acceleration (DSA) is known to be an effective algorithm for the iterative solution of the discretized BTE. Fourier and asymptotic analyses have been applied to various idealizations (e.g., problems on infinite domains with constant coefficients) to obtain sharp bounds on the convergence rate of DSA in such cases. While DSA has been shown to be a highly effective acceleration (or preconditioning) technique in one-dimensional problems, it has been observed to be less effective in higher dimensions. This is due in part to the expense of solving the related diffusion linear system. We investigate here the effectiveness of a parallel semicoarsening multigrid (SMG) solution approach to DSA preconditioning in several three dimensional problems. In particular, we consider the algorithmic and implementation scalability of a parallel SMG-DSA preconditioner on several types of test problems
Hsu, Liang-Yan; Wu, Ning; Rabitz, Herschel
2016-11-30
We investigate electron transport through series and parallel intramolecular circuits in the framework of the multi-level Redfield theory. Based on the assumption of weak monomer-bath couplings, the simulations depict the length and temperature dependence in six types of intramolecular circuits. In the tunneling regime, we find that the intramolecular circuit rule is only valid in the weak monomer coupling limit. In the thermally activated hopping regime, for circuits based on two different molecular units M a and M b with distinct activation energies E act,a > E act,b , the activation energies of M a and M b in series are nearly the same as E act,a while those in parallel are nearly the same as E act,b . This study gives a comprehensive description of electron transport through intramolecular circuits from tunneling to thermally activated hopping. We hope that this work can motivate additional studies to design intramolecular circuits based on different types of building blocks, and to explore the corresponding circuit laws and the length and temperature dependence of conductance.
Parallel unstructured mesh optimisation for 3D radiation transport and fluids modelling
International Nuclear Information System (INIS)
Gorman, G.J.; Pain, Ch. C.; Oliveira, C.R.E. de; Umpleby, A.P.; Goddard, A.J.H.
2003-01-01
In this paper we describe the theory and application of a parallel mesh optimisation procedure to obtain self-adapting finite element solutions on unstructured tetrahedral grids. The optimisation procedure adapts the tetrahedral mesh to the solution of a radiation transport or fluid flow problem without sacrificing the integrity of the boundary (geometry), or internal boundaries (regions) of the domain. The objective is to obtain a mesh which has both a uniform interpolation error in any direction and the element shapes are of good quality. This is accomplished with use of a non-Euclidean (anisotropic) metric which is related to the Hessian of the solution field. Appropriate scaling of the metric enables the resolution of multi-scale phenomena as encountered in transient incompressible fluids and multigroup transport calculations. The resulting metric is used to calculate element size and shape quality. The mesh optimisation method is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality which is gauged by a functional. The mesh modification thus fits the solution field(s) in an optimal manner. The parallel mesh optimisation/adaptivity procedure presented in this paper is of general applicability. We illustrate this by applying it to a transient CFD (computational fluid dynamics) problem. Incompressible flow past a cylinder at moderate Reynolds numbers is modelled to demonstrate that the mesh can follow transient flow features. (authors)
Yang, Jianwen
2012-04-01
A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.
3D-radiative transfer in terrestrial atmosphere: An efficient parallel numerical procedure
Bass, L. P.; Germogenova, T. A.; Nikolaeva, O. V.; Kokhanovsky, A. A.; Kuznetsov, V. S.
2003-04-01
Light propagation and scattering in terrestrial atmosphere is usually studied in the framework of the 1D radiative transfer theory [1]. However, in reality particles (e.g., ice crystals, solid and liquid aerosols, cloud droplets) are randomly distributed in 3D space. In particular, their concentrations vary both in vertical and horizontal directions. Therefore, 3D effects influence modern cloud and aerosol retrieval procedures, which are currently based on the 1D radiative transfer theory. It should be pointed out that the standard radiative transfer equation allows to study these more complex situations as well [2]. In recent year the parallel version of the 2D and 3D RADUGA code has been developed. This version is successfully used in gammas and neutrons transport problems [3]. Applications of this code to radiative transfer in atmosphere problems are contained in [4]. Possibilities of code RADUGA are presented in [5]. The RADUGA code system is an universal solver of radiative transfer problems for complicated models, including 2D and 3D aerosol and cloud fields with arbitrary scattering anisotropy, light absorption, inhomogeneous underlying surface and topography. Both delta type and distributed light sources can be accounted for in the framework of the algorithm developed. The accurate numerical procedure is based on the new discrete ordinate SWDD scheme [6]. The algorithm is specifically designed for parallel supercomputers. The version RADUGA 5.1(P) can run on MBC1000M [7] (768 processors with 10 Gb of hard disc memory for each processor). The peak productivity is equal 1 Tfl. Corresponding scalar version RADUGA 5.1 is working on PC. As a first example of application of the algorithm developed, we have studied the shadowing effects of clouds on neighboring cloudless atmosphere, depending on the cloud optical thickness, surface albedo, and illumination conditions. This is of importance for modern satellite aerosol retrieval algorithms development. [1] Sobolev
International Nuclear Information System (INIS)
Zhang, B.; Li, G.; Wang, W.; Shangguan, D.; Deng, L.
2015-01-01
This paper introduces the Strategy of multilevel hybrid parallelism of JCOGIN Infrastructure on Monte Carlo Particle Transport for the large-scale full-core pin-by-pin simulations. The particle parallelism, domain decomposition parallelism and MPI/OpenMP parallelism are designed and implemented. By the testing, JMCT presents the parallel scalability of JCOGIN, which reaches the parallel efficiency 80% on 120,000 cores for the pin-by-pin computation of the BEAVRS benchmark. (author)
Overview of development and design of MPACT: Michigan parallel characteristics transport code
Energy Technology Data Exchange (ETDEWEB)
Kochunas, B.; Collins, B.; Jabaay, D.; Downar, T. J.; Martin, W. R. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2200 Bonisteel, Ann Arbor, MI 48109 (United States)
2013-07-01
MPACT (Michigan Parallel Characteristics Transport Code) is a new reactor analysis tool. It is being developed by students and research staff at the University of Michigan to be used for an advanced pin-resolved transport capability within VERA (Virtual Environment for Reactor Analysis). VERA is the end-user reactor simulation tool being produced by the Consortium for the Advanced Simulation of Light Water Reactors (CASL). The MPACT development project is itself unique for the way it is changing how students do research to achieve the instructional and research goals of an academic institution, while providing immediate value to industry. The MPACT code makes use of modern lean/agile software processes and extensive testing to maintain a level of productivity and quality required by CASL. MPACT's design relies heavily on object-oriented programming concepts and design patterns and is programmed in Fortran 2003. These designs are explained and illustrated as to how they can be readily extended to incorporate new capabilities and research ideas in support of academic research objectives. The transport methods currently implemented in MPACT include the 2-D and 3-D method of characteristics (MOC) and 2-D and 3-D method of collision direction probabilities (CDP). For the cross section resonance treatment, presently the subgroup method and the new embedded self-shielding method (ESSM) are implemented within MPACT. (authors)
Bentonite electrical conductivity: a model based on series–parallel transport
Lima, Ana T.
2010-01-30
Bentonite has significant applications nowadays, among them as landfill liners, in concrete industry as a repairing material, and as drilling mud in oil well construction. The application of an electric field to such perimeters is under wide discussion, and subject of many studies. However, to understand the behaviour of such an expansive and plastic material under the influence of an electric field, the perception of its electrical properties is essential. This work serves to compare existing data of such electrical behaviour with new laboratorial results. Electrical conductivity is a pertinent parameter since it indicates how much a material is prone to conduct electricity. In the current study, total conductivity of a compacted porous medium was established to be dependent upon density of the bentonite plug. Therefore, surface conductivity was addressed and a series-parallel transport model used to quantify/predict the total conductivity of the system. © The Author(s) 2010.
Gudmundsson, Vidar; Abdulla, Nzar Rauf; Sitek, Anna; Goan, Hsi-Sheng; Tang, Chi-Shung; Manolescu, Andrei
2018-02-01
We show that a Rabi-splitting of the states of strongly interacting electrons in parallel quantum dots embedded in a short quantum wire placed in a photon cavity can be produced by either the para- or the dia-magnetic electron-photon interactions when the geometry of the system is properly accounted for and the photon field is tuned close to a resonance with the electron system. We use these two resonances to explore the electroluminescence caused by the transport of electrons through the one- and two-electron ground states of the system and their corresponding conventional and vacuum electroluminescense as the central system is opened up by coupling it to external leads acting as electron reservoirs. Our analysis indicates that high-order electron-photon processes are necessary to adequately construct the cavity-photon dressed electron states needed to describe both types of electroluminescence.
Classical parallel transport in a multi-species plasma from a 21 moment approximation
International Nuclear Information System (INIS)
Radford, G.J.
1993-11-01
Momentum equations from a 21 moment Grad approximation are presented, including full expressions for the collision terms for the case of elastic collisions. Collision terms for the particular case of an electron-ion-impurity plasma are then given. In addition, for the positive ions, approximations to the collision terms are given for a common ion temperature, T z = T i , and a massive impurity species, m z >> m i and general temperatures. The moment equations are solved for the classical parallel transport coefficients for the specific case of a low impurity density plasma and the results compared with those give by other authors. The range of forms for the collision terms is given to allow more general or other types of solutions to be obtained. (Author)
A massively parallel method of characteristic neutral particle transport code for GPUs
International Nuclear Information System (INIS)
Boyd, W. R.; Smith, K.; Forget, B.
2013-01-01
Over the past 20 years, parallel computing has enabled computers to grow ever larger and more powerful while scientific applications have advanced in sophistication and resolution. This trend is being challenged, however, as the power consumption for conventional parallel computing architectures has risen to unsustainable levels and memory limitations have come to dominate compute performance. Heterogeneous computing platforms, such as Graphics Processing Units (GPUs), are an increasingly popular paradigm for solving these issues. This paper explores the applicability of GPUs for deterministic neutron transport. A 2D method of characteristics (MOC) code - OpenMOC - has been developed with solvers for both shared memory multi-core platforms as well as GPUs. The multi-threading and memory locality methodologies for the GPU solver are presented. Performance results for the 2D C5G7 benchmark demonstrate 25-35 x speedup for MOC on the GPU. The lessons learned from this case study will provide the basis for further exploration of MOC on GPUs as well as design decisions for hardware vendors exploring technologies for the next generation of machines for scientific computing. (authors)
International Nuclear Information System (INIS)
Downar, T.
2009-01-01
The overall objective of the work here has been to eliminate the approximations used in current resonance treatments by developing continuous energy multi-dimensional transport calculations for problem dependent self-shielding calculations. The work here builds on the existing resonance treatment capabilities in the ORNL SCALE code system. The overall objective of the work here has been to eliminate the approximations used in current resonance treatments by developing continuous energy multidimensional transport calculations for problem dependent self-shielding calculations. The work here builds on the existing resonance treatment capabilities in the ORNL SCALE code system. Specifically, the methods here utilize the existing continuous energy SCALE5 module, CENTRM, and the multi-dimensional discrete ordinates solver, NEWT to develop a new code, CENTRM( ) NEWT. The work here addresses specific theoretical limitations in existing CENTRM resonance treatment, as well as investigates advanced numerical and parallel computing algorithms for CENTRM and NEWT in order to reduce the computational burden. The result of the work here will be a new computer code capable of performing problem dependent self-shielding analysis for both existing and proposed GENIV fuel designs. The objective of the work was to have an immediate impact on the safety analysis of existing reactors through improvements in the calculation of fuel temperature effects, as well as on the analysis of more sophisticated GENIV/NGNP systems through improvements in the depletion/transmutation of actinides for Advanced Fuel Cycle Initiatives.
Effect of parallel transport currents on the d-wave Josephson junction
International Nuclear Information System (INIS)
Rashedi, Gholamreza
2009-01-01
In this paper, the non-local mixing of coherent current states in d-wave superconducting banks is investigated. The superconducting banks are connected via a ballistic point contact. The banks have mis-orientation and phase difference. Furthermore, they are subjected to a tangential transport current along the ab plane of d-wave crystals and parallel to the interface between the superconductors. The effects of mis-orientation and external transport current on the current-phase relations and current distributions are the subjects of this paper. It is observed that, at values of phase difference close to 0, π and 2π, the current distribution may have a vortex-like form in the vicinity of the point contact. The current distribution of the above-mentioned junction between d-wave superconductors is totally different from the junction between s-wave superconductors. The interesting result which this study shows is that spontaneous and Josephson currents are observed for the case of φ = 0.
Parallel Transport and Profile of Boundary Plasma with a Low Recycling Wall
Energy Technology Data Exchange (ETDEWEB)
Tang, X.; Guo, Z., E-mail: xtang@lanl.gov [Los Alamos National Laboratory, Los Alamos (United States)
2012-09-15
Full text: Reduction of wall recycling by, for example, a flowing liquid surface at the divertor and first wall, holds the promise of accessing the distinct tokamak reactor operational mode with boundary plasmas of high temperature and low density. Earlier work has indicated that such a boundary plasma would reduce the temperature gradient across the entire plasma and hence remove the primary micro-instability drive responsibly for anomalous particle and energy transport. Here we present a systematic study solving the kinetic equations both analytically and numerically, with and without Coulomb collision. The distinct roles of magnetic field strength modulation and the ambipolar electric field on the electron and ion distribution functions are clarified. The resulting behavior on plasma profile and parallel heat flux, which are often surprising and counter the expectations from the collisional fluid models, on which previous work were based, are explained both intuitively and with a contrast between analytical calculation and numerical simulations. The transport-induced plasma instabilities, and their essential role in maintaining ambipolarity, are clarified, along with the subtle effect of Coulomb collision on electron temperature and wall potential as small but finite collisionality is taken into account. (author)
Application of preconditioned GMRES to the numerical solution of the neutron transport equation
International Nuclear Information System (INIS)
Patton, B.W.; Holloway, J.P.
2002-01-01
The generalized minimal residual (GMRES) method with right preconditioning is examined as an alternative to both standard and accelerated transport sweeps for the iterative solution of the diamond differenced discrete ordinates neutron transport equation. Incomplete factorization (ILU) type preconditioners are used to determine their effectiveness in accelerating GMRES for this application. ILU(τ), which requires the specification of a dropping criteria τ, proves to be a good choice for the types of problems examined in this paper. The combination of ILU(τ) and GMRES is compared with both DSA and unaccelerated transport sweeps for several model problems. It is found that the computational workload of the ILU(τ)-GMRES combination scales nonlinearly with the number of energy groups and quadrature order, making this technique most effective for problems with a small number of groups and discrete ordinates. However, the cost of preconditioner construction can be amortized over several calculations with different source and/or boundary values. Preconditioners built upon standard transport sweep algorithms are also evaluated as to their effectiveness in accelerating the convergence of GMRES. These preconditioners show better scaling with such problem parameters as the scattering ratio, the number of discrete ordinates, and the number of spatial meshes. These sweeps based preconditioners can also be cast in a matrix free form that greatly reduces storage requirements
A scalar flux - oriented method for the transport equation in slab geometry
International Nuclear Information System (INIS)
Budd, C.
1981-01-01
A new method for solving the neutron transport equation is described. An unusual feature of this method is that it deals principally with scalar fluxes rather than angular fluxes. An alternative approach in slab geometry promises to be cheaper to run and does not suffer from many of the problems of the discrete ordinates method. It also appears possible to extend the method to several dimensions and this is discussed. (U.K.)
A general analytical approach to the one-group, one-dimensional transport equation
International Nuclear Information System (INIS)
Barichello, L.B.; Vilhena, M.T.
1993-01-01
The main feature of the presented approach to solve the neutron transport equation consists in the application of the Laplace transform to the discrete ordinates equations, which yields a linear system of order N to be solved (LTS N method). In this paper this system is solved analytically and the inversion is performed using the Heaviside expansion technique. The general formulation achieved by this procedure is then applied to homogeneous and heterogeneous one-group slab-geometry problems. (orig.) [de
Steady-state and time-dependent modelling of parallel transport in the scrape-off layer
DEFF Research Database (Denmark)
Havlickova, E.; Fundamenski, W.; Naulin, Volker
2011-01-01
The one-dimensional fluid code SOLF1D has been used for modelling of plasma transport in the scrape-off layer (SOL) along magnetic field lines, both in steady state and under transient conditions that arise due to plasma turbulence. The presented work summarizes results of SOLF1D with attention...... given to transient parallel transport which reveals two distinct time scales due to the transport mechanisms of convection and diffusion. Time-dependent modelling combined with the effect of ballooning shows propagation of particles along the magnetic field line with Mach number up to M ≈ 1...... temperature calculated in SOLF1D is compared with the approximative model used in the turbulence code ESEL both for steady-state and turbulent SOL. Dynamics of the parallel transport are investigated for a simple transient event simulating the propagation of particles and energy to the targets from a blob...
Quasineutral plasma expansion into infinite vacuum as a model for parallel ELM transport
Moulton, D.; Ghendrih, Ph; Fundamenski, W.; Manfredi, G.; Tskhakaya, D.
2013-08-01
An analytic solution for the expansion of a plasma into vacuum is assessed for its relevance to the parallel transport of edge localized mode (ELM) filaments along field lines. This solution solves the 1D1V Vlasov-Poisson equations for the adiabatic (instantaneous source), collisionless expansion of a Gaussian plasma bunch into an infinite space in the quasineutral limit. The quasineutral assumption is found to hold as long as λD0/σ0 ≲ 0.01 (where λD0 is the initial Debye length at peak density and σ0 is the parallel length of the Gaussian filament), a condition that is physically realistic. The inclusion of a boundary at x = L and consequent formation of a target sheath is found to have a negligible effect when L/σ0 ≳ 5, a condition that is physically plausible. Under the same condition, the target flux densities predicted by the analytic solution are well approximated by the ‘free-streaming’ equations used in previous experimental studies, strengthening the notion that these simple equations are physically reasonable. Importantly, the analytic solution predicts a zero heat flux density so that a fluid approach to the problem can be used equally well, at least when the source is instantaneous. It is found that, even for JET-like pedestal parameters, collisions can affect the expansion dynamics via electron temperature isotropization, although this is probably a secondary effect. Finally, the effect of a finite duration, τsrc, for the plasma source is investigated. As is found for an instantaneous source, when L/σ0 ≳ 5 the presence of a target sheath has a negligible effect, at least up to the explored range of τsrc = L/cs (where cs is the sound speed at the initial temperature).
International Nuclear Information System (INIS)
Jones, D.B.
1986-01-01
EPRI-LATTICE is a multigroup neutron transport computer code for the analysis of light water reactor fuel assemblies. It can solve the two-dimensional neutron transport problem by two distinct methods: (a) the method of collision probabilities and (b) the method of discrete ordinates. The code was developed by S. Levy Inc. as an account of work sponsored by the Electric Power Research Institute (EPRI). The collision probabilities calculation in EPRI-LATTICE (L-CP) is based on the same methodology that exists in the lattice codes CPM-2 and EPRI-CPM. Certain extensions have been made to the data representations of the CPM programs to improve the overall accuracy of the calculation. The important extensions include unique representations of scattering matrices and fission fractions (chi) for each composition in the problem. A new capability specifically developed for the EPRI-LATTICE code is a discrete ordinates methodology. The discrete ordinates calculation in EPRI-LATTICE (L-SN) is based on the discrete S/sub n/ methodology that exists in the TWODANT program. In contrast to TWODANT, which utilizes synthetic diffusion acceleration and supports multiple geometries, only the transport equations are solved by L-SN and only the data representations for the two-dimensional geometry are treated
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
International Nuclear Information System (INIS)
Larsen, E.W.; Morel, J.E.; Miller, W.F. Jr.
1987-01-01
We present an asymptotic analysis of spatial differencing schemes for the discrete-ordinates equations, for diffusive media with spatial cells that are not optically thin. Our theoretical tool is an asymptotic expansion that has previously been used to describe the transform from analytic transport to analytic diffusion theory for such media. To introduce this expansion and its physical rationale, we first describe it for the analytic discrete-ordinates equations. Then, we apply the expansion to the spatially discretized discrete-ordinates equations, with the spatial mesh scaled in either of two physically relevant ways such that the optical thickness of the spatial cells is not small. If the result of either expansion is a legitimate diffusion description for either the cell-averaged or cell-edge fluxes, then we say that the approximate flux has the appropriate diffusion limit; otherwise, we say it does not. We consider several transport differencing schemes that are applicable in neutron transport and thermal radiation applications. We also include numerical results which demonstrate the validity of our theory and show that differencing schemes that do have a particular diffusion limit are substantially more accurate, in the regime described by the limit, than those that do not. copyright 1987 Academic Press, Inc
International Nuclear Information System (INIS)
Fischer, G.A.
2010-01-01
The PCA Benchmark is analyzed using RAPTOR-M3G, a parallel SN radiation transport code. A variety of mesh structures, angular quadrature sets, cross section treatments, and reactor dosimetry cross sections are presented. The results show that RAPTOR-M3G is generally suitable for PWR neutron dosimetry applications. (authors)
Biomedical applications of two- and three-dimensional deterministic radiation transport methods
International Nuclear Information System (INIS)
Nigg, D.W.
1992-01-01
Multidimensional deterministic radiation transport methods are routinely used in support of the Boron Neutron Capture Therapy (BNCT) Program at the Idaho National Engineering Laboratory (INEL). Typical applications of two-dimensional discrete-ordinates methods include neutron filter design, as well as phantom dosimetry. The epithermal-neutron filter for BNCT that is currently available at the Brookhaven Medical Research Reactor (BMRR) was designed using such methods. Good agreement between calculated and measured neutron fluxes was observed for this filter. Three-dimensional discrete-ordinates calculations are used routinely for dose-distribution calculations in three-dimensional phantoms placed in the BMRR beam, as well as for treatment planning verification for live canine subjects. Again, good agreement between calculated and measured neutron fluxes and dose levels is obtained
International Nuclear Information System (INIS)
Miller, W.F. Jr.
1975-10-01
The coarse-mesh rebalance method, based on neutron conservation, is used in discrete ordinates neutron transport codes to accelerate convergence of the within-group scattering source. Though very powerful for this application, the method is ineffective in accelerating the iteration on the discrete-ordinates-to-spherical-harmonics fictitious sources used for ray-effect elimination. This is largely because this source makes a minimum contribution to the neutron balance equation. The traditional rebalance approach is derived in a variational framework and compared with new rebalance approaches tailored to be compatible with the fictitious source. The new approaches are compared numerically to determine their relative advantages. It is concluded that there is little incentive to use the new methods. (3 tables, 5 figures)
International Nuclear Information System (INIS)
Nunes, Carlos Eduardo A.; Barros, Ricardo C.
2009-01-01
This paper describes a computational program for result simulation of neutron transport problems at one velocity with isotropic scattering in Cartesian onedimensional geometry. Describing the physical modelling, the next phase is a mathematical modelling of the physical problem for simulation of the neutron distribution. The mathematical modelling uses the linearized Boltzmann equation which represents a balance among the production and loss of particles. The formulation of the discrete ordinates S N consists of discretization of angular variables at N directions (discrete ordinates), and using a set of angular quadratures for the approximation of integral terms of scattering sources. The S N equations are numerically solved. This work describes three numerical methods: diamond difference, step and characteristic step. The paper also presents numerical results for illustration of the efficiency of the developed program
Comparison of TITAN hybrid deterministic transport code and MCNP5 for simulation of SPECT
International Nuclear Information System (INIS)
Royston, K.; Haghighat, A.; Yi, C.
2010-01-01
Traditionally, Single Photon Emission Computed Tomography (SPECT) simulations use Monte Carlo methods. The hybrid deterministic transport code TITAN has recently been applied to the simulation of a SPECT myocardial perfusion study. The TITAN SPECT simulation uses the discrete ordinates formulation in the phantom region and a simplified ray-tracing formulation outside of the phantom. A SPECT model has been created in the Monte Carlo Neutral particle (MCNP)5 Monte Carlo code for comparison. In MCNP5 the collimator is directly modeled, but TITAN instead simulates the effect of collimator blur using a circular ordinate splitting technique. Projection images created using the TITAN code are compared to results using MCNP5 for three collimator acceptance angles. Normalized projection images for 2.97 deg, 1.42 deg and 0.98 deg collimator acceptance angles had maximum relative differences of 21.3%, 11.9% and 8.3%, respectively. Visually the images are in good agreement. Profiles through the projection images were plotted to find that the TITAN results followed the shape of the MCNP5 results with some differences in magnitude. A timing comparison on 16 processors found that the TITAN code completed the calculation 382 to 2787 times faster than MCNP5. Both codes exhibit good parallel performance. (author)
Massively parallel red-black algorithms for x-y-z response matrix equations
International Nuclear Information System (INIS)
Hanebutte, U.R.; Laurin-Kovitz, K.; Lewis, E.E.
1992-01-01
Recently, both discrete ordinates and spherical harmonic (S n and P n ) methods have been cast in the form of response matrices. In x-y geometry, massively parallel algorithms have been developed to solve the resulting response matrix equations on the Connection Machine family of parallel computers, the CM-2, CM-200, and CM-5. These algorithms utilize two-cycle iteration on a red-black checkerboard. In this work we examine the use of massively parallel red-black algorithms to solve response matric equations in three dimensions. This longer term objective is to utilize massively parallel algorithms to solve S n and/or P n response matrix problems. In this exploratory examination, however, we consider the simple 6 x 6 response matrices that are derivable from fine-mesh diffusion approximations in three dimensions
Romano, Paul Kollath
Monte Carlo particle transport methods are being considered as a viable option for high-fidelity simulation of nuclear reactors. While Monte Carlo methods offer several potential advantages over deterministic methods, there are a number of algorithmic shortcomings that would prevent their immediate adoption for full-core analyses. In this thesis, algorithms are proposed both to ameliorate the degradation in parallel efficiency typically observed for large numbers of processors and to offer a means of decomposing large tally data that will be needed for reactor analysis. A nearest-neighbor fission bank algorithm was proposed and subsequently implemented in the OpenMC Monte Carlo code. A theoretical analysis of the communication pattern shows that the expected cost is O( N ) whereas traditional fission bank algorithms are O(N) at best. The algorithm was tested on two supercomputers, the Intrepid Blue Gene/P and the Titan Cray XK7, and demonstrated nearly linear parallel scaling up to 163,840 processor cores on a full-core benchmark problem. An algorithm for reducing network communication arising from tally reduction was analyzed and implemented in OpenMC. The proposed algorithm groups only particle histories on a single processor into batches for tally purposes---in doing so it prevents all network communication for tallies until the very end of the simulation. The algorithm was tested, again on a full-core benchmark, and shown to reduce network communication substantially. A model was developed to predict the impact of load imbalances on the performance of domain decomposed simulations. The analysis demonstrated that load imbalances in domain decomposed simulations arise from two distinct phenomena: non-uniform particle densities and non-uniform spatial leakage. The dominant performance penalty for domain decomposition was shown to come from these physical effects rather than insufficient network bandwidth or high latency. The model predictions were verified with
Energy Technology Data Exchange (ETDEWEB)
Kostin, Mikhail [Michigan State Univ., East Lansing, MI (United States); Mokhov, Nikolai [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Niita, Koji [Research Organization for Information Science and Technology, Ibaraki-ken (Japan)
2013-09-25
A parallel computing framework has been developed to use with general-purpose radiation transport codes. The framework was implemented as a C++ module that uses MPI for message passing. It is intended to be used with older radiation transport codes implemented in Fortran77, Fortran 90 or C. The module is significantly independent of radiation transport codes it can be used with, and is connected to the codes by means of a number of interface functions. The framework was developed and tested in conjunction with the MARS15 code. It is possible to use it with other codes such as PHITS, FLUKA and MCNP after certain adjustments. Besides the parallel computing functionality, the framework offers a checkpoint facility that allows restarting calculations with a saved checkpoint file. The checkpoint facility can be used in single process calculations as well as in the parallel regime. The framework corrects some of the known problems with the scheduling and load balancing found in the original implementations of the parallel computing functionality in MARS15 and PHITS. The framework can be used efficiently on homogeneous systems and networks of workstations, where the interference from the other users is possible.
An extended step characteristic method for solving the transport equation in general geometries
International Nuclear Information System (INIS)
DeHart, M.D.; Pevey, R.E.; Parish, T.A.
1994-01-01
A method for applying the discrete ordinates method to solve the Boltzmann transport equation on arbitrary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the geometrical shape of a mesh element characteristic of a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. By using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. Results for a number of test problems have been compared with solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well as numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN-II computer programs
A Krylov Subspace Method for Unstructured Mesh SN Transport Computation
International Nuclear Information System (INIS)
Yoo, Han Jong; Cho, Nam Zin; Kim, Jong Woon; Hong, Ser Gi; Lee, Young Ouk
2010-01-01
Hong, et al., have developed a computer code MUST (Multi-group Unstructured geometry S N Transport) for the neutral particle transport calculations in three-dimensional unstructured geometry. In this code, the discrete ordinates transport equation is solved by using the discontinuous finite element method (DFEM) or the subcell balance methods with linear discontinuous expansion. In this paper, the conventional source iteration in the MUST code is replaced by the Krylov subspace method to reduce computing time and the numerical test results are given
International Nuclear Information System (INIS)
Le Roux, J. A.
2011-01-01
Earlier work based on nonlinear guiding center (NLGC) theory suggested that perpendicular cosmic-ray transport is diffusive when cosmic rays encounter random three-dimensional magnetohydrodynamic turbulence dominated by uniform two-dimensional (2D) turbulence with a minor uniform slab turbulence component. In this approach large-scale perpendicular cosmic-ray transport is due to cosmic rays microscopically diffusing along the meandering magnetic field dominated by 2D turbulence because of gyroresonant interactions with slab turbulence. However, turbulence in the solar wind is intermittent and it has been suggested that intermittent turbulence might be responsible for the observation of 'dropout' events in solar energetic particle fluxes on small scales. In a previous paper le Roux et al. suggested, using NLGC theory as a basis, that if gyro-scale slab turbulence is intermittent, large-scale perpendicular cosmic-ray transport in weak uniform 2D turbulence will be superdiffusive or subdiffusive depending on the statistical characteristics of the intermittent slab turbulence. In this paper we expand and refine our previous work further by investigating how both parallel and perpendicular transport are affected by intermittent slab turbulence for weak as well as strong uniform 2D turbulence. The main new finding is that both parallel and perpendicular transport are the net effect of an interplay between diffusive and nondiffusive (superdiffusive or subdiffusive) transport effects as a consequence of this intermittency.
Energy Technology Data Exchange (ETDEWEB)
Le Roux, J. A. [Department of Physics, University of Alabama in Huntsville, Huntsville, AL 35899 (United States)
2011-12-10
Earlier work based on nonlinear guiding center (NLGC) theory suggested that perpendicular cosmic-ray transport is diffusive when cosmic rays encounter random three-dimensional magnetohydrodynamic turbulence dominated by uniform two-dimensional (2D) turbulence with a minor uniform slab turbulence component. In this approach large-scale perpendicular cosmic-ray transport is due to cosmic rays microscopically diffusing along the meandering magnetic field dominated by 2D turbulence because of gyroresonant interactions with slab turbulence. However, turbulence in the solar wind is intermittent and it has been suggested that intermittent turbulence might be responsible for the observation of 'dropout' events in solar energetic particle fluxes on small scales. In a previous paper le Roux et al. suggested, using NLGC theory as a basis, that if gyro-scale slab turbulence is intermittent, large-scale perpendicular cosmic-ray transport in weak uniform 2D turbulence will be superdiffusive or subdiffusive depending on the statistical characteristics of the intermittent slab turbulence. In this paper we expand and refine our previous work further by investigating how both parallel and perpendicular transport are affected by intermittent slab turbulence for weak as well as strong uniform 2D turbulence. The main new finding is that both parallel and perpendicular transport are the net effect of an interplay between diffusive and nondiffusive (superdiffusive or subdiffusive) transport effects as a consequence of this intermittency.
Energy Technology Data Exchange (ETDEWEB)
Basso Barichello, Liliane; Dias da Cunha, Rudnei [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst. de Matematica; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2015-05-15
A nodal formulation of a fixed-source two-dimensional neutron transport problem, in Cartesian geometry, defined in a heterogeneous medium, is solved by an analytical approach. Explicit expressions, in terms of the spatial variables, are derived for averaged fluxes in each region in which the domain is subdivided. The procedure is an extension of an analytical discrete ordinates method, the ADO method, for the solution of the two-dimensional homogeneous medium case. The scheme is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric quadrature scheme. As usual for nodal schemes, relations between the averaged fluxes and the unknown angular fluxes at the contours are introduced as auxiliary equations. Numerical results are in agreement with results available in the literature.
International Nuclear Information System (INIS)
Wagner, John C.; Mosher, Scott W.; Evans, Thomas M.; Peplow, Douglas E.; Turner, John A.
2010-01-01
attempts to achieve uniform statistical uncertainty throughout a designated problem space. The MC DD development is being implemented in conjunction with the Denovo deterministic radiation transport package to have direct access to the 3-D, massively parallel discrete-ordinates solver (to support the hybrid method) and the associated parallel routines and structure. This paper describes the hybrid method, its implementation, and initial testing results for a realistic 2-D quarter core pressurized-water reactor model and also describes the MC DD algorithm and its implementation.
International Nuclear Information System (INIS)
Wagner, J.C.; Mosher, S.W.; Evans, T.M.; Peplow, D.E.; Turner, J.A.
2010-01-01
, which attempts to achieve uniform statistical uncertainty throughout a designated problem space. The MC DD development is being implemented in conjunction with the Denovo deterministic radiation transport package to have direct access to the 3-D, massively parallel discrete-ordinates solver (to support the hybrid method) and the associated parallel routines and structure. This paper describes the hybrid method, its implementation, and initial testing results for a realistic 2-D quarter core pressurized-water reactor model and also describes in MC DD algorithm and its implementation. (author)
Steady-state and time-dependent modelling of parallel transport in the scrape-off layer
Czech Academy of Sciences Publication Activity Database
Havlíčková, E.; Fundameski, W.; Naulin, V.; Nielsen, A.H.; Zagórski, R.; Seidl, Jakub; Horáček, Jan
2011-01-01
Roč. 53, č. 6 (2011), 065004-065004 ISSN 0741-3335 R&D Projects: GA ČR GAP205/10/2055; GA MŠk 7G09042 Institutional research plan: CEZ:AV0Z20430508 Keywords : Parallel transport * , SOLF1D Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.425, year: 2011 http://iopscience.iop.org/0741-3335/53/6/065004/pdf/0741-3335_53_6_065004.pdf
Chen, Kewei; Zhan, Hongbin
2018-06-01
The reactive solute transport in a single fracture bounded by upper and lower matrixes is a classical problem that captures the dominant factors affecting transport behavior beyond pore scale. A parallel fracture-matrix system which considers the interaction among multiple paralleled fractures is an extension to a single fracture-matrix system. The existing analytical or semi-analytical solution for solute transport in a parallel fracture-matrix simplifies the problem to various degrees, such as neglecting the transverse dispersion in the fracture and/or the longitudinal diffusion in the matrix. The difficulty of solving the full two-dimensional (2-D) problem lies in the calculation of the mass exchange between the fracture and matrix. In this study, we propose an innovative Green's function approach to address the 2-D reactive solute transport in a parallel fracture-matrix system. The flux at the interface is calculated numerically. It is found that the transverse dispersion in the fracture can be safely neglected due to the small scale of fracture aperture. However, neglecting the longitudinal matrix diffusion would overestimate the concentration profile near the solute entrance face and underestimate the concentration profile at the far side. The error caused by neglecting the longitudinal matrix diffusion decreases with increasing Peclet number. The longitudinal matrix diffusion does not have obvious influence on the concentration profile in long-term. The developed model is applied to a non-aqueous-phase-liquid (DNAPL) contamination field case in New Haven Arkose of Connecticut in USA to estimate the Trichloroethylene (TCE) behavior over 40 years. The ratio of TCE mass stored in the matrix and the injected TCE mass increases above 90% in less than 10 years.
International Nuclear Information System (INIS)
Petrosyan, Lyudvig S
2016-01-01
We study coherent transport in a system of periodic linear chain of quantum dots situated between two parallel quantum wires. We show that the resonant-tunneling conductance between the wires exhibits a Rabi splitting of the resonance peak as a function of Fermi energy in the wires. This effect is an electron transport analogue of the Rabi splitting in optical spectra of two interacting systems. The conductance peak splitting originates from the anticrossing of Bloch bands in a periodic system that is caused by a strong coupling between the electron states in the quantum dot chain and quantum wires. (paper)
Energy Technology Data Exchange (ETDEWEB)
Lichtner, Peter C. [OFM Research, Redmond, WA (United States); Hammond, Glenn E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lu, Chuan [Idaho National Lab. (INL), Idaho Falls, ID (United States); Karra, Satish [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Bisht, Gautam [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Andre, Benjamin [National Center for Atmospheric Research, Boulder, CO (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Mills, Richard [Intel Corporation, Portland, OR (United States); Univ. of Tennessee, Knoxville, TN (United States); Kumar, Jitendra [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2015-01-20
PFLOTRAN solves a system of generally nonlinear partial differential equations describing multi-phase, multicomponent and multiscale reactive flow and transport in porous materials. The code is designed to run on massively parallel computing architectures as well as workstations and laptops (e.g. Hammond et al., 2011). Parallelization is achieved through domain decomposition using the PETSc (Portable Extensible Toolkit for Scientific Computation) libraries for the parallelization framework (Balay et al., 1997). PFLOTRAN has been developed from the ground up for parallel scalability and has been run on up to 218 processor cores with problem sizes up to 2 billion degrees of freedom. Written in object oriented Fortran 90, the code requires the latest compilers compatible with Fortran 2003. At the time of this writing this requires gcc 4.7.x, Intel 12.1.x and PGC compilers. As a requirement of running problems with a large number of degrees of freedom, PFLOTRAN allows reading input data that is too large to fit into memory allotted to a single processor core. The current limitation to the problem size PFLOTRAN can handle is the limitation of the HDF5 file format used for parallel IO to 32 bit integers. Noting that 2^{32} = 4; 294; 967; 296, this gives an estimate of the maximum problem size that can be currently run with PFLOTRAN. Hopefully this limitation will be remedied in the near future.
High-speed parallel forward error correction for optical transport networks
DEFF Research Database (Denmark)
Rasmussen, Anders; Ruepp, Sarah Renée; Berger, Michael Stübert
2010-01-01
This paper presents a highly parallelized hardware implementation of the standard OTN Reed-Solomon Forward Error Correction algorithm. The proposed circuit is designed to meet the immense throughput required by OTN4, using commercially available FPGA technology....
The new Exponential Directional Iterative (EDI) 3-D Sn scheme for parallel adaptive differencing
International Nuclear Information System (INIS)
Sjoden, G.E.
2005-01-01
The new Exponential Directional Iterative (EDI) discrete ordinates (Sn) scheme for 3-D Cartesian Coordinates is presented. The EDI scheme is a logical extension of the positive, efficient Exponential Directional Weighted (EDW) Sn scheme currently used as the third level of the adaptive spatial differencing algorithm in the PENTRAN parallel discrete ordinates solver. Here, the derivation and advantages of the EDI scheme are presented; EDI uses EDW-rendered exponential coefficients as initial starting values to begin a fixed point iteration of the exponential coefficients. One issue that required evaluation was an iterative cutoff criterion to prevent the application of an unstable fixed point iteration; although this was needed in some cases, it was readily treated with a default to EDW. Iterative refinement of the exponential coefficients in EDI typically converged in fewer than four fixed point iterations. Moreover, EDI yielded more accurate angular fluxes compared to the other schemes tested, particularly in streaming conditions. Overall, it was found that the EDI scheme was up to an order of magnitude more accurate than the EDW scheme on a given mesh interval in streaming cases, and is potentially a good candidate as a fourth-level differencing scheme in the PENTRAN adaptive differencing sequence. The 3-D Cartesian computational cost of EDI was only about 20% more than the EDW scheme, and about 40% more than Diamond Zero (DZ). More evaluation and testing are required to determine suitable upgrade metrics for EDI to be fully integrated into the current adaptive spatial differencing sequence in PENTRAN. (author)
International Nuclear Information System (INIS)
Won, Jong Hyuck; Cho, Nam Zin
2011-01-01
In deterministic neutron transport methods, a process called fine-group to few-group condensation is used to reduce the computational burden. However, recent results on the core-reflector problem in fast reactor cores show that use of a small number of energy groups has limitation to describe neutron flux around core reflector interface. Therefore, researches are still ongoing to overcome this limitation. Recently, the authors proposed I) direct application of equivalently condensed angle-dependent total cross section to discrete ordinates method to overcome the limitation of conventional multi-group approximations, and II) local/global iteration framework in which fine-group discrete ordinates calculation is used in local problems while few-group transport calculation is used in the global problem iteratively. In this paper, an analysis of the core-reflector problem is performed in few-group structure using equivalent angle-dependent total cross section with local/global iteration. Numerical results are obtained under S 12 discrete ordinates-like transport method with scattering cross section up to P1 Legendre expansion
Recent developments in the Los Alamos radiation transport code system
International Nuclear Information System (INIS)
Forster, R.A.; Parsons, K.
1997-01-01
A brief progress report on updates to the Los Alamos Radiation Transport Code System (LARTCS) for solving criticality and fixed-source problems is provided. LARTCS integrates the Diffusion Accelerated Neutral Transport (DANT) discrete ordinates codes with the Monte Carlo N-Particle (MCNP) code. The LARCTS code is being developed with a graphical user interface for problem setup and analysis. Progress in the DANT system for criticality applications include a two-dimensional module which can be linked to a mesh-generation code and a faster iteration scheme. Updates to MCNP Version 4A allow statistical checks of calculated Monte Carlo results
Parallel SOL transport in MAST and JET: the impact of the mirror force
International Nuclear Information System (INIS)
Kirk, A; Fundamenski, W; Ahn, J-W; Counsell, G
2003-01-01
Interpretative modelling of the SOL plasma in conventional (JET) and tight (MAST) aspect ratio devices has been performed using OSM2/EIRENE. A detailed comparison has been made of the solutions of the fluid equations and one key issue uncovered by this modelling is the significance of the mirror force for the spherical tokamak (ST) SOL. This force is proportional to ∇ parallel B/B, which is typically a factor 10 larger in an ST due to the low aspect ratio. This term leads to changes in the charged particle velocity distributions near regions with large V parallel B/B representing an effective, upstream particle and momentum source. The modelling performed in this paper indicates that exclusion of the ∇ parallel B term may lead to incorrect conclusions on, for example, the upstream density, especially in STs
Implementation of a Monte Carlo algorithm for neutron transport on a massively parallel SIMD machine
International Nuclear Information System (INIS)
Baker, R.S.
1992-01-01
We present some results from the recent adaptation of a vectorized Monte Carlo algorithm to a massively parallel architecture. The performance of the algorithm on a single processor Cray Y-MP and a Thinking Machine Corporations CM-2 and CM-200 is compared for several test problems. The results show that significant speedups are obtainable for vectorized Monte Carlo algorithms on massively parallel machines, even when the algorithms are applied to realistic problems which require extensive variance reduction. However, the architecture of the Connection Machine does place some limitations on the regime in which the Monte Carlo algorithm may be expected to perform well
Implementation of a Monte Carlo algorithm for neutron transport on a massively parallel SIMD machine
International Nuclear Information System (INIS)
Baker, R.S.
1993-01-01
We present some results from the recent adaptation of a vectorized Monte Carlo algorithm to a massively parallel architecture. The performance of the algorithm on a single processor Cray Y-MP and a Thinking Machine Corporations CM-2 and CM-200 is compared for several test problems. The results show that significant speedups are obtainable for vectorized Monte Carlo algorithms on massively parallel machines, even when the algorithms are applied to realistic problems which require extensive variance reduction. However, the architecture of the Connection Machine does place some limitations on the regime in which the Monte Carlo algorithm may be expected to perform well. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Philip, Bobby, E-mail: philipb@ornl.gov [Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831 (United States); Berrill, Mark A.; Allu, Srikanth; Hamilton, Steven P.; Sampath, Rahul S.; Clarno, Kevin T. [Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831 (United States); Dilts, Gary A. [Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545 (United States)
2015-04-01
This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.
International Nuclear Information System (INIS)
Procassini, R J; Beck, B R
2004-01-01
It might be assumed that use of a ''high-quality'' random number generator (RNG), producing a sequence of ''pseudo random'' numbers with a ''long'' repetition period, is crucial for producing unbiased results in Monte Carlo particle transport simulations. While several theoretical and empirical tests have been devised to check the quality (randomness and period) of an RNG, for many applications it is not clear what level of RNG quality is required to produce unbiased results. This paper explores the issue of RNG quality in the context of parallel, Monte Carlo transport simulations in order to determine how ''good'' is ''good enough''. This study employs the MERCURY Monte Carlo code, which incorporates the CNPRNG library for the generation of pseudo-random numbers via linear congruential generator (LCG) algorithms. The paper outlines the usage of random numbers during parallel MERCURY simulations, and then describes the source and criticality transport simulations which comprise the empirical basis of this study. A series of calculations for each test problem in which the quality of the RNG (period of the LCG) is varied provides the empirical basis for determining the minimum repetition period which may be employed without producing a bias in the mean integrated results
Directory of Open Access Journals (Sweden)
Xueli Chen
2010-01-01
Full Text Available During the past decade, Monte Carlo method has obtained wide applications in optical imaging to simulate photon transport process inside tissues. However, this method has not been effectively extended to the simulation of free-space photon transport at present. In this paper, a uniform framework for noncontact optical imaging is proposed based on Monte Carlo method, which consists of the simulation of photon transport both in tissues and in free space. Specifically, the simplification theory of lens system is utilized to model the camera lens equipped in the optical imaging system, and Monte Carlo method is employed to describe the energy transformation from the tissue surface to the CCD camera. Also, the focusing effect of camera lens is considered to establish the relationship of corresponding points between tissue surface and CCD camera. Furthermore, a parallel version of the framework is realized, making the simulation much more convenient and effective. The feasibility of the uniform framework and the effectiveness of the parallel version are demonstrated with a cylindrical phantom based on real experimental results.
PARALLEL MEASUREMENT AND MODELING OF TRANSPORT IN THE DARHT II BEAMLINE ON ETA II
International Nuclear Information System (INIS)
Chambers, F W; Raymond, B A; Falabella, S; Lee, B S; Richardson, R A; Weir, J T; Davis, H A; Schultze, M E
2005-01-01
To successfully tune the DARHT II transport beamline requires the close coupling of a model of the beam transport and the measurement of the beam observables as the beam conditions and magnet settings are varied. For the ETA II experiment using the DARHT II beamline components this was achieved using the SUICIDE (Simple User Interface Connecting to an Integrated Data Environment) data analysis environment and the FITS (Fully Integrated Transport Simulation) model. The SUICIDE environment has direct access to the experimental beam transport data at acquisition and the FITS predictions of the transport for immediate comparison. The FITS model is coupled into the control system where it can read magnet current settings for real time modeling. We find this integrated coupling is essential for model verification and the successful development of a tuning aid for the efficient convergence on a useable tune. We show the real time comparisons of simulation and experiment and explore the successes and limitations of this close coupled approach
Energy Technology Data Exchange (ETDEWEB)
Miranda, A.B. de; Delmas, A; Sacadura, J F [Institut National des Sciences Appliquees (INSA), 69 - Villeurbanne (France)
1997-12-31
A formulation based on the use of the discrete ordinate method applied to the integral form of the radiant heat transfer equation is proposed for non-grey gases. The correlations between transmittances are neglected and no explicit wall reflexion is considered. The configuration analyzed consists in a flat layer of non-isothermal steam-nitrogen mixture. Cavity walls are grey with diffuse reflexion and emission. A narrow band statistical model is used to represent the radiative properties of the gas. The distribution of the radiative source term inside the cavity is calculated along two temperature profiles in a uniform steam concentration. Results obtained using this simplified approach are in good agreement with those found in the literature for the same temperature and concentration distributions. This preliminary study seems to indicate that the algorithm based on the integration of radiant heat transfer along the luminance path is less sensitive to de-correlation effects than formulations based on the differential form the the radiant heat transfer. Thus, a more systematic study of the influence of the neglecting of correlations on the integral approach is analyzed in this work. (J.S.) 16 refs.
Energy Technology Data Exchange (ETDEWEB)
Miranda, A.B. de; Delmas, A.; Sacadura, J.F. [Institut National des Sciences Appliquees (INSA), 69 - Villeurbanne (France)
1996-12-31
A formulation based on the use of the discrete ordinate method applied to the integral form of the radiant heat transfer equation is proposed for non-grey gases. The correlations between transmittances are neglected and no explicit wall reflexion is considered. The configuration analyzed consists in a flat layer of non-isothermal steam-nitrogen mixture. Cavity walls are grey with diffuse reflexion and emission. A narrow band statistical model is used to represent the radiative properties of the gas. The distribution of the radiative source term inside the cavity is calculated along two temperature profiles in a uniform steam concentration. Results obtained using this simplified approach are in good agreement with those found in the literature for the same temperature and concentration distributions. This preliminary study seems to indicate that the algorithm based on the integration of radiant heat transfer along the luminance path is less sensitive to de-correlation effects than formulations based on the differential form the the radiant heat transfer. Thus, a more systematic study of the influence of the neglecting of correlations on the integral approach is analyzed in this work. (J.S.) 16 refs.
Kuiroukidis, Ap.; Throumoulopoulos, G. N.
2015-08-01
We construct nonlinear toroidal equilibria of fixed diverted boundary shaping with reversed magnetic shear and flows parallel to the magnetic field. The equilibria have hole-like current density and the reversed magnetic shear increases as the equilibrium nonlinearity becomes stronger. Also, application of a sufficient condition for linear stability implies that the stability is improved as the equilibrium nonlinearity correlated to the reversed magnetic shear gets stronger with a weaker stabilizing contribution from the flow. These results indicate synergetic stabilizing effects of reversed magnetic shear, equilibrium nonlinearity and flow in the establishment of Internal Transport Barriers (ITBs).
Mills, R. T.; Rupp, K.; Smith, B. F.; Brown, J.; Knepley, M.; Zhang, H.; Adams, M.; Hammond, G. E.
2017-12-01
As the high-performance computing community pushes towards the exascale horizon, power and heat considerations have driven the increasing importance and prevalence of fine-grained parallelism in new computer architectures. High-performance computing centers have become increasingly reliant on GPGPU accelerators and "manycore" processors such as the Intel Xeon Phi line, and 512-bit SIMD registers have even been introduced in the latest generation of Intel's mainstream Xeon server processors. The high degree of fine-grained parallelism and more complicated memory hierarchy considerations of such "manycore" processors present several challenges to existing scientific software. Here, we consider how the massively parallel, open-source hydrologic flow and reactive transport code PFLOTRAN - and the underlying Portable, Extensible Toolkit for Scientific Computation (PETSc) library on which it is built - can best take advantage of such architectures. We will discuss some key features of these novel architectures and our code optimizations and algorithmic developments targeted at them, and present experiences drawn from working with a wide range of PFLOTRAN benchmark problems on these architectures.
Variational approach in transport theory
International Nuclear Information System (INIS)
Panta Pazos, R.; Tullio de Vilhena, M.
2004-01-01
In this work we present a variational approach to some methods to solve transport problems of neutral particles. We consider a convex domain X (for example the geometry of a slab, or a convex set in the plane, or a convex bounded set in the space) and we use discrete ordinates quadrature to get a system of differential equations derived from the neutron transport equation. The boundary conditions are vacuum for a subset of the boundary, and of specular reflection for the complementary subset of the boundary. Recently some different approximation methods have been presented to solve these transport problems. We introduce in this work the adjoint equations and the conjugate functions obtained by means of the variational approach. First we consider the general formulation, and then some numerical methods such as spherical harmonics and spectral collocation method. (authors)
Variational approach in transport theory
Energy Technology Data Exchange (ETDEWEB)
Panta Pazos, R. [Nucler Engineering Department, UFRGS, Porto-Alegre (Brazil); Tullio de Vilhena, M. [Institute of Mathematics, UFRGS, Porto-Alegre (Brazil)
2004-07-01
In this work we present a variational approach to some methods to solve transport problems of neutral particles. We consider a convex domain X (for example the geometry of a slab, or a convex set in the plane, or a convex bounded set in the space) and we use discrete ordinates quadrature to get a system of differential equations derived from the neutron transport equation. The boundary conditions are vacuum for a subset of the boundary, and of specular reflection for the complementary subset of the boundary. Recently some different approximation methods have been presented to solve these transport problems. We introduce in this work the adjoint equations and the conjugate functions obtained by means of the variational approach. First we consider the general formulation, and then some numerical methods such as spherical harmonics and spectral collocation method. (authors)
E.J. Spee (Edwin); P.M. de Zeeuw (Paul); J.G. Verwer (Jan); J.G. Blom (Joke); W. Hundsdorfer (Willem)
1996-01-01
textabstractAtmospheric air quality modeling relies in part on numerical simulation. Required numerical simulations are often hampered by lack of computer capacity and computational speed. This problem is most severe in the field of global modeling where transport and exchange of trace constituents
Multi-agent model predictive control for transportation networks : Serial versus parallel schemes
Negenborn, R.R.; De Schutter, B.; Hellendoorn, J.
2006-01-01
We consider the control of large-scale transportation networks, like road traffic networks, power distribution networks, water distribution networks, etc. Control of these networks is often not possible from a single point by a single intelligent control agent; instead control has to be performed
libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2015-04-01
This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2014-11-01
This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
International Nuclear Information System (INIS)
Rosa, Massimiliano; Warsa, James S.; Perks, Michael
2011-01-01
We have implemented a cell-wise, block-Gauss-Seidel (bGS) iterative algorithm, for the solution of the S_n transport equations on the Roadrunner hybrid, parallel computer architecture. A compute node of this massively parallel machine comprises AMD Opteron cores that are linked to a Cell Broadband Engine™ (Cell/B.E.)"1. LAPACK routines have been ported to the Cell/B.E. in order to make use of its parallel Synergistic Processing Elements (SPEs). The bGS algorithm is based on the LU factorization and solution of a linear system that couples the fluxes for all S_n angles and energy groups on a mesh cell. For every cell of a mesh that has been parallel decomposed on the higher-level Opteron processors, a linear system is transferred to the Cell/B.E. and the parallel LAPACK routines are used to compute a solution, which is then transferred back to the Opteron, where the rest of the computations for the S_n transport problem take place. Compared to standard parallel machines, a hundred-fold speedup of the bGS was observed on the hybrid Roadrunner architecture. Numerical experiments with strong and weak parallel scaling demonstrate the bGS method is viable and compares favorably to full parallel sweeps (FPS) on two-dimensional, unstructured meshes when it is applied to optically thick, multi-material problems. As expected, however, it is not as efficient as FPS in optically thin problems. (author)
Angular interpolations and splice options for three-dimensional transport computations
International Nuclear Information System (INIS)
Abu-Shumays, I.K.; Yehnert, C.E.
1996-01-01
New, accurate and mathematically rigorous angular Interpolation strategies are presented. These strategies preserve flow and directionality separately over each octant of the unit sphere, and are based on a combination of spherical harmonics expansions and least squares algorithms. Details of a three-dimensional to three-dimensional (3-D to 3-D) splice method which utilizes the new angular interpolations are summarized. The method has been implemented in a multidimensional discrete ordinates transport computer program. Various features of the splice option are illustrated by several applications to a benchmark Dog-Legged Void Neutron (DLVN) streaming and transport experimental assembly
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
International Nuclear Information System (INIS)
Zawaideh, E.; Najmabadi, F.; Conn, R.W.
1986-01-01
A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the magnetic field gradient L/sub B/ approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (lambda/L/sub B/) 2 , are found to have errors of order (lambda/L/sub u/) 2 = (lambda/L/sub B/) 2 /(1-M 2 ) 2 , where L/sub u/ is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (Mroughly-equal1)
The effect of plasma fluctuations on parallel transport parameters in the SOL
Czech Academy of Sciences Publication Activity Database
Havlíčková, Eva; Fundameski, W.; Naulin, V.; Nielsen, A.H.; Wiesen, S.; Horáček, Jan; Seidl, Jakub
2011-01-01
Roč. 415, č. 1 (2011), S471-S474 ISSN 0022-3115. [International Conference on Plasma-Surface Interactions in Controlled Fusion Device/19th./. San Diego, 24.05.2010-28.05.2010] R&D Projects: GA ČR GAP205/10/2055; GA MŠk 7G09042 Institutional research plan: CEZ:AV0Z20430508 Keywords : Tokamak * plasma * transport Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.052, year: 2011 http://www.sciencedirect.com/science/article/pii/S002231151000560X
International Nuclear Information System (INIS)
Santos, Marcelo C. dos; Pereira, Claudio M.N.A.; Schirru, Roberto; Pinheiro, André; Coordenacao de Pos-Graduacao e Pesquisa de Engenharia
2017-01-01
Atmospheric radionuclide dispersion systems (ARDS) are essential mechanisms to predict the consequences of unexpected radioactive releases from nuclear power plants. Considering, that during an eventuality of an accident with a radioactive material release, an accurate forecast is vital to guide the evacuation plan of the possible affected areas. However, in order to predict the dispersion of the radioactive material and its impact on the environment, the model must process information about source term (radioactive materials released, activities and location), weather condition (wind, humidity and precipitation) and geographical characteristics (topography). Furthermore, ARDS is basically composed of 4 main modules: Source Term, Wind Field, Plume Dispersion and Doses Calculations. The Wind Field and Plume Dispersion modules are the ones that require a high computational performance to achieve accurate results within an acceptable time. Taking this into account, this work focuses on the development of a GPU-based parallel Plume Dispersion module, focusing on the radionuclide transport and diffusion calculations, which use a given wind field and a released source term as parameters. The program is being developed using the C ++ programming language, allied with CUDA libraries. In comparative case study between a parallel and sequential version of the slower function of the Plume Dispersion module, a speedup of 11.63 times could be observed. (author)
Energy Technology Data Exchange (ETDEWEB)
Santos, Marcelo C. dos; Pereira, Claudio M.N.A.; Schirru, Roberto; Pinheiro, André, E-mail: jovitamarcelo@gmail.com, E-mail: cmnap@ien.gov.br, E-mail: schirru@lmp.ufrj.br, E-mail: apinheiro99@gmail.com [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil); Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear
2017-07-01
Atmospheric radionuclide dispersion systems (ARDS) are essential mechanisms to predict the consequences of unexpected radioactive releases from nuclear power plants. Considering, that during an eventuality of an accident with a radioactive material release, an accurate forecast is vital to guide the evacuation plan of the possible affected areas. However, in order to predict the dispersion of the radioactive material and its impact on the environment, the model must process information about source term (radioactive materials released, activities and location), weather condition (wind, humidity and precipitation) and geographical characteristics (topography). Furthermore, ARDS is basically composed of 4 main modules: Source Term, Wind Field, Plume Dispersion and Doses Calculations. The Wind Field and Plume Dispersion modules are the ones that require a high computational performance to achieve accurate results within an acceptable time. Taking this into account, this work focuses on the development of a GPU-based parallel Plume Dispersion module, focusing on the radionuclide transport and diffusion calculations, which use a given wind field and a released source term as parameters. The program is being developed using the C ++ programming language, allied with CUDA libraries. In comparative case study between a parallel and sequential version of the slower function of the Plume Dispersion module, a speedup of 11.63 times could be observed. (author)
Towards scalable parallelism in Monte Carlo particle transport codes using remote memory access
International Nuclear Information System (INIS)
Romano, Paul K.; Forget, Benoit; Brown, Forrest
2010-01-01
One forthcoming challenge in the area of high-performance computing is having the ability to run large-scale problems while coping with less memory per compute node. In this work, we investigate a novel data decomposition method that would allow Monte Carlo transport calculations to be performed on systems with limited memory per compute node. In this method, each compute node remotely retrieves a small set of geometry and cross-section data as needed and remotely accumulates local tallies when crossing the boundary of the local spatial domain. Initial results demonstrate that while the method does allow large problems to be run in a memory-limited environment, achieving scalability may be difficult due to inefficiencies in the current implementation of RMA operations. (author)
A fast, parallel algorithm to solve the basic fluvial erosion/transport equations
Braun, J.
2012-04-01
Quantitative models of landform evolution are commonly based on the solution of a set of equations representing the processes of fluvial erosion, transport and deposition, which leads to predict the geometry of a river channel network and its evolution through time. The river network is often regarded as the backbone of any surface processes model (SPM) that might include other physical processes acting at a range of spatial and temporal scales along hill slopes. The basic laws of fluvial erosion requires the computation of local (slope) and non-local (drainage area) quantities at every point of a given landscape, a computationally expensive operation which limits the resolution of most SPMs. I present here an algorithm to compute the various components required in the parameterization of fluvial erosion (and transport) and thus solve the basic fluvial geomorphic equation, that is very efficient because it is O(n) (the number of required arithmetic operations is linearly proportional to the number of nodes defining the landscape), and is fully parallelizable (the computation cost decreases in a direct inverse proportion to the number of processors used to solve the problem). The algorithm is ideally suited for use on latest multi-core processors. Using this new technique, geomorphic problems can be solved at an unprecedented resolution (typically of the order of 10,000 X 10,000 nodes) while keeping the computational cost reasonable (order 1 sec per time step). Furthermore, I will show that the algorithm is applicable to any regular or irregular representation of the landform, and is such that the temporal evolution of the landform can be discretized by a fully implicit time-marching algorithm, making it unconditionally stable. I will demonstrate that such an efficient algorithm is ideally suited to produce a fully predictive SPM that links observationally based parameterizations of small-scale processes to the evolution of large-scale features of the landscapes on
Introduction of Parallel GPGPU Acceleration Algorithms for the Solution of Radiative Transfer
Godoy, William F.; Liu, Xu
2011-01-01
General-purpose computing on graphics processing units (GPGPU) is a recent technique that allows the parallel graphics processing unit (GPU) to accelerate calculations performed sequentially by the central processing unit (CPU). To introduce GPGPU to radiative transfer, the Gauss-Seidel solution of the well-known expressions for 1-D and 3-D homogeneous, isotropic media is selected as a test case. Different algorithms are introduced to balance memory and GPU-CPU communication, critical aspects of GPGPU. Results show that speed-ups of one to two orders of magnitude are obtained when compared to sequential solutions. The underlying value of GPGPU is its potential extension in radiative solvers (e.g., Monte Carlo, discrete ordinates) at a minimal learning curve.
International Nuclear Information System (INIS)
Chen, C.T.; Li, S.H.
1997-01-01
Analytical solutions are developed for the problem of radionuclide transport in a system of parallel fractures situated in a porous rock matrix. A constant flux is used as the inlet boundary condition. The solutions consider the following processes: (a) advective transport along the fractures; (b) mechanical dispersion and molecular diffusion along the fractures; (c) molecular diffusion from a fracture to the porous matrix; (d) molecular diffusion within the porous matrix in the direction perpendicular to the fracture axis; (e) adsorption onto the fracture wall; (f) adsorption within the porous matrix, and (g) radioactive decay. The solutions are based on the Laplace transform method. The general transient solution is in the form of a double integral that is evaluated using composite Gauss-Legendre quadrature. A simpler transient solution that is in the form of a single integral is also presented for the case that assumes negligible longitudinal dispersion along the fractures. The steady-state solutions are also provided. A number of examples are given to illustrate the effects of various important parameters, including: (a) fracture spacing; (b) fracture dispersion coefficient; (c) matrix diffusion coefficient; (d) fracture width; (e) groundwater velocity; (f) matrix retardation factor; and (g) matrix porosity
Parallel transport studies of high-Z impurities in the core of Alcator C-Mod plasmas
Energy Technology Data Exchange (ETDEWEB)
Reinke, M. L.; Hutchinson, I. H.; Rice, J. E.; Greenwald, M.; Howard, N. T.; Hubbard, A.; Hughes, J. W.; Terry, J. L.; Wolfe, S. M. [MIT-Plasma Science and Fusion Center Cambridge, Massachusetts 02139 (United States)
2013-05-15
Measurements of poloidal variation, ñ{sub z}/
International Nuclear Information System (INIS)
Bacon, Diana H.; White, Mark D.; McGrail, B PETER
2004-01-01
The U.S. Department of Energy must approve a performance assessment (PA) to support the design, construction, approval, and closure of disposal facilities for immobilized low-activity waste (ILAW) currently stored in underground tanks at Hanford, Washington. A critical component of the PA is to provide quantitative estimates of radionuclide release rates from the engineered portion of the disposal facilities. Computer simulations are essential for this purpose because impacts on groundwater resources must be projected to periods of 10,000 years and longer. The computer code selected for simulating the radionuclide release rates is the Subsurface Transport Over Reactive Multiphases (STORM) simulator. The STORM simulator solves coupled conservation equations for component mass and energy that describe subsurface flow over aqueous and gas phases through variably saturated geologic media. The resulting flow fields are used to sequentially solve conservation equations for reactive aqueous phase transport through variably saturated geologic media. These conservation equations for component mass, energy, and solute mass are partial differential equations that mathematically describe flow and transport through porous media. The STORM simulator solves the governing-conservation equations and constitutive functions using numerical techniques for nonlinear systems. The partial differential equations governing thermal and fluid flow processes are solved by the integral volume finite difference method. These governing equations are solved simultaneously using Newton-Raphson iteration. The partial differential equations governing reactive solute transport are solved using either an operator split technique where geochemical reactions and solute transport are solved separately, or a fully coupled technique where these equations are solved simultaneously. The STORM simulator is written in the FORTRAN 77 language, following American National Standards Institute (ANSI) standards
International Nuclear Information System (INIS)
Mordant, Maurice.
1981-04-01
To solve a multigroup stationary neutron transport equation in two-dimensional geometries (X-Y), (R-O) or (R-Z) generally on uses discrete ordinates and rectangular meshes. The way to do it is then well known, well documented and somewhat obvious. If one needs to treat awkward geometries or distorted meshes, things are not so easy and the way to do it is no longer straightforward. We have studied this problem at Limeil Nuclear Center and as an alternative to Monte Carlo methods and code we have implemented in ZEPHYR code at least two efficient finite element solutions for Lagrangian meshes involving any kind of triangles and quadrilaterals
International Nuclear Information System (INIS)
Kobayashi, K.
2009-01-01
In 2001, an international cooperation on the 3D radiation transport benchmarks for simple geometries with void region was performed under the leadership of E. Sartori of OECD/NEA. There were contributions from eight institutions, where 6 contributions were by the discrete ordinate method and only two were by the spherical harmonics method. The 3D spherical harmonics program FFT3 by the finite Fourier transformation method has been improved for this presentation, and benchmark solutions for the 2D and 3D simple geometries with void region by the FFT2 and FFT3 are given showing fairly good accuracy. (authors)
Normal scheme for solving the transport equation independently of spatial discretization
International Nuclear Information System (INIS)
Zamonsky, O.M.
1993-01-01
To solve the discrete ordinates neutron transport equation, a general order nodal scheme is used, where nodes are allowed to have different orders of approximation and the whole system reaches a final order distribution. Independence in the election of system discretization and order of approximation is obtained without loss of accuracy. The final equations and the iterative method to reach a converged order solution were implemented in a two-dimensional computer code to solve monoenergetic, isotropic scattering, external source problems. Two benchmark problems were solved using different automatic selection order methods. Results show accurate solutions without spatial discretization, regardless of the initial selection of distribution order. (author)
Application of the Arbitrarily High Order Method to Coupled Electron Photon Transport
International Nuclear Information System (INIS)
Duo, Jose Ignacio
2004-01-01
This work is about the application of the Arbitrary High Order Nodal Method to coupled electron photon transport.A Discrete Ordinates code was enhanced and validated which permited to evaluate the advantages of using variable spatial development order per particle.The results obtained using variable spatial development and adaptive mesh refinement following an a posteriori error estimator are encouraging.Photon spectra for clinical accelerator target and, dose and charge depositio profiles are simulated in one-dimensional problems using cross section generated with CEPXS code.Our results are in good agreement with ONELD and MCNP codes
Li, Jiuyi; Busscher, Henk J.; van der Mei, Henny C.; Norde, Willem; Krom, Bastiaan P.; Sjollema, Jelmer
2011-01-01
Using a new phase-contrast microscopy-based method of analysis, sedimentation has recently been demonstrated to be the major mass transport mechanism of bacteria towards substratum surfaces in a parallel plate flow chamber (J. Li, H.J. Busscher, W. Norde, J. Sjollema, Colloid Surf. B. 84 (2011)76).
Los Alamos radiation transport code system on desktop computing platforms
International Nuclear Information System (INIS)
Briesmeister, J.F.; Brinkley, F.W.; Clark, B.A.; West, J.T.
1990-01-01
The Los Alamos Radiation Transport Code System (LARTCS) consists of state-of-the-art Monte Carlo and discrete ordinates transport codes and data libraries. These codes were originally developed many years ago and have undergone continual improvement. With a large initial effort and continued vigilance, the codes are easily portable from one type of hardware to another. The performance of scientific work-stations (SWS) has evolved to the point that such platforms can be used routinely to perform sophisticated radiation transport calculations. As the personal computer (PC) performance approaches that of the SWS, the hardware options for desk-top radiation transport calculations expands considerably. The current status of the radiation transport codes within the LARTCS is described: MCNP, SABRINA, LAHET, ONEDANT, TWODANT, TWOHEX, and ONELD. Specifically, the authors discuss hardware systems on which the codes run and present code performance comparisons for various machines
Unconditionally stable diffusion-acceleration of the transport equation
International Nuclear Information System (INIS)
Larson, E.W.
1982-01-01
The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically thick regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems, the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results
Unconditionally stable diffusion-acceleration of the transport equation
International Nuclear Information System (INIS)
Larsen, E.W.
1982-01-01
The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically large regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results
International Nuclear Information System (INIS)
Mula-Hernandez, Olga
2014-01-01
In this thesis, we have first developed a time dependent 3D neutron transport solver on unstructured meshes with discontinuous Galerkin finite elements spatial discretization. The solver (called MINARET) represents in itself an important contribution in reactor physics thanks to the accuracy that it can provide in the knowledge of the state of the core during severe accidents. It will also play an important role on vessel fluence calculations. From a mathematical point of view, the most important contribution has consisted in the implementation of modern algorithms that are well adapted for modern parallel architectures and that significantly decrease the computing times. A special effort has been done in order to efficiently parallelize the time variable by the use of the parareal in time algorithm. For this, we have first analyzed the performances that the classical scheme of parareal can provide when applied to the resolution of the neutron transport equation in a reactor core. Then, with the purpose of improving these performances, a parareal scheme that takes more efficiently into account the presence of other iterative schemes in the resolution of each time step has been proposed. The main idea consists in limiting the number of internal iterations for each time step and to reach convergence across the parareal iterations. A second phase of our work has been motivated by the following question: given the high degree of accuracy that MINARET can provide in the modeling of the neutron population, could we somehow use it as a tool to monitor in real time the population of neutrons on the purpose of helping in the operation of the reactor? And, what is more, how to make such a tool be coherent in some sense with the measurements taken in situ? One of the main challenges of this problem is the real time aspect of the simulations. Indeed, despite all of our efforts to speed-up the calculations, the discretization methods used in MINARET do not provide simulations
Calculations on safe storage and transportation of radioactive materials
Energy Technology Data Exchange (ETDEWEB)
Hathout, A M; El-Messiry, A M; Amin, E [National Center for Nuclear Safety and Radiation Control and AEA, Cairo (Egypt)
1997-12-31
In this work the safe storage and transportation of fresh fuel as a radioactive material studied. Egypt planned ET RR 2 reactor which is of relatively high power and would require adequate handling and transportation. Therefore, the present work is initiated to develop a procedure for safe handling and transportation of radioactive materials. The possibility of reducing the magnitude of radiation transmitted on the exterior of the packages is investigated. Neutron absorbers are used to decrease the neutron flux. Criticality calculations are carried out to ensure the achievement of subcriticality so that the inherent safety can be verified. The discrete ordinate transport code ANISN was used. The results show good agreement with other techniques. 2 figs., 2 tabs.
International Nuclear Information System (INIS)
Mori, Takamasa; Nakagawa, Masayuki; Sasaki, Makoto.
1988-11-01
We have developed a group of computer codes to realize the accurate transport calculation by using the multi-group double-differential form cross section. This type of cross section can correctly take account of the energy-angle correlated reaction kinematics. Accordingly, the transport phenomena in materials with highly anisotropic scattering are accurately calculated by using this cross section. They include the following four codes or code systems: PROF-DD : a code system to generate the multi-group double-differential form cross section library by processing basic nuclear data file compiled in the ENDF / B-IV or -V format, ANISN-DD : a one-dimensional transport code based on the discrete ordinate method, DOT-DD : a two-dimensional transport code based on the discrete ordinate method, MORSE-DD : a three-dimensional transport code based on the Monte Carlo method. In addition to these codes, several auxiliary codes have been developed to process calculated results. This report describes the calculation algorithm employed in these codes and how to use them. (author)
International Nuclear Information System (INIS)
Masahiro, Tatsumi; Akio, Yamamoto
2003-01-01
A production code SCOPE2 was developed based on the fine-grained parallel algorithm by the red/black iterative method targeting parallel computing environments such as a PC-cluster. It can perform a depletion calculation in a few hours using a PC-cluster with the model based on a 9-group nodal-SP3 transport method in 3-dimensional pin-by-pin geometry for in-core fuel management of commercial PWRs. The present algorithm guarantees the identical convergence process as that in serial execution, which is very important from the viewpoint of quality management. The fine-mesh geometry is constructed by hierarchical decomposition with introduction of intermediate management layer as a block that is a quarter piece of a fuel assembly in radial direction. A combination of a mesh division scheme forcing even meshes on each edge and a latency-hidden communication algorithm provided simplicity and efficiency to message passing to enhance parallel performance. Inter-processor communication and parallel I/O access were realized using the MPI functions. Parallel performance was measured for depletion calculations by the 9-group nodal-SP3 transport method in 3-dimensional pin-by-pin geometry with 340 x 340 x 26 meshes for full core geometry and 170 x 170 x 26 for quarter core geometry. A PC cluster that consists of 24 Pentium-4 processors connected by the Fast Ethernet was used for the performance measurement. Calculations in full core geometry gave better speedups compared to those in quarter core geometry because of larger granularity. Fine-mesh sweep and feedback calculation parts gave almost perfect scalability since granularity is large enough, while 1-group coarse-mesh diffusion acceleration gave only around 80%. The speedup and parallel efficiency for total computation time were 22.6 and 94%, respectively, for the calculation in full core geometry with 24 processors. (authors)
International Nuclear Information System (INIS)
Blakeman, E.D.
2000-01-01
A software system, GRAVE (Geometry Rendering and Visual Editor), has been developed at the Oak Ridge National Laboratory (ORNL) to perform interactive visualization and development of models used as input to the TORT three-dimensional discrete ordinates radiation transport code. Three-dimensional and two-dimensional visualization displays are included. Display capabilities include image rotation, zoom, translation, wire-frame and translucent display, geometry cuts and slices, and display of individual component bodies and material zones. The geometry can be interactively edited and saved in TORT input file format. This system is an advancement over the current, non-interactive, two-dimensional display software. GRAVE is programmed in the Java programming language and can be implemented on a variety of computer platforms. Three- dimensional visualization is enabled through the Visualization Toolkit (VTK), a free-ware C++ software library developed for geometric and data visual display. Future plans include an extension of the system to read inputs using binary zone maps and combinatorial geometry models containing curved surfaces, such as those used for Monte Carlo code inputs. Also GRAVE will be extended to geometry visualization/editing for the DORT two-dimensional transport code and will be integrated into a single GUI-based system for all of the ORNL discrete ordinates transport codes
Energy Technology Data Exchange (ETDEWEB)
Lillie, R.A.; Robinson, J.C.
1976-05-01
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures.
International Nuclear Information System (INIS)
Lillie, R.A.; Robinson, J.C.
1976-05-01
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures
International Nuclear Information System (INIS)
Peeters, A. G.; Camenen, Y.; Casson, F. J.; Hornsby, W. A.; Snodin, A. P.; Strintzi, D.; Angioni, C.
2009-01-01
The paper derives the gyro-kinetic equation in the comoving frame of a toroidally rotating plasma, including both the Coriolis drift effect [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)] as well as the centrifugal force. The relation with the laboratory frame is discussed. A low field side gyro-fluid model is derived from the gyro-kinetic equation and applied to the description of parallel momentum transport. The model includes the effects of the Coriolis and centrifugal force as well as the parallel dynamics. The latter physics effect allows for a consistent description of both the Coriolis drift effect as well as the ExB shear effect [R. R. Dominguez and G. M. Staebler, Phys. Fluids B 5, 3876 (1993)] on the momentum transport. Strong plasma rotation as well as parallel dynamics reduce the Coriolis (inward) pinch of momentum and can lead to a sign reversal generating an outward pinch velocity. Also, the ExB shear effect is, in a similar manner, reduced by the parallel dynamics and stronger rotation.
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Wienke, H.; Herman, M.
1998-01-01
Evaluated neutron reaction data and photon-atom interaction cross sections for materials contained in the general purpose Fusion Evaluated Nuclear Data Library (FENDL/E2.0) have been processed with the NJOY code system into VITAMIN-J multigroup structure, for use in discrete-ordinates transport codes, and into continuous energy ACE format, for use in the Monte Carlo transport code MCNP. This document summarizes the resulting data libraries FENDL/MG-2.0 version 1 and FENDL/MC-2.0 version 1. The data are available costfree from the IAEA Nuclear Data Section online or on magnetic tape. (author)
Charged-particle calculations using Boltzmann transport methods
International Nuclear Information System (INIS)
Hoffman, T.J.; Dodds, H.L. Jr.; Robinson, M.T.; Holmes, D.K.
1981-01-01
Several aspects of radiation damage effects in fusion reactor neutron and ion irradiation environments are amenable to treatment by transport theory methods. In this paper, multigroup transport techniques are developed for the calculation of charged particle range distributions, reflection coefficients, and sputtering yields. The Boltzmann transport approach can be implemented, with minor changes, in standard neutral particle computer codes. With the multigroup discrete ordinates code, ANISN, determination of ion and target atom distributions as functions of position, energy, and direction can be obtained without the stochastic error associated with atomistic computer codes such as MARLOWE and TRIM. With the multigroup Monte Carlo code, MORSE, charged particle effects can be obtained for problems associated with very complex geometries. Results are presented for several charged particle problems. Good agreement is obtained between quantities calculated with the multigroup approach and those obtained experimentally or by atomistic computer codes
Spatial domain decomposition for neutron transport problems
International Nuclear Information System (INIS)
Yavuz, M.; Larsen, E.W.
1989-01-01
A spatial Domain Decomposition method is proposed for modifying the Source Iteration (SI) and Diffusion Synthetic Acceleration (DSA) algorithms for solving discrete ordinates problems. The method, which consists of subdividing the spatial domain of the problem and performing the transport sweeps independently on each subdomain, has the advantage of being parallelizable because the calculations in each subdomain can be performed on separate processors. In this paper we describe the details of this spatial decomposition and study, by numerical experimentation, the effect of this decomposition on the SI and DSA algorithms. Our results show that the spatial decomposition has little effect on the convergence rates until the subdomains become optically thin (less than about a mean free path in thickness)
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Jejcic, A.; Maillard, J.; Maurel, G.; Silva, J.; Wolff-Bacha, F.
1997-01-01
The work in the field of parallel processing has developed as research activities using several numerical Monte Carlo simulations related to basic or applied current problems of nuclear and particle physics. For the applications utilizing the GEANT code development or improvement works were done on parts simulating low energy physical phenomena like radiation, transport and interaction. The problem of actinide burning by means of accelerators was approached using a simulation with the GEANT code. A program of neutron tracking in the range of low energies up to the thermal region has been developed. It is coupled to the GEANT code and permits in a single pass the simulation of a hybrid reactor core receiving a proton burst. Other works in this field refers to simulations for nuclear medicine applications like, for instance, development of biological probes, evaluation and characterization of the gamma cameras (collimators, crystal thickness) as well as the method for dosimetric calculations. Particularly, these calculations are suited for a geometrical parallelization approach especially adapted to parallel machines of the TN310 type. Other works mentioned in the same field refer to simulation of the electron channelling in crystals and simulation of the beam-beam interaction effect in colliders. The GEANT code was also used to simulate the operation of germanium detectors designed for natural and artificial radioactivity monitoring of environment
Energy Technology Data Exchange (ETDEWEB)
Bian, Nicolas H.; Kontar, Eduard P. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom); Emslie, A. Gordon, E-mail: n.bian@physics.gla.ac.uk, E-mail: emslieg@wku.edu [Department of Physics and Astronomy, Western Kentucky University, Bowling Green, KY 42101 (United States)
2016-06-20
The transport of the energy contained in electrons, both thermal and suprathermal, in solar flares plays a key role in our understanding of many aspects of the flare phenomenon, from the spatial distribution of hard X-ray emission to global energetics. Motivated by recent RHESSI observations that point to the existence of a mechanism that confines electrons to the coronal parts of flare loops more effectively than Coulomb collisions, we here consider the impact of pitch-angle scattering off turbulent magnetic fluctuations on the parallel transport of electrons in flaring coronal loops. It is shown that the presence of such a scattering mechanism in addition to Coulomb collisional scattering can significantly reduce the parallel thermal and electrical conductivities relative to their collisional values. We provide illustrative expressions for the resulting thermoelectric coefficients that relate the thermal flux and electrical current density to the temperature gradient and the applied electric field. We then evaluate the effect of these modified transport coefficients on the flare coronal temperature that can be attained, on the post-impulsive-phase cooling of heated coronal plasma, and on the importance of the beam-neutralizing return current on both ambient heating and the energy loss rate of accelerated electrons. We also discuss the possible ways in which anomalous transport processes have an impact on the required overall energy associated with accelerated electrons in solar flares.
An analytical approach for a nodal scheme of two-dimensional neutron transport problems
International Nuclear Information System (INIS)
Barichello, L.B.; Cabrera, L.C.; Prolo Filho, J.F.
2011-01-01
Research highlights: → Nodal equations for a two-dimensional neutron transport problem. → Analytical Discrete Ordinates Method. → Numerical results compared with the literature. - Abstract: In this work, a solution for a two-dimensional neutron transport problem, in cartesian geometry, is proposed, on the basis of nodal schemes. In this context, one-dimensional equations are generated by an integration process of the multidimensional problem. Here, the integration is performed for the whole domain such that no iterative procedure between nodes is needed. The ADO method is used to develop analytical discrete ordinates solution for the one-dimensional integrated equations, such that final solutions are analytical in terms of the spatial variables. The ADO approach along with a level symmetric quadrature scheme, lead to a significant order reduction of the associated eigenvalues problems. Relations between the averaged fluxes and the unknown fluxes at the boundary are introduced as the usually needed, in nodal schemes, auxiliary equations. Numerical results are presented and compared with test problems.
International Nuclear Information System (INIS)
Torres, L.M.R.; Gomes, I.C.; Maiorino, J.R.
1986-01-01
The ANISN and DOT 3.5 codes solve the transport equation using the discrete ordinate method, in one and two-dimensions, respectively. The objectives of the study were to modify these two codes, frequently used in reactor shielding problems, to include nuclear heating calculations due to the interaction of neutrons and gamma-rays with matter. In order to etermine the temperature distribution, a numerical algorithm was developed using the finite difference method to solve the heat conduction equation, in one and two-dimensions, considering the nuclear heating from neutron and gamma-rays, as the source term. (Author) [pt
Zhang, Ya-Jing; Zhang, Lian-Lian; Jiang, Cui; Gong, Wei-Jiang
2018-02-01
We theoretically investigate the electronic transport through a parallel-coupled multi-quantum-dot system, in which the terminal dots of a one-dimensional quantum-dot chain are embodied in the two arms of an Aharonov-Bohm interferometer. It is found that in the structures of odd(even) dots, all their even(odd) molecular states have opportunities to decouple from the leads, and in this process antiresonance occurs which are accordant with the odd(even)-numbered eigenenergies of the sub-molecule without terminal dots. Next when Majorana zero modes are introduced to couple laterally to the terminal dots, the antiresonance and decoupling phenomena still co-exist in the quantum transport process. Such a result can be helpful in understanding the special influence of Majorana zero mode on the electronic transport through quantum-dot systems.
Integro-differential transport approaches
International Nuclear Information System (INIS)
Stepanek, J.; Arkuszewski, J.; Boffi, V.; Matausek, M.V.
1981-01-01
This chapter summarizes the work done in Italy, Poland, Switzerland and Yugoslavia in the field of integro-differential neutron transport theory. It reflects different viewpoints in the handling of the subject. Some of the methods are based only on the solution of the integro-differential equation, others use only the integral form of the transport equation. Use of the characteristic solution closely related to the integral equation (ARKUSZEWSKI et al.,(1979)) seems to be a rather effective way to accelerate the 2 dimensional discrete ordinates (Ssub(n)) transport methods and supress one of the main disadvantages, the ray effect. The advanced ''Surface Currents'' (MAEDER (1975)) and ''Surface Flux'' (STEPANEK (1979)) methods are based on the solution of both the integro-differential and integral form of the transport equation. As long as the spatial fluxes were considered to be flat in each region only the integral form of the transport equation was considered. The solution seems to be the best method of simple handling the higher order Legendre polynomials used to approximate spatial and angular flux distribution. The coupling of the Bsub(n) integral transport equations with the related Psub(n) equations removes the greatest disadvantage of the Psub(n) theory and closes the system of the Psub(n) equations (LIGOU, STEPANEK (1974))
MORSE-C, Neutron Transport, Gamma Transport for Criticality Calculation by Monte-Carlo Method
International Nuclear Information System (INIS)
2002-01-01
1 - Description of program or function: MORSE-C is a Monte-Carlo code to solve the multiple energy group form of the Boltzmann transport equation in order to obtain the eigenvalue (multiplication) when fissionable materials are present. Cross sections for up to 100 energy groups may be employed. The angular scattering is treated by the usual Legendre expansion as used in the discrete ordinates codes. Up-scattering may be specified. The geometry is defined by relationships to general 1. or 2. degree surfaces. Array units may be specified. Output includes, besides the usual values of input quantities, plots of the geometry, calculated volumes and masses, and graphs of results to assist the user in determining the correctness of the problem's solution
A vector/parallel method for a three-dimensional transport model coupled with bio-chemical terms
B.P. Sommeijer (Ben); J. Kok (Jan)
1995-01-01
textabstractA so-called fractional step method is considered for the time integration of a three-dimensional transport-chemical model in shallow seas. In this method, the transport part and the chemical part are treated separately by appropriate integration techniques. This separation is motivated
The spectral volume method as applied to transport problems
International Nuclear Information System (INIS)
McClarren, Ryan G.
2011-01-01
We present a new spatial discretization for transport problems: the spectral volume method. This method, rst developed by Wang for computational fluid dynamics, divides each computational cell into several sub-cells and enforces particle balance on each of these sub-cells. Also, these sub-cells are used to build a polynomial reconstruction in the cell. The idea of dividing cells into many cells is a generalization of the simple corner balance and other similar schemes. The spectral volume method preserves particle conservation and preserves the asymptotic diffusion limit. We present results from the method on two transport problems in slab geometry using discrete ordinates and second through sixth order spectral volume schemes. The numerical results demonstrate the accuracy and preservation of the diffusion limit of the spectral volume method. Future work will explore possible bene ts of the scheme for high-performance computing and for resolving diffusive boundary layers. (author)
International Nuclear Information System (INIS)
Odry, Nans
2016-01-01
Deterministic calculation schemes are devised to numerically solve the neutron transport equation in nuclear reactors. Dealing with core-sized problems is very challenging for computers, so much that the dedicated core calculations have no choice but to allow simplifying assumptions (assembly- then core scale steps..). The PhD work aims at overcoming some of these approximations: thanks to important changes in computer architecture and capacities (HPC), nowadays one can solve 3D core-sized problems, using both high mesh refinement and the transport operator. It is an essential step forward in order to perform, in the future, reference calculations using deterministic schemes. This work focuses on a spatial domain decomposition method (DDM). Using massive parallelism, DDM allows much more ambitious computations in terms of both memory requirements and calculation time. Developments were performed inside the Sn core solver Minaret, from the new CEA neutronics platform APOLLO3. Only fast reactors (hexagonal periodicity) are considered, even if all kinds of geometries can be dealt with, using Minaret. The work has been divided in four steps: 1) The spatial domain decomposition with no overlap is inserted into the standard algorithmic structure of Minaret. The fundamental idea involves splitting a core-sized problem into smaller, independent, spatial sub-problems. angular flux is exchanged between adjacent sub-domains. In doing so, all combined sub-problems converge to the global solution at the outcome of an iterative process. Various strategies were explored regarding both data management and algorithm design. Results (k eff and flux) are systematically compared to the reference in a numerical verification step. 2) Introducing more parallelism is an unprecedented opportunity to heighten performances of deterministic schemes. Domain decomposition is particularly suited to this. A two-layer hybrid parallelism strategy, suited to HPC, is chosen. It benefits from the
International Nuclear Information System (INIS)
Hong, Ser Gi; Lee, Deokjung
2015-01-01
A highly accurate S 4 eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S N order angular quadrature using two sub-cell balance equations and the S 4 eigenfunctions of within-group transport equation. The four eigenfunctions from S 4 approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes. (author)
Masciopinto, Costantino; Volpe, Angela; Palmiotta, Domenico; Cherubini, Claudia
2010-09-01
A combination of a parallel fracture model with the PHREEQC-2 geochemical model was developed to simulate sequential flow and chemical transport with reactions in fractured media where both laminar and turbulent flows occur. The integration of non-laminar flow resistances in one model produced relevant effects on water flow velocities, thus improving model prediction capabilities on contaminant transport. The proposed conceptual model consists of 3D rock-blocks, separated by horizontal bedding plane fractures with variable apertures. Particle tracking solved the transport equations for conservative compounds and provided input for PHREEQC-2. For each cluster of contaminant pathways, PHREEQC-2 determined the concentration for mass-transfer, sorption/desorption, ion exchange, mineral dissolution/precipitation and biodegradation, under kinetically controlled reactive processes of equilibrated chemical species. Field tests have been performed for the code verification. As an example, the combined model has been applied to a contaminated fractured aquifer of southern Italy in order to simulate the phenol transport. The code correctly fitted the field available data and also predicted a possible rapid depletion of phenols as a result of an increased biodegradation rate induced by a simulated artificial injection of nitrates, upgradient to the sources.
International Nuclear Information System (INIS)
Moriakov, A.; Vasyukhno, V.; Netecha, M.; Khacheresov, G.
2003-01-01
Powerful supercomputers are available today. MBC-1000M is one of Russian supercomputers that may be used by distant way access. Programs LUCKY and LUCKY C were created to work for multi-processors systems. These programs have algorithms created especially for these computers and used MPI (message passing interface) service for exchanges between processors. LUCKY may resolved shielding tasks by multigroup discreet ordinate method. LUCKY C may resolve critical tasks by same method. Only XYZ orthogonal geometry is available. Under little space steps to approximate discreet operator this geometry may be used as universal one to describe complex geometrical structures. Cross section libraries are used up to P8 approximation by Legendre polynomials for nuclear data in GIT format. Programming language is Fortran-90. 'Vector' processors may be used that lets get a time profit up to 30 times. But unfortunately MBC-1000M has not these processors. Nevertheless sufficient value for efficiency of parallel calculations was obtained under 'space' (LUCKY) and 'space and energy' (LUCKY C ) paralleling. AUTOCAD program is used to control geometry after a treatment of input data. Programs have powerful geometry module, it is a beautiful tool to achieve any geometry. Output results may be processed by graphic programs on personal computer. (authors)
International Nuclear Information System (INIS)
Badal, Andreu; Badano, Aldo
2009-01-01
Purpose: It is a known fact that Monte Carlo simulations of radiation transport are computationally intensive and may require long computing times. The authors introduce a new paradigm for the acceleration of Monte Carlo simulations: The use of a graphics processing unit (GPU) as the main computing device instead of a central processing unit (CPU). Methods: A GPU-based Monte Carlo code that simulates photon transport in a voxelized geometry with the accurate physics models from PENELOPE has been developed using the CUDA programming model (NVIDIA Corporation, Santa Clara, CA). Results: An outline of the new code and a sample x-ray imaging simulation with an anthropomorphic phantom are presented. A remarkable 27-fold speed up factor was obtained using a GPU compared to a single core CPU. Conclusions: The reported results show that GPUs are currently a good alternative to CPUs for the simulation of radiation transport. Since the performance of GPUs is currently increasing at a faster pace than that of CPUs, the advantages of GPU-based software are likely to be more pronounced in the future.
Energy Technology Data Exchange (ETDEWEB)
Badal, Andreu; Badano, Aldo [Division of Imaging and Applied Mathematics, OSEL, CDRH, U.S. Food and Drug Administration, Silver Spring, Maryland 20993-0002 (United States)
2009-11-15
Purpose: It is a known fact that Monte Carlo simulations of radiation transport are computationally intensive and may require long computing times. The authors introduce a new paradigm for the acceleration of Monte Carlo simulations: The use of a graphics processing unit (GPU) as the main computing device instead of a central processing unit (CPU). Methods: A GPU-based Monte Carlo code that simulates photon transport in a voxelized geometry with the accurate physics models from PENELOPE has been developed using the CUDA programming model (NVIDIA Corporation, Santa Clara, CA). Results: An outline of the new code and a sample x-ray imaging simulation with an anthropomorphic phantom are presented. A remarkable 27-fold speed up factor was obtained using a GPU compared to a single core CPU. Conclusions: The reported results show that GPUs are currently a good alternative to CPUs for the simulation of radiation transport. Since the performance of GPUs is currently increasing at a faster pace than that of CPUs, the advantages of GPU-based software are likely to be more pronounced in the future.
Badal, Andreu; Badano, Aldo
2009-11-01
It is a known fact that Monte Carlo simulations of radiation transport are computationally intensive and may require long computing times. The authors introduce a new paradigm for the acceleration of Monte Carlo simulations: The use of a graphics processing unit (GPU) as the main computing device instead of a central processing unit (CPU). A GPU-based Monte Carlo code that simulates photon transport in a voxelized geometry with the accurate physics models from PENELOPE has been developed using the CUDATM programming model (NVIDIA Corporation, Santa Clara, CA). An outline of the new code and a sample x-ray imaging simulation with an anthropomorphic phantom are presented. A remarkable 27-fold speed up factor was obtained using a GPU compared to a single core CPU. The reported results show that GPUs are currently a good alternative to CPUs for the simulation of radiation transport. Since the performance of GPUs is currently increasing at a faster pace than that of CPUs, the advantages of GPU-based software are likely to be more pronounced in the future.
Solution and study of nodal neutron transport equation applying the LTSN-DiagExp method
International Nuclear Information System (INIS)
Hauser, Eliete Biasotto; Pazos, Ruben Panta; Vilhena, Marco Tullio de; Barros, Ricardo Carvalho de
2003-01-01
In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtained the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)
Multigroup calculations of low-energy neutral transport in tokamak plasmas
International Nuclear Information System (INIS)
Gilligan, J.G.; Gralnick, S.L.; Price, W.G. Jr.; Kammash, T.
1978-01-01
Multigroup discrete ordinates methods avoid many of the approximations that have been used in previous neutral transport analyses. Of particular interest are the neutral profiles generated as an integral part of larger plasma system simulation codes. To determine the appropriateness of utilizing a particular multigroup code, ANISN, for this purpose, results are compared with the neutral transport module of the Duechs code. For a typical TFTR plasma, predicted neutral densities differ by a maximum factor of three on axis and outfluxes at the plasma boundary by approximately 40%. This is found to be significant for a neutral transport module. Possible sources of the observed discrepancies are indicated from an analysis of the approximations used in the Duechs model. Recommendations are made concerning the future application of the multigroup method. (author)
Transport calculation of medium-energy protons and neutrons by Monte Carlo method
International Nuclear Information System (INIS)
Ban, Syuuichi; Hirayama, Hideo; Katoh, Kazuaki.
1978-09-01
A Monte Carlo transport code, ARIES, has been developed for protons and neutrons at medium energy (25 -- 500 MeV). Nuclear data provided by R.G. Alsmiller, Jr. were used for the calculation. To simulate the cascade development in the medium, each generation was represented by a single weighted particle and an average number of emitted particles was used as the weight. Neutron fluxes were stored by the collisions density method. The cutoff energy was set to 25 MeV. Neutrons below the cutoff were stored to be used as the source for the low energy neutron transport calculation upon the discrete ordinates method. Then transport calculations were performed for both low energy neutrons (thermal -- 25 MeV) and secondary gamma-rays. Energy spectra of emitted neutrons were calculated and compared with those of published experimental and calculated results. The agreement was good for the incident particles of energy between 100 and 500 MeV. (author)
Olbrant, Edgar; Frank, Martin
2010-12-01
In this paper, we study a deterministic method for particle transport in biological tissues. The method is specifically developed for dose calculations in cancer therapy and for radiological imaging. Generalized Fokker-Planck (GFP) theory [Leakeas and Larsen, Nucl. Sci. Eng. 137 (2001), pp. 236-250] has been developed to improve the Fokker-Planck (FP) equation in cases where scattering is forward-peaked and where there is a sufficient amount of large-angle scattering. We compare grid-based numerical solutions to FP and GFP in realistic medical applications. First, electron dose calculations in heterogeneous parts of the human body are performed. Therefore, accurate electron scattering cross sections are included and their incorporation into our model is extensively described. Second, we solve GFP approximations of the radiative transport equation to investigate reflectance and transmittance of light in biological tissues. All results are compared with either Monte Carlo or discrete-ordinates transport solutions.
Quadratic Finite Element Method for 1D Deterministic Transport
International Nuclear Information System (INIS)
Tolar, D R Jr.; Ferguson, J M
2004-01-01
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ((und r)) and angular ((und (Omega))) dependences on the angular flux ψ(und r),(und (Omega))are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of ψ(und r),(und (Omega)). Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable (μ) in developing the one-dimensional (1D) spherical geometry S N equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S N algorithms
Error Estimation and Accuracy Improvements in Nodal Transport Methods
International Nuclear Information System (INIS)
Zamonsky, O.M.
2000-01-01
The accuracy of the solutions produced by the Discrete Ordinates neutron transport nodal methods is analyzed.The obtained new numerical methodologies increase the accuracy of the analyzed scheems and give a POSTERIORI error estimators. The accuracy improvement is obtained with new equations that make the numerical procedure free of truncation errors and proposing spatial reconstructions of the angular fluxes that are more accurate than those used until present. An a POSTERIORI error estimator is rigurously obtained for one dimensional systems that, in certain type of problems, allows to quantify the accuracy of the solutions. From comparisons with the one dimensional results, an a POSTERIORI error estimator is also obtained for multidimensional systems. LOCAL indicators, which quantify the spatial distribution of the errors, are obtained by the decomposition of the menctioned estimators. This makes the proposed methodology suitable to perform adaptive calculations. Some numerical examples are presented to validate the theoretical developements and to illustrate the ranges where the proposed approximations are valid
International Nuclear Information System (INIS)
Barros, R. C.; Filho, H. A.; Platt, G. M.; Oliveira, F. B. S.; Militao, D. S.
2009-01-01
Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two analytical reconstruction schemes for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S N ) transport model in slab geometry. The first scheme we describe is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the spatial grid set up on the slab. The second scheme is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction schemes, as described in this paper. (authors)
Directory of Open Access Journals (Sweden)
Sang Soon Hwang
2008-03-01
Full Text Available Modeling and simulation for heat and mass transport in micro channel are beingused extensively in researches and industrial applications to gain better understanding of thefundamental processes and to optimize fuel cell designs before building a prototype forengineering application. In this study, we used a single-phase, fully three dimensionalsimulation model for PEMFC that can deal with both anode and cathode flow field forexamining the micro flow channel with electrochemical reaction. The results show thathydrogen and oxygen were solely supplied to the membrane by diffusion mechanism ratherthan convection transport, and the higher pressure drop at cathode side is thought to becaused by higher flow rate of oxygen at cathode. And it is found that the amount of water incathode channel was determined by water formation due to electrochemical reaction pluselectro-osmotic mass flux directing toward the cathode side. And it is very important tomodel the back diffusion and electro-osmotic mass flux accurately since the two flux wasclosely correlated each other and greatly influenced for determination of ionic conductivityof the membrane which directly affects the performance of fuel cell.
Lee, Pil Hyong; Han, Sang Seok; Hwang, Sang Soon
2008-03-03
Modeling and simulation for heat and mass transport in micro channel are beingused extensively in researches and industrial applications to gain better understanding of thefundamental processes and to optimize fuel cell designs before building a prototype forengineering application. In this study, we used a single-phase, fully three dimensionalsimulation model for PEMFC that can deal with both anode and cathode flow field forexamining the micro flow channel with electrochemical reaction. The results show thathydrogen and oxygen were solely supplied to the membrane by diffusion mechanism ratherthan convection transport, and the higher pressure drop at cathode side is thought to becaused by higher flow rate of oxygen at cathode. And it is found that the amount of water incathode channel was determined by water formation due to electrochemical reaction pluselectro-osmotic mass flux directing toward the cathode side. And it is very important tomodel the back diffusion and electro-osmotic mass flux accurately since the two flux wasclosely correlated each other and greatly influenced for determination of ionic conductivityof the membrane which directly affects the performance of fuel cell.
International Nuclear Information System (INIS)
Fevotte, F.; Lathuiliere, B.
2013-01-01
The large increase in computing power over the past few years now makes it possible to consider developing 3D full-core heterogeneous deterministic neutron transport solvers for reference calculations. Among all approaches presented in the literature, the method first introduced in [1] seems very promising. It consists in iterating over resolutions of 2D and ID MOC problems by taking advantage of prismatic geometries without introducing approximations of a low order operator such as diffusion. However, before developing a solver with all industrial options at EDF, several points needed to be clarified. In this work, we first prove the convergence of this iterative process, under some assumptions. We then present our high-performance, parallel implementation of this algorithm in the MICADO solver. Benchmarking the solver against the Takeda case shows that the 2D-1D coupling algorithm does not seem to affect the spatial convergence order of the MOC solver. As for performance issues, our study shows that even though the data distribution is suited to the 2D solver part, the efficiency of the ID part is sufficient to ensure a good parallel efficiency of the global algorithm. After this study, the main remaining difficulty implementation-wise is about the memory requirement of a vector used for initialization. An efficient acceleration operator will also need to be developed. (authors)
Radiation transport calculation methods in BNCT
International Nuclear Information System (INIS)
Koivunoro, H.; Seppaelae, T.; Savolainen, S.
2000-01-01
Boron neutron capture therapy (BNCT) is used as a radiotherapy for malignant brain tumours. Radiation dose distribution is necessary to determine individually for each patient. Radiation transport and dose distribution calculations in BNCT are more complicated than in conventional radiotherapy. Total dose in BNCT consists of several different dose components. The most important dose component for tumour control is therapeutic boron dose D B . The other dose components are gamma dose D g , incident fast neutron dose D f ast n and nitrogen dose D N . Total dose is a weighted sum of the dose components. Calculation of neutron and photon flux is a complex problem and requires numerical methods, i.e. deterministic or stochastic simulation methods. Deterministic methods are based on the numerical solution of Boltzmann transport equation. Such are discrete ordinates (SN) and spherical harmonics (PN) methods. The stochastic simulation method for calculation of radiation transport is known as Monte Carlo method. In the deterministic methods the spatial geometry is partitioned into mesh elements. In SN method angular integrals of the transport equation are replaced with weighted sums over a set of discrete angular directions. Flux is calculated iteratively for all these mesh elements and for each discrete direction. Discrete ordinates transport codes used in the dosimetric calculations are ANISN, DORT and TORT. In PN method a Legendre expansion for angular flux is used instead of discrete direction fluxes, land the angular dependency comes a property of vector function space itself. Thus, only spatial iterations are required for resulting equations. A novel radiation transport code based on PN method and tree-multigrid technique (TMG) has been developed at VTT (Technical Research Centre of Finland). Monte Carlo method solves the radiation transport by randomly selecting neutrons and photons from a prespecified boundary source and following the histories of selected particles
Energy Technology Data Exchange (ETDEWEB)
Yang, R [University of Alberta, Edmonton, AB (Canada); Fallone, B [University of Alberta, Edmonton, AB (Canada); Cross Cancer Institute, Edmonton, AB (Canada); MagnetTx Oncology Solutions, Edmonton, AB (Canada); St Aubin, J [University of Alberta, Edmonton, AB (Canada); Cross Cancer Institute, Edmonton, AB (Canada)
2016-06-15
Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. The LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been
International Nuclear Information System (INIS)
Li, S.H.; Chen, C.T.
1997-01-01
Analytical solutions are developed for the problem of radionuclide transport in a system of parallel fractures situated in a porous rock matrix. A kinetic solubility-limited dissolution model is used as the inlet boundary condition. The solutions consider the following processes: (a) advective transport in the fractures, (b) mechanical dispersion and molecular diffusion along the fractures, (c) molecular diffusion from a fracture to the porous matrix, (d) molecular diffusion within the porous matrix in the direction perpendicular to the fracture axis, (e) adsorption onto the fracture wall, (f) adsorption within the porous matrix, and (g) radioactive decay. The solutions are based on the Laplace transform method. The general transient solution is in the form of a double integral that is evaluated using composite Gauss-Legendre quadrature. A simpler transient solution that is in the form of a single integral is also presented for the case that assumes negligible longitudinal dispersion along the fractures. The steady-state solutions are also provided. A number of examples are given to illustrate the effects of the following important parameters: (a) fracture spacings, (b) dissolution-rate constants, (c) fracture dispersion coefficient, (d) matrix retardation factor, and (e) fracture retardation factor
International Nuclear Information System (INIS)
Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.
2011-01-01
We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)
The discrete cones methods for two-dimensional neutral particle transport problems with voids
International Nuclear Information System (INIS)
Watanabe, Y.; Maynard, C.W.
1983-01-01
One of the most widely applied deterministic methods for time-independent, two-dimensional neutron transport calculations is the discrete ordinates method (DSN). The DSN solution, however, fails to be accurate in a void due to the ray effect. In order to circumvent this drawback, the authors have been developing a novel approximation: the discrete cones method (DCN), where a group of particles in a cone are simultaneously traced instead of particles in discrete directions for the DSN method. Programs, which apply to the DSN method in a non-vacuum region and the DCN method in a void, have been written for transport calculations in X-Y coordinates. The solutions for test problems demonstrate mitigation of the ray effect in voids without loosing the computational efficiency of the DSN method
International Nuclear Information System (INIS)
Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.
2010-01-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
International Nuclear Information System (INIS)
Girardi, E.; Ruggieri, J.M.
2003-01-01
The aim of this paper is to present the last developments made on a domain decomposition method applied to reactor core calculations. In this method, two kind of balance equation with two different numerical methods dealing with two different unknowns are coupled. In the first part the two balance transport equations (first order and second order one) are presented with the corresponding following numerical methods: Variational Nodal Method and Discrete Ordinate Nodal Method. In the second part, the Multi-Method/Multi-Domain algorithm is introduced by applying the Schwarz domain decomposition to the multigroup eigenvalue problem of the transport equation. The resulting algorithm is then provided. The projection operators used to coupled the two methods are detailed in the last part of the paper. Finally some preliminary numerical applications on benchmarks are given showing encouraging results. (authors)
RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry
International Nuclear Information System (INIS)
Valle, Edmundo del; Mund, Ernest H.
2004-01-01
This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature
Implicit Monte Carlo methods and non-equilibrium Marshak wave radiative transport
International Nuclear Information System (INIS)
Lynch, J.E.
1985-01-01
Two enhancements to the Fleck implicit Monte Carlo method for radiative transport are described, for use in transparent and opaque media respectively. The first introduces a spectral mean cross section, which applies to pseudoscattering in transparent regions with a high frequency incident spectrum. The second provides a simple Monte Carlo random walk method for opaque regions, without the need for a supplementary diffusion equation formulation. A time-dependent transport Marshak wave problem of radiative transfer, in which a non-equilibrium condition exists between the radiation and material energy fields, is then solved. These results are compared to published benchmark solutions and to new discrete ordinate S-N results, for both spatially integrated radiation-material energies versus time and to new spatially dependent temperature profiles. Multigroup opacities, which are independent of both temperature and frequency, are used in addition to a material specific heat which is proportional to the cube of the temperature. 7 refs., 4 figs
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Crockett, Thomas W.
1995-01-01
This article provides a broad introduction to the subject of parallel rendering, encompassing both hardware and software systems. The focus is on the underlying concepts and the issues which arise in the design of parallel rendering algorithms and systems. We examine the different types of parallelism and how they can be applied in rendering applications. Concepts from parallel computing, such as data decomposition, task granularity, scalability, and load balancing, are considered in relation to the rendering problem. We also explore concepts from computer graphics, such as coherence and projection, which have a significant impact on the structure of parallel rendering algorithms. Our survey covers a number of practical considerations as well, including the choice of architectural platform, communication and memory requirements, and the problem of image assembly and display. We illustrate the discussion with numerous examples from the parallel rendering literature, representing most of the principal rendering methods currently used in computer graphics.
Fraser, Graham M.; Goldman, Daniel; Ellis, Christopher G.
2013-01-01
Objective We compare Reconstructed Microvascular Networks (RMN) to Parallel Capillary Arrays (PCA) under several simulated physiological conditions to determine how the use of different vascular geometry affects oxygen transport solutions. Methods Three discrete networks were reconstructed from intravital video microscopy of rat skeletal muscle (84×168×342 μm, 70×157×268 μm and 65×240×571 μm) and hemodynamic measurements were made in individual capillaries. PCAs were created based on statistical measurements from RMNs. Blood flow and O2 transport models were applied and the resulting solutions for RMN and PCA models were compared under 4 conditions (rest, exercise, ischemia and hypoxia). Results Predicted tissue PO2 was consistently lower in all RMN simulations compared to the paired PCA. PO2 for 3D reconstructions at rest were 28.2±4.8, 28.1±3.5, and 33.0±4.5 mmHg for networks I, II, and III compared to the PCA mean values of 31.2±4.5, 30.6±3.4, and 33.8±4.6 mmHg. Simulated exercise yielded mean tissue PO2 in the RMN of 10.1±5.4, 12.6±5.7, and 19.7±5.7 mmHg compared to 15.3±7.3, 18.8±5.3, and 21.7±6.0 in PCA. Conclusions These findings suggest that volume matched PCA yield different results compared to reconstructed microvascular geometries when applied to O2 transport modeling; the predominant characteristic of this difference being an over estimate of mean tissue PO2. Despite this limitation, PCA models remain important for theoretical studies as they produce PO2 distributions with similar shape and parameter dependence as RMN. PMID:23841679
International Nuclear Information System (INIS)
1982-01-01
1 - Description of problem or function: Format: SAIL format; Number of groups: 23 neutron / 17 gamma-ray; Nuclides: Type 04 Concrete and Low Carbon Steel (A533B). Origin: Science Applications, Inc (SAI); Weighting spectrum: yes. SAIL is a library of albedo scattering data to be used in three-dimensional Monte Carlo codes to solve radiation transport problems specific to the reactor pressure vessel cavity region of a LWR. The library contains data for Type 04 Concrete and Low Carbon Steel (A533B). 2 - Method of solution: The calculation of the albedo data was perform- ed with a version of the discrete ordinates transport code DOT which treats the transport of neutrons, secondary gamma-rays and gamma- rays in one dimension, while maintaining the complete two-dimension- al treatment of the angular dependence
1982-01-01
Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed.Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techn
Energy Technology Data Exchange (ETDEWEB)
Nunes, Rogerio Chaffin
2002-03-15
In this work, the system of differential equations obtained by the angular approach of the two-dimensional transport equation by the discrete ordinates method is solved through the formulation of finite elements with the objective of investigating the sensitivity of the outgoing flux of radiation with the incoming flux and the properties of absorption and scattering of the medium. The variational formulation for the system of differential equations of second order with the generalized boundary conditions of Neumann (third type) allows an easy implementation of the method of the finite elements with triangular mesh and approximation space of first order. The geometry chosen for the simulations is a circle with a non homogeneous circular form in its interior. The mapping of Dirichlet-Neumann is studied through various simulations involving the incoming flux, the outgoing flux and the properties of the medium. (author)
Energy Technology Data Exchange (ETDEWEB)
Zamonsky, O M [Comision Nacional de Energia Atomica, Centro Atomico Bariloche (Argentina)
2000-07-01
The accuracy of the solutions produced by the Discrete Ordinates neutron transport nodal methods is analyzed.The obtained new numerical methodologies increase the accuracy of the analyzed scheems and give a POSTERIORI error estimators. The accuracy improvement is obtained with new equations that make the numerical procedure free of truncation errors and proposing spatial reconstructions of the angular fluxes that are more accurate than those used until present. An a POSTERIORI error estimator is rigurously obtained for one dimensional systems that, in certain type of problems, allows to quantify the accuracy of the solutions. From comparisons with the one dimensional results, an a POSTERIORI error estimator is also obtained for multidimensional systems. LOCAL indicators, which quantify the spatial distribution of the errors, are obtained by the decomposition of the menctioned estimators. This makes the proposed methodology suitable to perform adaptive calculations. Some numerical examples are presented to validate the theoretical developements and to illustrate the ranges where the proposed approximations are valid.
Directory of Open Access Journals (Sweden)
Hyun Cheol Roh
2013-05-01
Full Text Available Zinc is an essential metal involved in a wide range of biological processes, and aberrant zinc metabolism is implicated in human diseases. The gastrointestinal tract of animals is a critical site of zinc metabolism that is responsible for dietary zinc uptake and distribution to the body. However, the role of the gastrointestinal tract in zinc excretion remains unclear. Zinc transporters are key regulators of zinc metabolism that mediate the movement of zinc ions across membranes. Here, we identified a comprehensive list of 14 predicted Cation Diffusion Facilitator (CDF family zinc transporters in Caenorhabditis elegans and demonstrated that zinc is excreted from intestinal cells by one of these CDF proteins, TTM-1B. The ttm-1 locus encodes two transcripts, ttm-1a and ttm-1b, that use different transcription start sites. ttm-1b expression was induced by high levels of zinc specifically in intestinal cells, whereas ttm-1a was not induced by zinc. TTM-1B was localized to the apical plasma membrane of intestinal cells, and analyses of loss-of-function mutant animals indicated that TTM-1B promotes zinc excretion into the intestinal lumen. Zinc excretion mediated by TTM-1B contributes to zinc detoxification. These observations indicate that ttm-1 is a component of a negative feedback circuit, since high levels of cytoplasmic zinc increase ttm-1b transcript levels and TTM-1B protein functions to reduce the level of cytoplasmic zinc. We showed that TTM-1 isoforms function in tandem with CDF-2, which is also induced by high levels of cytoplasmic zinc and reduces cytoplasmic zinc levels by sequestering zinc in lysosome-related organelles. These findings define a parallel negative feedback circuit that promotes zinc homeostasis and advance the understanding of the physiological roles of the gastrointestinal tract in zinc metabolism in animals.
Casanova, Henri; Robert, Yves
2008-01-01
""…The authors of the present book, who have extensive credentials in both research and instruction in the area of parallelism, present a sound, principled treatment of parallel algorithms. … This book is very well written and extremely well designed from an instructional point of view. … The authors have created an instructive and fascinating text. The book will serve researchers as well as instructors who need a solid, readable text for a course on parallelism in computing. Indeed, for anyone who wants an understandable text from which to acquire a current, rigorous, and broad vi
International Nuclear Information System (INIS)
Roberds, R.M.
1975-01-01
A space-angle synthesis (SAS) method has been developed for treating the steady-state, two-dimensional transport of neutrons and gamma rays from a point source of simulated nuclear weapon radiation in air. The method was validated by applying it to the problem of neutron transport from a point source in air over a ground interface, and then comparing the results to those obtained by DOT, a state-of-the-art, discrete-ordinates code. In the SAS method, the energy dependence of the Boltzmann transport equation was treated in the standard multigroup manner. The angular dependence was treated by expanding the flux in specially tailored trial functions and applying the method of weighted residuals which analytically integrated the transport equation over all angles. The weighted-residual approach was analogous to the conventional spherical-harmonics (P/sub N/) method with the exception that the tailored expansion allowed for more rapid convergence than a spherical-harmonics P 1 expansion and resulted in a greater degree of accuracy. The trial functions used in the expansion were odd and even combinations of selected trial solutions, the trial solutions being shaped ellipsoids which approximated the angular distribution of the neutron flux in one-dimensional space. The parameters which described the shape of the ellipsoid varied with energy group and the spatial medium, only, and were obtained from a one-dimensional discrete-ordinates calculation. Thus, approximate transport solutions were made available for all two-dimensional problems of a certain class by using tabulated parameters obtained from a single, one-dimensional calculation
International Nuclear Information System (INIS)
Kucukboyaci, Vefa; Haghighat, Alireza
2001-01-01
We have developed new angular multigrid formulations, including the Simplified Angular Multigrid (SAM), Nested Iteration (NI), and V-Cycle schemes, that are compatible with the parallel environment and the adaptive differencing strategy of the PENTRAN three-dimensional parallel S N code. Using the Fourier analysis method for an infinite, homogenous medium, we have investigated the effectiveness of the V-Cycle scheme for different problem parameters including scattering ratio, spatial differencing weights, quadrature order, and mesh size. We have further investigated the effectiveness of the new schemes for practical shielding applications such as the Kobayashi benchmark problem and the boiling water reactor core shroud problem. In this paper, we summarize the angular V-Cycle scheme implemented in the PENTRAN code, the Fourier Analysis of the V-Cycle scheme, and results of convergence analysis of the V-Cycle scheme using different problem parameters. The theoretical analysis reveals that the V-Cycle scheme is effective for a large range of scattering ratios and is insensitive to mesh size. Besides the theoretical analysis, we have applied the new angular multigrid schemes to shielding problems. In comparison to the standard PCR formulation, combinations of the new angular multigrid schemes and PCR (e.g., SAM+V-Cycle+PCR) have proved to be very effective for scattering ratios in a range of 0.6 to 0.9. (authors)
The discrete cones method for two-dimensional neutron transport calculations
International Nuclear Information System (INIS)
Watanabe, Y.; Maynard, C.W.
1986-01-01
A novel method, the discrete cones method (DC/sub N/), is proposed as an alternative to the discrete ordinates method (S/sub N/) for solutions of the two-dimensional neutron transport equation. The new method utilizes a new concept, discrete cones, which are made by partitioning a unit spherical surface that the direction vector of particles covers. In this method particles in a cone are simultaneously traced instead of those in discrete directions so that an anomaly of the S/sub N/ method, the ray effects, can be eliminated. The DC/sub N/ method has been formulated for X-Y geometry and a program has been creaed by modifying the standard S/sub N/ program TWOTRAN-II. Our sample calculations demonstrate a strong mitigation of the ray effects without a computing cost penalty
International Nuclear Information System (INIS)
Cao Liangzhi; Wu Hongchun; Zheng Youqi
2008-01-01
Daubechies' wavelet expansion is introduced to discretize the angular variables of the neutron transport equation when the neutron angular flux varies very acutely with the angular directions. An improvement is made by coupling one-dimensional wavelet expansion and discrete ordinate method to make two-dimensional angular discretization efficient and stable. The angular domain is divided into several subdomains for treating the vacuum boundary condition exactly in the unstructured geometry. A set of wavelet equations coupled with each other is obtained in each subdomain. An iterative method is utilized to decouple the wavelet moments. The numerical results of several benchmark problems demonstrate that the wavelet expansion method can provide more accurate results by lower-order expansion than other angular discretization methods
Analysis of EBR-II neutron and photon physics by multidimensional transport-theory techniques
International Nuclear Information System (INIS)
Jacqmin, R.P.; Finck, P.J.; Palmiotti, G.
1994-01-01
This paper contains a review of the challenges specific to the EBR-II core physics, a description of the methods and techniques which have been developed for addressing these challenges, and the results of some validation studies relative to power-distribution calculations. Numerical tests have shown that the VARIANT nodal code yields eigenvalue and power predictions as accurate as finite difference and discrete ordinates transport codes, at a small fraction of the cost. Comparisons with continuous-energy Monte Carlo results have proven that the errors introduced by the use of the diffusion-theory approximation in the collapsing procedure to obtain broad-group cross sections, kerma factors, and photon-production matrices, have a small impact on the EBR-II neutron/photon power distribution
Time-dependent anisotropic distributed source capability in transient 3-d transport code tort-TD
International Nuclear Information System (INIS)
Seubert, A.; Pautz, A.; Becker, M.; Dagan, R.
2009-01-01
The transient 3-D discrete ordinates transport code TORT-TD has been extended to account for time-dependent anisotropic distributed external sources. The extension aims at the simulation of the pulsed neutron source in the YALINA-Thermal subcritical assembly. Since feedback effects are not relevant in this zero-power configuration, this offers a unique opportunity to validate the time-dependent neutron kinetics of TORT-TD with experimental data. The extensions made in TORT-TD to incorporate a time-dependent anisotropic external source are described. The steady state of the YALINA-Thermal assembly and its response to an artificial square-wave source pulse sequence have been analysed with TORT-TD using pin-wise homogenised cross sections in 18 prompt energy groups with P 1 scattering order and 8 delayed neutron groups. The results demonstrate the applicability of TORT-TD to subcritical problems with a time-dependent external source. (authors)
Time-dependent anisotropic external sources in transient 3-D transport code TORT-TD
International Nuclear Information System (INIS)
Seubert, A.; Pautz, A.; Becker, M.; Dagan, R.
2009-01-01
This paper describes the implementation of a time-dependent distributed external source in TORT-TD by explicitly considering the external source in the ''fixed-source'' term of the implicitly time-discretised 3-D discrete ordinates transport equation. Anisotropy of the external source is represented by a spherical harmonics series expansion similar to the angular fluxes. The YALINA-Thermal subcritical assembly serves as a test case. The configuration with 280 fuel rods has been analysed with TORT-TD using cross sections in 18 energy groups and P1 scattering order generated by the KAPROS code system. Good agreement is achieved concerning the multiplication factor. The response of the system to an artificial time-dependent source consisting of two square-wave pulses demonstrates the time-dependent external source capability of TORT-TD. The result is physically plausible as judged from validation calculations. (orig.)
International Nuclear Information System (INIS)
Dominguez, Dany S.; Oliveira, Francisco B.S.; Barros, Ricardo C.
2003-01-01
We present in this paper a multiplatform computational code to calculate elements of Gauss-Legendre angular quadrature sets of arbitrary order used in slab-geometry discrete ordinates (S N ) formulation of neutron transport equation. In the code, the values can be computed with arbitrary arithmetic precision based on the approach of exact computing floating-point numbers. Calculation routines have been developed in the common language ANSI C using standard compiler gcc and the libraries of the open code GMP (GNU Multi precision Library). The code has a graphical interface in order to facilitate user interaction and numerical results analysis. The code architecture allows it to run on different platforms such as Unix, Linux and Windows. Numerical results and performance measures are also given. (author)
Sensitivity analysis of the titan hybrid deterministic transport code for SPECT simulation
International Nuclear Information System (INIS)
Royston, Katherine K.; Haghighat, Alireza
2011-01-01
Single photon emission computed tomography (SPECT) has been traditionally simulated using Monte Carlo methods. The TITAN code is a hybrid deterministic transport code that has recently been applied to the simulation of a SPECT myocardial perfusion study. For modeling SPECT, the TITAN code uses a discrete ordinates method in the phantom region and a combined simplified ray-tracing algorithm with a fictitious angular quadrature technique to simulate the collimator and generate projection images. In this paper, we compare the results of an experiment with a physical phantom with predictions from the MCNP5 and TITAN codes. While the results of the two codes are in good agreement, they differ from the experimental data by ∼ 21%. In order to understand these large differences, we conduct a sensitivity study by examining the effect of different parameters including heart size, collimator position, collimator simulation parameter, and number of energy groups. (author)
Study of the sensitivity of the radiation transport problem in a scattering medium
International Nuclear Information System (INIS)
Nunes, Rogerio Chaffin
2002-03-01
In this work, the system of differential equations obtained by the angular approach of the two-dimensional transport equation by the discrete ordinates method is solved through the formulation of finite elements with the objective of investigating the sensitivity of the outgoing flux of radiation with the incoming flux and the properties of absorption and scattering of the medium. The variational formulation for the system of differential equations of second order with the generalized boundary conditions of Neumann (third type) allows an easy implementation of the method of the finite elements with triangular mesh and approximation space of first order. The geometry chosen for the simulations is a circle with a non homogeneous circular form in its interior. The mapping of Dirichlet-Neumann is studied through various simulations involving the incoming flux, the outgoing flux and the properties of the medium. (author)
Parallel Monte Carlo reactor neutronics
International Nuclear Information System (INIS)
Blomquist, R.N.; Brown, F.B.
1994-01-01
The issues affecting implementation of parallel algorithms for large-scale engineering Monte Carlo neutron transport simulations are discussed. For nuclear reactor calculations, these include load balancing, recoding effort, reproducibility, domain decomposition techniques, I/O minimization, and strategies for different parallel architectures. Two codes were parallelized and tested for performance. The architectures employed include SIMD, MIMD-distributed memory, and workstation network with uneven interactive load. Speedups linear with the number of nodes were achieved
International Nuclear Information System (INIS)
Azmy, Yousry; Wang, Yaqi
2013-01-01
The research team has developed a practical, high-order, discrete-ordinates, short characteristics neutron transport code for three-dimensional configurations represented on unstructured tetrahedral grids that can be used for realistic reactor physics applications at both the assembly and core levels. This project will perform a comprehensive verification and validation of this new computational tool against both a continuous-energy Monte Carlo simulation (e.g. MCNP) and experimentally measured data, an essential prerequisite for its deployment in reactor core modeling. Verification is divided into three phases. The team will first conduct spatial mesh and expansion order refinement studies to monitor convergence of the numerical solution to reference solutions. This is quantified by convergence rates that are based on integral error norms computed from the cell-by-cell difference between the code's numerical solution and its reference counterpart. The latter is either analytic or very fine- mesh numerical solutions from independent computational tools. For the second phase, the team will create a suite of code-independent benchmark configurations to enable testing the theoretical order of accuracy of any particular discretization of the discrete ordinates approximation of the transport equation. For each tested case (i.e. mesh and spatial approximation order), researchers will execute the code and compare the resulting numerical solution to the exact solution on a per cell basis to determine the distribution of the numerical error. The final activity comprises a comparison to continuous-energy Monte Carlo solutions for zero-power critical configuration measurements at Idaho National Laboratory's Advanced Test Reactor (ATR). Results of this comparison will allow the investigators to distinguish between modeling errors and the above-listed discretization errors introduced by the deterministic method, and to separate the sources of uncertainty.
Energy Technology Data Exchange (ETDEWEB)
Girardi, E
2004-12-15
A new methodology for the solution of the neutron transport equation, based on domain decomposition has been developed. This approach allows us to employ different numerical methods together for a whole core calculation: a variational nodal method, a discrete ordinate nodal method and a method of characteristics. These new developments authorize the use of independent spatial and angular expansion, non-conformal Cartesian and unstructured meshes for each sub-domain, introducing a flexibility of modeling which is not allowed in today available codes. The effectiveness of our multi-domain/multi-method approach has been tested on several configurations. Among them, one particular application: the benchmark model of the Phebus experimental facility at Cea-Cadarache, shows why this new methodology is relevant to problems with strong local heterogeneities. This comparison has showed that the decomposition method brings more accuracy all along with an important reduction of the computer time.
Radiation transport in earth for neutron and gamma ray point sources above an air-ground interface
International Nuclear Information System (INIS)
Lillie, R.A.; Santoro, R.T.
1979-03-01
Two-dimensional discrete ordinates methods were used to calculate the instantaneous dose rate in silicon and neutron and gamma ray fluences as a function of depth in earth from point sources at various heights (1.0, 61.3, and 731.5 meters) above an air--ground interface. The radiation incident on the earth's surface was transported through an earth-only and an earth--concrete model containing 0.9 meters of borated concrete beginning 0.5 meters below the earth's surface to obtain fluence distributions to a depth of 3.0 meters. The inclusion of borated concrete did not significantly reduce the total instantaneous dose rate in silicon and, in all cases, the secondary gamma ray fluence and corresponding dose are substantially larger than the primary neutron fluence and corresponding dose for depths greater than 0.6 meter. 4 figures, 4 tables
International Nuclear Information System (INIS)
Le Tellier, R.; Fournier, D.; Suteau, C.
2011-01-01
Within the framework of a Discontinuous Galerkin spatial approximation of the multigroup discrete ordinates transport equation, we present a generalization of the exact standard perturbation formula that takes into account spatial discretization-induced reactivity changes. It encompasses in two separate contributions the nuclear data-induced reactivity change and the reactivity modification induced by two different spatial discretizations. The two potential uses of such a formulation when considering adaptive mesh refinement are discussed, and numerical results on a simple two-group Cartesian two-dimensional benchmark are provided. In particular, such a formulation is shown to be useful to filter out a more accurate estimate of nuclear data-related reactivity effects from initial and perturbed calculations based on independent adaptation processes. (authors)
Radiation transport in earth for neutron and gamma-ray point sources above an air-ground interface
International Nuclear Information System (INIS)
Lillie, R.A.; Santoro, R.T.
1980-01-01
Two-dimensional discrete-ordinates methods have been used to calculate the instantaneous dose rate in silicon and neutron and gamma-ray fluences as a function of depth in earth from point sources at various heights (1.0, 61.3, and 731.5 m) above an air-ground interface. The radiation incident on the earth's surface was transported through an earth-only and an earth-concrete model containing 0.9 m of borated concrete beginning 0.5 m below the earth's surface to obtain fluence distributions to a depth of 3.0 m. The inclusion of borated concrete did not significantly reduce the total instantaneous dose rate in silicon, and in all cases, the secondary gamma-ray fluence and corresponding dose are substantially larger than the primary neutron fluence and corresponding dose for depths > 0.6 m
Eckerle, Kate
This dissertation begins with a review of Calabi-Yau manifolds and their moduli spaces, flux compactification largely tailored to the case of type IIb supergravity, and Coleman-De Luccia vacuum decay. The three chapters that follow present the results of novel research conducted as a graduate student. Our first project is concerned with bubble collisions in single scalar field theories with multiple vacua. Lorentz boosted solitons traveling in one spatial dimension are used as a proxy to the colliding 3-dimensional spherical bubble walls. Recent work found that at sufficiently high impact velocities collisions between such bubble vacua are governed by "free passage" dynamics in which field interactions can be ignored during the collision, providing a systematic process for populating local minima without quantum nucleation. We focus on the time period that follows the bubble collision and provide evidence that, for certain potentials, interactions can drive significant deviations from the free passage bubble profile, thwarting the production of a new patch with different field value. However, for simple polynomial potentials a fine-tuning of vacuum locations is required to reverse the free passage kick enough that the field in the collision region returns to the original bubble vacuum. Hence we deem classical transitions mediated by free passage robust. Our second project continues with soliton collisions in the limit of relativistic impact velocity, but with the new feature of nontrivial field space curvature. We establish a simple geometrical interpretation of such collisions in terms of a double family of field profiles whose tangent vector fields stand in mutual parallel transport. This provides a generalization of the well-known limit in flat field space (free passage). We investigate the limits of this approximation and illustrate our analytical results with numerical simulations. In our third and final project we investigate the distribution of field
Implementation of the kinetics in the transport code AZTRAN
International Nuclear Information System (INIS)
Duran G, J. A.; Del Valle G, E.; Gomez T, A. M.
2017-09-01
This paper shows the implementation of the time dependence in the three-dimensional transport code AZTRAN (AZtlan TRANsport), which belongs to the AZTLAN platform, for the analysis of nuclear reactors (currently under development). The AZTRAN code with this implementation is able to numerically solve the time-dependent transport equation in XYZ geometry, for several energy groups, using the discrete ordinate method S n for the discretization of the angular variable, the nodal method RTN-0 for spatial discretization and method 0 for discretization in time. Initially, the code only solved the neutrons transport equation in steady state, so the implementation of the temporal part was made integrating the neutrons transport equation with respect to time and balance equations corresponding to the concentrations of delayed neutron precursors, for which method 0 was applied. After having directly implemented code kinetics, the improved quasi-static method was implemented, which is a tool for reducing computation time, where the angular flow is factored by the product of two functions called shape function and amplitude function, where the first is calculated for long time steps, called macro-steps and the second is resolved for small time steps called micro-steps. In the new version of AZTRAN several Benchmark problems that were taken from the literature were simulated, the problems used are of two and three dimensions which allowed corroborating the accuracy and stability of the code, showing in general in the reference tests a good behavior. (Author)
Energy Technology Data Exchange (ETDEWEB)
Duran G, J. A.; Del Valle G, E. [IPN, Escuela Superior de Fisica y Matematicas, Av. IPN s/n, San Pedro Zacatenco, 07738 Ciudad de Mexico (Mexico); Gomez T, A. M., E-mail: redfield1290@gmail.com [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico)
2017-09-15
This paper shows the implementation of the time dependence in the three-dimensional transport code AZTRAN (AZtlan TRANsport), which belongs to the AZTLAN platform, for the analysis of nuclear reactors (currently under development). The AZTRAN code with this implementation is able to numerically solve the time-dependent transport equation in XYZ geometry, for several energy groups, using the discrete ordinate method S{sub n} for the discretization of the angular variable, the nodal method RTN-0 for spatial discretization and method 0 for discretization in time. Initially, the code only solved the neutrons transport equation in steady state, so the implementation of the temporal part was made integrating the neutrons transport equation with respect to time and balance equations corresponding to the concentrations of delayed neutron precursors, for which method 0 was applied. After having directly implemented code kinetics, the improved quasi-static method was implemented, which is a tool for reducing computation time, where the angular flow is factored by the product of two functions called shape function and amplitude function, where the first is calculated for long time steps, called macro-steps and the second is resolved for small time steps called micro-steps. In the new version of AZTRAN several Benchmark problems that were taken from the literature were simulated, the problems used are of two and three dimensions which allowed corroborating the accuracy and stability of the code, showing in general in the reference tests a good behavior. (Author)
McCallum, Ethan
2011-01-01
It's tough to argue with R as a high-quality, cross-platform, open source statistical software product-unless you're in the business of crunching Big Data. This concise book introduces you to several strategies for using R to analyze large datasets. You'll learn the basics of Snow, Multicore, Parallel, and some Hadoop-related tools, including how to find them, how to use them, when they work well, and when they don't. With these packages, you can overcome R's single-threaded nature by spreading work across multiple CPUs, or offloading work to multiple machines to address R's memory barrier.
Transport synthetic acceleration scheme for multi-dimensional neutron transport problems
Energy Technology Data Exchange (ETDEWEB)
Modak, R S; Kumar, Vinod; Menon, S V.G. [Theoretical Physics Div., Bhabha Atomic Research Centre, Mumbai (India); Gupta, Anurag [Reactor Physics Design Div., Bhabha Atomic Research Centre, Mumbai (India)
2005-09-15
The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)
Transport synthetic acceleration scheme for multi-dimensional neutron transport problems
International Nuclear Information System (INIS)
Modak, R.S.; Vinod Kumar; Menon, S.V.G.; Gupta, Anurag
2005-09-01
The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)
Analytic approach to auroral electron transport and energy degradation
International Nuclear Information System (INIS)
Stamnes, K.
1980-01-01
The interaction of a beam of auroral electrons with the atmosphere is described by the linear transport equation, encompassing discrete energy loss, multiple scattering, and secondary electrons. A solution to the transport equation provides the electron intensity as a function of altitude, pitch angle (with respect to the geomagnetic field) and energy. A multi-stream (discrete ordinate) approximation to the transport equation is developed. An analytic solution is obtained in this approximation. The computational scheme obtained by combining the present transport code with the energy degradation method of Swartz (1979) conserves energy identically. The theory provides a framework within which angular distributions can be easily calculated and interpreted. Thus, a detailed study of the angular distributions of 'non-absorbed' electrons (i.e., electrons that have lost just a small fraction of their incident energy) reveals a systematic variation with incident angle and energy, and with penetration depth. The present approach also gives simple yet accurate solutions in low order multi-stream approximations. The accuracy of the four-stream approximation is generally within a few per cent, whereas two-stream results for backscattered mean intensities and fluxes are accurate to within 10-15%. (author)
Energy Technology Data Exchange (ETDEWEB)
Fang, Chin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Corttrell, R. A. [SLAC National Accelerator Lab., Menlo Park, CA (United States)
2015-05-06
This Technical Note provides an overview of high-performance parallel Big Data transfers with and without encryption for data in-transit over multiple network channels. It shows that with the parallel approach, it is feasible to carry out high-performance parallel "encrypted" Big Data transfers without serious impact to throughput. But other impacts, e.g. the energy-consumption part should be investigated. It also explains our rationales of using a statistics-based approach for gaining understanding from test results and for improving the system. The presentation is of high-level nature. Nevertheless, at the end we will pose some questions and identify potentially fruitful directions for future work.
National Research Council Canada - National Science Library
Adams, James; Carr, Ron; Chebl, Maroun; Coleman, Robert; Costantini, William; Cox, Robert; Dial, William; Jenkins, Robert; McGovern, James; Mueller, Peter
2006-01-01
...., trains, ships, etc.) and maximizing intermodal efficiency. A healthy balance must be achieved between the flow of international commerce and security requirements regardless of transportation mode...
Parallel hierarchical global illumination
Energy Technology Data Exchange (ETDEWEB)
Snell, Quinn O. [Iowa State Univ., Ames, IA (United States)
1997-10-08
Solving the global illumination problem is equivalent to determining the intensity of every wavelength of light in all directions at every point in a given scene. The complexity of the problem has led researchers to use approximation methods for solving the problem on serial computers. Rather than using an approximation method, such as backward ray tracing or radiosity, the authors have chosen to solve the Rendering Equation by direct simulation of light transport from the light sources. This paper presents an algorithm that solves the Rendering Equation to any desired accuracy, and can be run in parallel on distributed memory or shared memory computer systems with excellent scaling properties. It appears superior in both speed and physical correctness to recent published methods involving bidirectional ray tracing or hybrid treatments of diffuse and specular surfaces. Like progressive radiosity methods, it dynamically refines the geometry decomposition where required, but does so without the excessive storage requirements for ray histories. The algorithm, called Photon, produces a scene which converges to the global illumination solution. This amounts to a huge task for a 1997-vintage serial computer, but using the power of a parallel supercomputer significantly reduces the time required to generate a solution. Currently, Photon can be run on most parallel environments from a shared memory multiprocessor to a parallel supercomputer, as well as on clusters of heterogeneous workstations.
Krylov Techniques for 3D Problems in Transport Theory
International Nuclear Information System (INIS)
Ruben Panta Pazos
2006-01-01
When solving integral-differential equations by means of numerical methods one has to deal with large systems of linear equations, such as happens in transport theory [10]. Many iterative techniques are now used in Transport Theory in order to solve problems of 2D and 3D dimensions. In this paper, we choose two problems to solve the following transport equation, [Equation] where x: represents the spatial variable, μ: the cosine of the angle, ψ: the angular flux, h(x, μ): is the collision frequency, k(x, μ, μ'): the scattering kernel, q(x, μ): the source. The aim of this work is the straightforward application of the Krylov spaces technique [2] to the governing equation or to its discretizations derived of the discrete ordinates method (choosing a finite number of directions and then approximating the integral term by means of a proper sum). The equation (1) can be written in functional form as [Equation] with ψ in the Hilbert space L 2 ([0,a] x [-1,1])., and q is the source function. The operator derived from a discrete ordinates scheme that approximates the operator [Equation] generates the following subspace [Equation] i.e. the subspace generated by the iterations of order 0, 1, 2,..., m-1 of the source function q. Two methods are specially outstanding, the Lanczos method to solve the problem given by equation (2) with certain boundary conditions, and the conjugate gradient method to solve the same problem with identical boundary conditions. We discuss and accelerate the basic iterative method [8]. An important conclusion is the generation of these methods to solve linear systems in Hilbert spaces, if verify the convergence conditions, which are outlined in this work. The first problem is a cubic domain with two regions, one with a source near the vertex at the origin and the shield region. In this case, the Cartesian planes (specifically 0 < x < L, 0 < y < L, 0 < z < L) are reflexive boundaries and the rest faces of the cube are vacuum boundaries. The
Directory of Open Access Journals (Sweden)
James G. Worner
2017-05-01
Full Text Available James Worner is an Australian-based writer and scholar currently pursuing a PhD at the University of Technology Sydney. His research seeks to expose masculinities lost in the shadow of Australia’s Anzac hegemony while exploring new opportunities for contemporary historiography. He is the recipient of the Doctoral Scholarship in Historical Consciousness at the university’s Australian Centre of Public History and will be hosted by the University of Bologna during 2017 on a doctoral research writing scholarship. ‘Parallel Lines’ is one of a collection of stories, The Shapes of Us, exploring liminal spaces of modern life: class, gender, sexuality, race, religion and education. It looks at lives, like lines, that do not meet but which travel in proximity, simultaneously attracted and repelled. James’ short stories have been published in various journals and anthologies.
International Nuclear Information System (INIS)
Anon.
1998-01-01
Here is the decree of the thirtieth of July 1998 relative to road transportation, to trade and brokerage of wastes. It requires to firms which carry out a road transportation as well as to traders and to brokers of wastes to declare their operations to the prefect. The declaration has to be renewed every five years. (O.M.)
Neutron distribution modeling based on integro-probabilistic approach of discrete ordinates method
International Nuclear Information System (INIS)
Khromov, V.V.; Kryuchkov, E.F.; Tikhomirov, G.V.
1992-01-01
In this paper is described the universal nodal method for the neutron distribution calculation in reactor and shielding problems, based on using of influence functions and factors of local-integrated volume and surface neutron sources in phase subregions. This method permits to avoid the limited capabilities of collision-probability method concerning with the detailed calculation of angular neutron flux dependence, scattering anisotropy and empty channels. The proposed method may be considered as modification of S n - method with advantage of ray-effects elimination. There are presented the description of method theory and algorithm following by the examples of method applications for calculation of neutron distribution in three-dimensional model of fusion reactor blanket and in highly heterogeneous reactor with empty channel
Iterative discrete ordinates solution of the equation for surface-reflected radiance
Radkevich, Alexander
2017-11-01
This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.
DOQDP ADOQ, Discrete Ordinate Quadrature Generator for Programs DOT and ANISN
International Nuclear Information System (INIS)
1978-01-01
1 - Description of problem or function: DOQDP is used to generate direction sets (quadratures used as input to ANISN, DOT, and other related codes). If a fully symmetric quadrature is desired, DOQDP can generate the direction cosines to be used. If other than a fully quadrature is to be generated, the user must supply the appropriate direction cosines. Once the direction cosines are specified, the code will generate the quadrature weights. 2 - Method of solution: To determine point weights, DOQDP solves a set of simultaneous linear equations by Gaussian elimination with error improvement iterations. 3 - Restrictions on the complexity of the problem: None noted
Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Vector case
International Nuclear Information System (INIS)
Doicu, A.; Trautmann, T.
2009-01-01
The paper is devoted to the extension of the matrix-exponential formalism for the scalar radiative transfer to the vector case. Using basic results of the theory of matrix-exponential functions we provide a compact and versatile formulation of the vector radiative transfer. As in the scalar case, we operate with the concept of the layer equation incorporating the level values of the Stokes vector. The matrix exponentials which enter in the expression of the layer equation are computed by using the matrix eigenvalue method and the Pade approximation. A discussion of the computational efficiency of the proposed method for both an aerosol-loaded atmosphere as well as a cloudy atmosphere is also provided
Rational function approximation method for discrete ordinates problems in slab geometry
International Nuclear Information System (INIS)
Leal, Andre Luiz do C.; Barros, Ricardo C.
2009-01-01
In this work we use rational function approaches to obtain the transfer functions that appear in the spectral Green's function (SGF) auxiliary equations for one-speed isotropic scattering SN equations in one-dimensional Cartesian geometry. For this task we use the computation of the Pade approximants to compare the results with the standard SGF method's applied to deep penetration problems in homogeneous domains. This work is a preliminary investigation of a new proposal for handling leakage terms that appear in the two transverse integrated one-dimensional SN equations in the exponential SGF method (SGF-ExpN). Numerical results are presented to illustrate the rational function approximation accuracy. (author)
A DETERMINISTIC METHOD FOR TRANSIENT, THREE-DIMENSIONAL NUETRON TRANSPORT
International Nuclear Information System (INIS)
S. GOLUOGLU, C. BENTLEY, R. DEMEGLIO, M. DUNN, K. NORTON, R. PEVEY I.SUSLOV AND H.L. DODDS
1998-01-01
A deterministic method for solving the time-dependent, three-dimensional Boltzmam transport equation with explicit representation of delayed neutrons has been developed and evaluated. The methodology used in this study for the time variable of the neutron flux is known as the improved quasi-static (IQS) method. The position, energy, and angle-dependent neutron flux is computed deterministically by using the three-dimensional discrete ordinates code TORT. This paper briefly describes the methodology and selected results. The code developed at the University of Tennessee based on this methodology is called TDTORT. TDTORT can be used to model transients involving voided and/or strongly absorbing regions that require transport theory for accuracy. This code can also be used to model either small high-leakage systems, such as space reactors, or asymmetric control rod movements. TDTORT can model step, ramp, step followed by another step, and step followed by ramp type perturbations. It can also model columnwise rod movement can also be modeled. A special case of columnwise rod movement in a three-dimensional model of a boiling water reactor (BWR) with simple adiabatic feedback is also included. TDTORT is verified through several transient one-dimensional, two-dimensional, and three-dimensional benchmark problems. The results show that the transport methodology and corresponding code developed in this work have sufficient accuracy and speed for computing the dynamic behavior of complex multidimensional neutronic systems
Recently developed methods in neutral-particle transport calculations: overview
International Nuclear Information System (INIS)
Alcouffe, R.E.
1982-01-01
It has become increasingly apparent that successful, general methods for the solution of the neutral particle transport equation involve a close connection between the spatial-discretization method used and the source-acceleration method chosen. The first form of the transport equation, angular discretization which is discrete ordinates is considered as well as spatial discretization based upon a mesh arrangement. Characteristic methods are considered briefly in the context of future, desirable developments. The ideal spatial-discretization method is described as having the following attributes: (1) positive-positive boundary data yields a positive angular flux within the mesh including its boundaries; (2) satisfies the particle balance equation over the mesh, that is, the method is conservative; (3) possesses the diffusion limit independent of spatial mesh size, that is, for a linearly isotropic flux assumption, the transport differencing reduces to a suitable diffusion equation differencing; (4) the method is unconditionally acceleratable, i.e., for each mesh size, the method is unconditionally convergent with a source iteration acceleration. It is doubtful that a single method possesses all these attributes for a general problem. Some commonly used methods are outlined and their computational performance and usefulness are compared; recommendations for future development are detailed, which include practical computational considerations
Angular dependent transport of auroral electrons in the upper atmosphere
International Nuclear Information System (INIS)
Lummerzheim, D.; Rees, M.H.
1989-01-01
The transport of auroral electrons through the upper atmosphere is analyzed. The transport equation is solved using a discrete ordinate method including elastic and inelastic scattering of electrons resulting in changes of pitch angle, and degradation in energy as the electrons penetrate into the atmosphere. The transport equation is solved numerically for the electron intensity as a function of altitude, pitch angle, and energy. In situ measurements of the pitch angle and energy distribution of precipitating electrons over an auroral arc provide boundary conditions for the calculation. The electron spectra from various locations over the aurora present a variety of anisotropic pitch angle distributions and energy spectra. Good agreement is found between the observed backscattered electron energy spectra and model predictions. Differences occur at low energies (below 500 eV) in the structure of the pitch angle distribution. Model calculations were carried out with various different phase functions for elastic and inelastic collisions to attempt changing the angular scattering, but the observed pitch angle distributions remain unexplained. We suggest that mechanisms other than collisional scattering influence the angular distribution of auroral electrons at or below 300 km altitude in the low energy domain. (author)
Implementation of the quasi-static method for neutron transport
International Nuclear Information System (INIS)
Alcaro, Fabio; Dulla, Sandra; Ravetto, Piero; Le Tellier, Romain; Suteau, Christophe
2011-01-01
The study of the dynamic behavior of next generation nuclear reactors is a fundamental aspect for safety and reliability assessments. Despite the growing performances of modern computers, the full solution of the neutron Boltzmann equation in the time domain is still an impracticable task, thus several approximate dynamic models have been proposed for the simulation of nuclear reactor transients; the quasi-static method represents the standard tool currently adopted for the space-time solution of neutron transport problems. All the practical applications of this method that have been proposed contain a major limit, consisting in the use of isotropic quantities, such as scalar fluxes and isotropic external neutron sources, being the only data structures available in most deterministic transport codes. The loss of the angular information produces both inaccuracies in the solution of the kinetic model and the inconsistency of the quasi-static method itself. The present paper is devoted to the implementation of a consistent quasi-static method. The computational platform developed by CEA in Cadarache has been used for the creation of a kinetic package to be coupled with the existing SNATCH solver, a discrete-ordinate multi-dimensional neutron transport solver, employed for the solution of the steady-state Boltzmann equation. The work aims at highlighting the effects of the angular treatment of the neutron flux on the transient analysis, comparing the results with those produced by the previous implementations of the quasi-static method. (author)
Energy Technology Data Exchange (ETDEWEB)
Franz, A., LLNL
1998-02-17
The numerical simulation of chemically reacting flows is a topic, that has attracted a great deal of current research At the heart of numerical reactive flow simulations are large sets of coupled, nonlinear Partial Differential Equations (PDES). Due to the stiffness that is usually present, explicit time differencing schemes are not used despite their inherent simplicity and efficiency on parallel and vector machines, since these schemes require prohibitively small numerical stepsizes. Implicit time differencing schemes, although possessing good stability characteristics, introduce a great deal of computational overhead necessary to solve the simultaneous algebraic system at each timestep. This thesis examines an algorithm based on a preconditioned time differencing scheme. The algorithm is explicit and permits a large stable time step. An investigation of the algorithm`s accuracy, stability and performance on a parallel architecture is presented
National Research Council Canada - National Science Library
Allshouse, Michael; Armstrong, Frederick Henry; Burns, Stephen; Courts, Michael; Denn, Douglas; Fortunato, Paul; Gettings, Daniel; Hansen, David; Hoffman, D. W; Jones, Robert
2007-01-01
.... The ability of the global transportation industry to rapidly move passengers and products from one corner of the globe to another continues to amaze even those wise to the dynamics of such operations...
Schein, Jessica R; Hunt, Kevin A; Minton, Janet A; Schultes, Neil P; Mourad, George S
2013-09-01
The single cell alga Chlamydomonas reinhardtii is capable of importing purines as nitrogen sources. An analysis of the annotated C. reinhardtii genome reveals at least three distinct gene families encoding for known nucleobase transporters. In this study the solute transport and binding properties for the lone C. reinhardtii nucleobase cation symporter 1 (CrNCS1) are determined through heterologous expression in Saccharomyces cerevisiae. CrNCS1 acts as a transporter of adenine, guanine, uracil and allantoin, sharing similar - but not identical - solute recognition specificity with the evolutionary distant NCS1 from Arabidopsis thaliana. The results suggest that the solute specificity for plant NCS1 occurred early in plant evolution and are distinct from solute transport specificities of single cell fungal NCS1 proteins. Copyright © 2013 Elsevier Masson SAS. All rights reserved.
Mesh requirements for neutron transport calculations
International Nuclear Information System (INIS)
Askew, J.R.
1967-07-01
Fine-structure calculations are reported for a cylindrical natural uranium-graphite cell using different solution methods (discrete ordinate and collision probability codes) and varying the spatial mesh. It is suggested that of formulations assuming the source constant in a mesh interval the differential approach is generally to be preferred. Due to cancellation between approximations made in the derivation of the finite difference equations and the errors in neglecting source variation, the discrete ordinate code gave a more accurate estimate of fine structure for a given mesh even for unusually coarse representations. (author)
International Nuclear Information System (INIS)
Cho, Nam Zin; Park, Chang Je
2001-01-01
An additive angular-dependent re-balance (AADR) factor acceleration method is described to accelerate the source iteration of discrete ordinates transport calculation. The formulation of the AADR method follows that of the angular-dependent re-balance (ADR) method in that the re-balance factor is defined only on the cell interface and in that the low-order equation is derived by integrating the transport equation (high-order equation) over angular subspaces. But, the re-balance factor is applied additively. While the AADR method is similar to the boundary projection acceleration and the alpha-weighted linear acceleration, it is more general and does have distinct features. The method is easily extendible to DP N and low-order S N re-balancing, and it does not require consistent discretizations between the high- and low-order equations as in diffusion synthetic acceleration. We find by Fourier analysis and numerical results that the AADR method with a chosen form of weighting functions is unconditionally stable and very effective. There also exists an optimal weighting parameter that leads to the smallest spectral radius. The AADR acceleration method described in this paper is simple to implement, unconditionally stable, and very effective. It uses a physically based weighting function with an optimal parameter, leading to the best spectral radius of ρ<0.1865, compared to ρ<0.2247 of DSA. The application of the AADR acceleration method with the LMB scheme on a test problem shows encouraging results
A Monte Carlo Green's function method for three-dimensional neutron transport
International Nuclear Information System (INIS)
Gamino, R.G.; Brown, F.B.; Mendelson, M.R.
1992-01-01
This paper describes a Monte Carlo transport kernel capability, which has recently been incorporated into the RACER continuous-energy Monte Carlo code. The kernels represent a Green's function method for neutron transport from a fixed-source volume out to a particular volume of interest. This method is very powerful transport technique. Also, since kernels are evaluated numerically by Monte Carlo, the problem geometry can be arbitrarily complex, yet exact. This method is intended for problems where an ex-core neutron response must be determined for a variety of reactor conditions. Two examples are ex-core neutron detector response and vessel critical weld fast flux. The response is expressed in terms of neutron transport kernels weighted by a core fission source distribution. In these types of calculations, the response must be computed for hundreds of source distributions, but the kernels only need to be calculated once. The advance described in this paper is that the kernels are generated with a highly accurate three-dimensional Monte Carlo transport calculation instead of an approximate method such as line-of-sight attenuation theory or a synthesized three-dimensional discrete ordinates solution
Development and preliminary verification of 2-D transport module of radiation shielding code ARES
International Nuclear Information System (INIS)
Zhang Penghe; Chen Yixue; Zhang Bin; Zang Qiyong; Yuan Longjun; Chen Mengteng
2013-01-01
The 2-D transport module of radiation shielding code ARES is two-dimensional neutron and radiation shielding code. The theory model was based on the first-order steady state neutron transport equation, adopting the discrete ordinates method to disperse direction variables. Then a set of differential equations can be obtained and solved with the source iteration method. The 2-D transport module of ARES was capable of calculating k eff and fixed source problem with isotropic or anisotropic scattering in x-y geometry. The theoretical model was briefly introduced and series of benchmark problems were verified in this paper. Compared with the results given by the benchmark, the maximum relative deviation of k eff is 0.09% and the average relative deviation of flux density is about 0.60% in the BWR cells benchmark problem. As for the fixed source problem with isotropic and anisotropic scattering, the results of the 2-D transport module of ARES conform with DORT very well. These numerical results of benchmark problems preliminarily demonstrate that the development process of the 2-D transport module of ARES is right and it is able to provide high precision result. (authors)
2007-01-01
Faculty ii INDUSTRY TRAVEL Domestic Assistant Deputy Under Secretary of Defense (Transportation Policy), Washington, DC Department of...developed between the railroad and trucking industries. Railroads: Today’s seven Class I freight railroad systems move 42% of the nation’s intercity ...has been successfully employed in London to reduce congestion and observed by this industry study during its travels . It is currently being
DANTSYS: A diffusion accelerated neutral particle transport code system
International Nuclear Information System (INIS)
Alcouffe, R.E.; Baker, R.S.; Brinkley, F.W.; Marr, D.R.; O'Dell, R.D.; Walters, W.F.
1995-06-01
The DANTSYS code package includes the following transport codes: ONEDANT, TWODANT, TWODANT/GQ, TWOHEX, and THREEDANT. The DANTSYS code package is a modular computer program package designed to solve the time-independent, multigroup discrete ordinates form of the boltzmann transport equation in several different geometries. The modular construction of the package separates the input processing, the transport equation solving, and the post processing (or edit) functions into distinct code modules: the Input Module, one or more Solver Modules, and the Edit Module, respectively. The Input and Edit Modules are very general in nature and are common to all the Solver Modules. The ONEDANT Solver Module contains a one-dimensional (slab, cylinder, and sphere), time-independent transport equation solver using the standard diamond-differencing method for space/angle discretization. Also included in the package are solver Modules named TWODANT, TWODANT/GQ, THREEDANT, and TWOHEX. The TWODANT Solver Module solves the time-independent two-dimensional transport equation using the diamond-differencing method for space/angle discretization. The authors have also introduced an adaptive weighted diamond differencing (AWDD) method for the spatial and angular discretization into TWODANT as an option. The TWOHEX Solver Module solves the time-independent two-dimensional transport equation on an equilateral triangle spatial mesh. The THREEDANT Solver Module solves the time independent, three-dimensional transport equation for XYZ and RZΘ symmetries using both diamond differencing with set-to-zero fixup and the AWDD method. The TWODANT/GQ Solver Module solves the 2-D transport equation in XY and RZ symmetries using a spatial mesh of arbitrary quadrilaterals. The spatial differencing method is based upon the diamond differencing method with set-to-zero fixup with changes to accommodate the generalized spatial meshing
DANTSYS: A diffusion accelerated neutral particle transport code system
Energy Technology Data Exchange (ETDEWEB)
Alcouffe, R.E.; Baker, R.S.; Brinkley, F.W.; Marr, D.R.; O`Dell, R.D.; Walters, W.F.
1995-06-01
The DANTSYS code package includes the following transport codes: ONEDANT, TWODANT, TWODANT/GQ, TWOHEX, and THREEDANT. The DANTSYS code package is a modular computer program package designed to solve the time-independent, multigroup discrete ordinates form of the boltzmann transport equation in several different geometries. The modular construction of the package separates the input processing, the transport equation solving, and the post processing (or edit) functions into distinct code modules: the Input Module, one or more Solver Modules, and the Edit Module, respectively. The Input and Edit Modules are very general in nature and are common to all the Solver Modules. The ONEDANT Solver Module contains a one-dimensional (slab, cylinder, and sphere), time-independent transport equation solver using the standard diamond-differencing method for space/angle discretization. Also included in the package are solver Modules named TWODANT, TWODANT/GQ, THREEDANT, and TWOHEX. The TWODANT Solver Module solves the time-independent two-dimensional transport equation using the diamond-differencing method for space/angle discretization. The authors have also introduced an adaptive weighted diamond differencing (AWDD) method for the spatial and angular discretization into TWODANT as an option. The TWOHEX Solver Module solves the time-independent two-dimensional transport equation on an equilateral triangle spatial mesh. The THREEDANT Solver Module solves the time independent, three-dimensional transport equation for XYZ and RZ{Theta} symmetries using both diamond differencing with set-to-zero fixup and the AWDD method. The TWODANT/GQ Solver Module solves the 2-D transport equation in XY and RZ symmetries using a spatial mesh of arbitrary quadrilaterals. The spatial differencing method is based upon the diamond differencing method with set-to-zero fixup with changes to accommodate the generalized spatial meshing.
A time-dependent neutron transport model and its coupling to thermal-hydraulics
International Nuclear Information System (INIS)
Pautz, A.
2001-01-01
A new neutron transport code for time-dependent analyses of nuclear systems has been developed. The code system is based on the well-known Discrete Ordinates code DORT, which solves the steady-state neutron/photon transport equation in two dimensions for an arbitrary number of energy groups and the most common regular geometries. For the implementation of time-dependence a fully implicit first-order scheme was employed to minimize errors due to temporal discretization. This requires various modifications to the transport equation as well as the extensive use of elaborated acceleration mechanisms. The convergence criteria for fluxes, fission rates etc. had to be strongly tightened to ensure the reliability of results. To perform coupled analyses, an interface to the GRS system code ATHLET has been developed. The nodal power densities from the neutron transport code are passed to ATHLET to calculate thermal-hydraulic system parameters, e.g. fuel and coolant temperatures. These are in turn used to generate appropriate nuclear cross sections by interpolation of pre-calculated data sets for each time step. Finally, to demonstrate the transient capabilities of the coupled code system, the research reactor FRM-II has been analysed. Several design basis accidents were modelled, like the loss of off site power, loss of secondary heat sink and unintended control rod withdrawal. (author)
Two-dimensional radiation shielding optimization analysis of spent fuel transport container
International Nuclear Information System (INIS)
Tian Yingnan; Chen Yixue; Yang Shouhai
2013-01-01
The intelligent radiation shielding optimization design software platform is a one-dimensional multi-target radiation shielding optimization program which is developed on the basis of the genetic algorithm program and one-dimensional discrete ordinate program-ANISN. This program was applied in the optimization design analysis of the spent fuel transport container radiation shielding. The multi-objective optimization calculation model of the spent fuel transport container radiation shielding was established, and the optimization calculation of the spent fuel transport container weight and radiation dose rate was carried by this program. The calculation results were checked by Monte-Carlo program-MCNP/4C. The results show that the weight of the optimized spent fuel transport container decreases to 81.1% of the origin and the radiation dose rate decreases to below 65.4% of the origin. The maximum deviation between the calculated values from the program and the MCNP is below 5%. The results show that the optimization design scheme is feasible and the calculation result is correct. (authors)
Roy, Swarnendu; Chakraborty, Usha
2018-01-01
Comparative analyses of the responses to NaCl in Cynodon dactylon and a sensitive crop species like rice could effectively unravel the salt tolerance mechanism in the former. C. dactylon, a wild perennial chloridoid grass having a wide range of ecological distribution is generally adaptable to varying degrees of salinity stress. The role of salt exclusion mechanism present exclusively in the wild grass was one of the major factors contributing to its tolerance. Salt exclusion was found to be induced at 4 days when the plants were treated with a minimum conc. of 200 mM NaCl. The structural peculiarities of the salt exuding glands were elucidated by the SEM and TEM studies, which clearly revealed the presence of a bicellular salt gland actively functioning under NaCl stress to remove the excess amount of Na + ion from the mesophyll tissues. Moreover, the intracellular effect of NaCl on the photosynthetic apparatus was found to be lower in C. dactylon in comparison to rice; at the same time, the vacuolization process increased in the former. Accumulation of osmolytes like proline and glycine betaine also increased significantly in C. dactylon with a concurrent check on the H 2 O 2 levels, electrolyte leakage and membrane lipid peroxidation. This accounted for the proper functioning of the Na + ion transporters in the salt glands and also in the vacuoles for the exudation and loading of excess salts, respectively, to maintain the osmotic balance of the protoplasm. In real-time PCR analyses, CdSOS1 expression was found to increase by 2.5- and 5-fold, respectively, and CdNHX expression increased by 1.5- and 2-fold, respectively, in plants subjected to 100 and 200 mM NaCl treatment for 72 h. Thus, the comparative analyses of the expression pattern of the plasma membrane and tonoplast Na + ion transporters, SOS1 and NHX in both the plants revealed the significant role of these two ion transporters in conferring salinity tolerance in Cynodon.