Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

Science.gov (United States)

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

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

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.

Application of a discrete-energy, discrete-ordinates technique to the study of neutron transport in iron

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

Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

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 discrete ordinates method for solving the azimuthally dependent transport equation in plane geometry

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)

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

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

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

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.

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

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

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)

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)

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

The nodal discrete-ordinate transport calculation of anisotropy scattering problem in three-dimensional cartesian geometry

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

On the spectrum of the one-speed slab-geometry discrete ordinates operator in neutron transport theory

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

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)

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

Science.gov (United States)

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.

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

Improved treatment of two-dimensional neutral particle transport through voids within the discrete ordinates method by use of generalized view factors

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

Computational Modeling of a Time-Independent, Heterogeneous Reactor Core Using Simplified Discrete Ordinates Neutron Transport Techniques

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...

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)

On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

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.

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

Advanced quadrature sets and acceleration and preconditioning techniques for the discrete ordinates method in parallel computing environments

Science.gov (United States)

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

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

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

A Deep Penetration Problem Calculation Using AETIUS:An Easy Modeling Discrete Ordinates Transport Code UsIng Unstructured Tetrahedral Mesh, Shared Memory Parallel

Science.gov (United States)

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.

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

BALTORO a general purpose code for coupling discrete ordinates and Monte-Carlo radiation transport calculations

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)

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

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

An analytical discrete-ordinates solution for an improved one-dimensional model of three-dimensional transport in ducts

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.

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

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)

TRIDENT: a two-dimensional, multigroup, triangular mesh discrete ordinates, explicit neutron transport code

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

Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

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.

Description of a neutron field perturbed by a probe using coupled Monte Carlo and discrete ordinates radiation transport calculations

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

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

Method for coupling two-dimensional to three-dimensional discrete ordinates calculations

International Nuclear Information System (INIS)

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

Multiband discrete ordinates method: formalism and results; Methode multibande aux ordonnees discretes: formalisme et resultats

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.

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

Domain decomposition and CMFD acceleration applied to discrete-ordinate methods for the solution of the neutron transport equation in XYZ geometries

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)

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

Performance of the discrete ordinates method-like neutron transport computation with equivalent group condensation and angle-collapsing

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)

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

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.

First and second collision source for mitigating ray effects in discrete ordinate calculations

International Nuclear Information System (INIS)

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)

Computation of 2-D pinhole image-formation process of large-scale furnaces using the discrete ordinates method

CERN Document Server

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.

Computation of 2-D pinhole image-formation process of large-scale furnaces using the discrete ordinates method

International Nuclear Information System (INIS)

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

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

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)

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)

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

Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

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

Three-dimensional coupled Monte Carlo-discrete ordinates computational scheme for shielding calculations of large and complex nuclear facilities

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)

Two-dimensional discrete ordinates photon transport calculations for brachytherapy dosimetry applications

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 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

Particular solution of the discrete-ordinate method.

Science.gov (United States)

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.

Pin cell discontinuity factors in the transient 3-D discrete ordinates code TORT-TD - 237

International Nuclear Information System (INIS)

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)

An analytical discrete ordinates solution for a nodal model of a two-dimensional neutron transport problem

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)

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.

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)

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.

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.

On the equivalence between the discrete ordinates and the spherical harmonics methods in radiative transfer

International Nuclear Information System (INIS)

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

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)

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)

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

Vectorization, parallelization and porting of nuclear codes on the VPP500 system (parallelization). Progress report fiscal 1996

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)

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

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)

Discrete ordinate solution of the radiative transfer equation in the 'polarization normal wave representation'

Science.gov (United States)

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.

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

Ordinal Welfare Comparisons with Multiple Discrete Indicators

DEFF Research Database (Denmark)

Arndt, Channing; Distante, Roberta; Hussain, M. Azhar

We develop an ordinal method for making welfare comparisons between populations with multidimensional discrete well-being indicators observed at the micro level. The approach assumes that, for each well-being indicator, the levels can be ranked from worse to better; however, no assumptions are made...

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

Exponential characteristics spatial quadrature for discrete ordinates radiation transport in slab geometry

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

Verification of three dimensional triangular prismatic discrete ordinates transport code ENSEMBLE-TRIZ by comparison with Monte Carlo code GMVP

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)

Development of three-dimensional program based on Monte Carlo and discrete ordinates bidirectional coupling method

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)

Singular characteristic tracking algorithm for improved solution accuracy of the discrete ordinates method with isotropic scattering

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)

Reactor Dosimetry Applications Using RAPTOR-M3G:. a New Parallel 3-D Radiation Transport Code

Science.gov (United States)

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.

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

COMPUTATIONAL EFFICIENCY OF A MODIFIED SCATTERING KERNEL FOR FULL-COUPLED PHOTON-ELECTRON TRANSPORT PARALLEL COMPUTING WITH UNSTRUCTURED TETRAHEDRAL MESHES

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.

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

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

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)

Intercomparison of the finite difference and nodal discrete ordinates and surface flux transport methods for a LWR pool-reactor benchmark problem in X-Y geometry

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

Gamma-Weighted Discrete Ordinate Two-Stream Approximation for Computation of Domain Averaged Solar Irradiance

Science.gov (United States)

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.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

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

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)

Synchronization Techniques in Parallel Discrete Event Simulation

OpenAIRE

Lindén, Jonatan

2018-01-01

Discrete event simulation is an important tool for evaluating system models in many fields of science and engineering. To improve the performance of large-scale discrete event simulations, several techniques to parallelize discrete event simulation have been developed. In parallel discrete event simulation, the work of a single discrete event simulation is distributed over multiple processing elements. A key challenge in parallel discrete event simulation is to ensure that causally dependent ...

Explicit formulation of a nodal transport method for discrete ordinates calculations in two-dimensional fixed-source problems

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.)

Fourier analysis of parallel block-Jacobi splitting with transport synthetic acceleration in two-dimensional geometry

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)

Spectral nodal methodology for multigroup slab-geometry discrete ordinates neutron transport problems with linearly anisotropic scattering

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)

A coarse-mesh diffusion synthetic acceleration of the source iteration scheme for one-speed discrete ordinates transport calculations in Slab geometry

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)

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

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

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

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.)

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

Discrete ordinate theory of radiative transfer. 2: Scattering from maritime haze

Science.gov (United States)

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.

Exponential characteristic spatial quadrature for discrete ordinates radiation transport with rectangular cells

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

Fourier analysis of parallel inexact Block-Jacobi splitting with transport synthetic acceleration in slab geometry

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)

A Laplace transform method for energy multigroup hybrid discrete ordinates

International Nuclear Information System (INIS)

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.

Vectorization, parallelization and porting of nuclear codes on the VPP500 system (vectorization). Progress report fiscal 1996

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)

Vectorization, parallelization and porting of nuclear codes on the VPP500 system (porting). Progress report fiscal 1996

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)

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)

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)

A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

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)

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

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.

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

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.

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

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

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

ANISN-L, a CDC-7600 code which solves the one-dimensional, multigroup, time dependent transport equation by the method of discrete ordinates

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)

Coupling of discrete ordinates methods by transmission of boundary conditions in solving the neutron transport equation in slab geometry; Couplage de discretisations aux ordonnees discretes d`equations de transport 1D par passage de conditions frontieres

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.

Development of a discrete-ordinate approximation of the neutron transport equation for coupled xy-R-geometry

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

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

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.

Synchronization Of Parallel Discrete Event Simulations

Science.gov (United States)

Steinman, Jeffrey S.

1992-01-01

Adaptive, parallel, discrete-event-simulation-synchronization algorithm, Breathing Time Buckets, developed in Synchronous Parallel Environment for Emulation and Discrete Event Simulation (SPEEDES) operating system. Algorithm allows parallel simulations to process events optimistically in fluctuating time cycles that naturally adapt while simulation in progress. Combines best of optimistic and conservative synchronization strategies while avoiding major disadvantages. Algorithm processes events optimistically in time cycles adapting while simulation in progress. Well suited for modeling communication networks, for large-scale war games, for simulated flights of aircraft, for simulations of computer equipment, for mathematical modeling, for interactive engineering simulations, and for depictions of flows of information.

Parallel Sn Sweeps on Unstructured Grids: Algorithms for Prioritization, Grid Partitioning, and Cycle Detection

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

Multigroup discrete ordinates solution of Boltzmann-Fokker-Planck equations and cross section library development of ion transport

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

A Novel Algorithm for Solving the Multidimensional Neutron Transport Equation on Massively Parallel Architectures

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.

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

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)

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.)

The CNCSN: one, two- and three-dimensional coupled neutral and charged particle discrete ordinates code package

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

Methodology for solving the equation of transport ordered discrete TORT code in the reactor IPEN/MB-01; Metodologia para resolver la ecuacion del transporte con el codigo de Ordenadas Discretas TORT en el reactor IPEN/MB-01

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.

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

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)

Solution of neutron transport equation using Daubechies' wavelet expansion in the angular discretization

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

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)

Ordinance on the transport of dangerous goods by road (SDR)

International Nuclear Information System (INIS)

1985-04-01

This Ordinance regulates the transport of dangerous goods by road and replaces a similar Ordinance of 1972. The dangerous goods are listed in Annex A and the special provisions to be complied with for their transport are contained in Annex B. Radioactive materials, categorized as Class IVb, are included in the goods covered by the Ordinance. The Ordinance which entered into force on 1 May 1985 was amended on 9 April 1987 on a minor point and on 27 November 1989 so as to provide for special training for drivers of vehicles carrying such goods. This latter amendment entered into force on 1 January 1990. (NEA) [fr

Radiative heat transfer in strongly forward scattering media using the discrete ordinates method

Science.gov (United States)

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

GGVS. Ordinance on road transport of hazardous materials, including the European agreement on international road transport of hazardous materials (ADR), in their wording. Annexes A and B. Ordinances regarding exceptions from GGVS and from the ordinance on rail transport of hazardous materials, GGVE. Reasons. Selected guidelines. List of materials. 6. rev. and enlarged ed.

International Nuclear Information System (INIS)

Ridder, K.

1990-01-01

The brochure contains the following texts: (1) Ordinance on road transport of hazardous materials (GGVS), including the European agreement on international road transport of hazardous materials (ADR), as of 1990: Skeleton ordinance, annexes A and B, reasons given for the first version, and for the first amendment in 1988, execution guidelines - RS 002 (guidelines for executing the ordinance on road transport of hazardous materials, with catalogue of penalties), guidelines for drawing up written instructions for the event of accidents - RS 006, guiding principles for the training of vehicle conductors; (2) ordinance regarding exceptions from the ordinance on road transport of hazardous materials; (3) ordinance regarding exceptions from the ordinance on rail transport of hazardous materials; (4) selected guidelines: Technical guidelines TR IBC K 001, TRS 003, TRS 004, TRS 005, TRS 006; (5) listing of materials and objects governed by the ordinance on hazardous materials transport; (6) catalogue of penalties relative to road transport of hazardous materials. (orig./HP) [de

Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

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.

Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

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.

Applications of the Discrete ordinates of Oak ridge System (DOORS) package to Nuclear Engineering problems

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)

Applications of the Discrete ordinates of Oak ridge System (DOORS) package to Nuclear Engineering problems

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)

First ordinance amending the Ordinance on Rail Transport of Dangerous Goods (1. Amendment Ordinance Rail Transport of Dangerous Goods). As of June 22, 1983

International Nuclear Information System (INIS)

1983-01-01

This Amendment which came into force on September 1, 1983 brings about modifications of many items of the original Ordinance on Rail Transport of Dangerous Goods and its supplement, as of August 29, 1979. (HSCH) [de

New developments in the discrete ordinate method for the resolution of the radiative transfer equation

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

A response matrix method for one-speed discrete ordinates fixed source problems in slab geometry with no spatial truncation error

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)

Generating Importance Map for Geometry Splitting using Discrete Ordinates Code in Deep Shielding Problem

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

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

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)

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

Modifications Of Discrete Ordinate Method For Computations With High Scattering Anisotropy: Comparative Analysis

Science.gov (United States)

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.

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

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

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.

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

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.

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

The time-dependent 3D discrete ordinates code TORT-TD with thermal-hydraulic feedback by ATHLET models

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)

Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system.

Science.gov (United States)

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.

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

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)

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

Discrete Diffusion Monte Carlo for Electron Thermal Transport

Science.gov (United States)

Chenhall, Jeffrey; Cao, Duc; Wollaeger, Ryan; Moses, Gregory

2014-10-01

The iSNB (implicit Schurtz Nicolai Busquet electron thermal transport method of Cao et al. is adapted to a Discrete Diffusion Monte Carlo (DDMC) solution method for eventual inclusion in a hybrid IMC-DDMC (Implicit Monte Carlo) method. The hybrid method will combine the efficiency of a diffusion method in short mean free path regions with the accuracy of a transport method in long mean free path regions. The Monte Carlo nature of the approach allows the algorithm to be massively parallelized. Work to date on the iSNB-DDMC method will be presented. This work was supported by Sandia National Laboratory - Albuquerque.

Monte Carlo and discrete-ordinate simulations of irradiances in the coupled atmosphere-ocean system.

Science.gov (United States)

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.

TIMEX: a time-dependent explicit discrete ordinates program for the solution of multigroup transport equations with delayed neutrons

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

Discrete Hadamard transformation algorithm's parallelism analysis and achievement

Science.gov (United States)

Hu, Hui

2009-07-01

With respect to Discrete Hadamard Transformation (DHT) wide application in real-time signal processing while limitation in operation speed of DSP. The article makes DHT parallel research and its parallel performance analysis. Based on multiprocessor platform-TMS320C80 programming structure, the research is carried out to achieve two kinds of parallel DHT algorithms. Several experiments demonstrated the effectiveness of the proposed algorithms.

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)

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.

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

Out-of-order parallel discrete event simulation for electronic system-level design

CERN Document Server

Chen, Weiwei

2014-01-01

This book offers readers a set of new approaches and tools a set of tools and techniques for facing challenges in parallelization with design of embedded systems.? It provides an advanced parallel simulation infrastructure for efficient and effective system-level model validation and development so as to build better products in less time.? Since parallel discrete event simulation (PDES) has the potential to exploit the underlying parallel computational capability in today's multi-core simulation hosts, the author begins by reviewing the parallelization of discrete event simulation, identifyin

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

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

A numerical method for multigroup slab-geometry discrete ordinates problems with no spatial truncation error

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

Slab geometry spatial discretization schemes with infinite-order convergence

International Nuclear Information System (INIS)

Adams, M.L.; Martin, W.R.

1985-01-01

Spatial discretization schemes for the slab geometry discrete ordinates transport equation have received considerable attention in the past several years, with particular interest shown in developing methods that are more computationally efficient that standard schemes. Here the authors apply to the discrete ordinates equations a spectral method that is significantly more efficient than previously proposed schemes for high-accuracy calculations of homogeneous problems. This is a direct consequence of the exponential (infinite-order) convergence of spectral methods for problems with every smooth solutions. For heterogeneous problems where smooth solutions do not exist and exponential convergence is not observed with spectral methods, a spectral element method is proposed which does exhibit exponential convergence

A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals

Directory of Open Access Journals (Sweden)

Pablo Soto-Quiros

2015-01-01

Full Text Available This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT: the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

A coarse-mesh diffusion synthetic acceleration of the scattering source iteration scheme for one-speed slab-geometry discrete ordinates problems

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)

Parallel image encryption algorithm based on discretized chaotic map

International Nuclear Information System (INIS)

Zhou Qing; Wong Kwokwo; Liao Xiaofeng; Xiang Tao; Hu Yue

2008-01-01

Recently, a variety of chaos-based algorithms were proposed for image encryption. Nevertheless, none of them works efficiently in parallel computing environment. In this paper, we propose a framework for parallel image encryption. Based on this framework, a new algorithm is designed using the discretized Kolmogorov flow map. It fulfills all the requirements for a parallel image encryption algorithm. Moreover, it is secure and fast. These properties make it a good choice for image encryption on parallel computing platforms

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

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

On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media

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.

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)

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)

Analysis of QUADOS problem on TLD-ALBEDO personal dosemeter responses using discrete ordinates and Monte Carlo methods

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)

Program For Parallel Discrete-Event Simulation

Science.gov (United States)

Beckman, Brian C.; Blume, Leo R.; Geiselman, John S.; Presley, Matthew T.; Wedel, John J., Jr.; Bellenot, Steven F.; Diloreto, Michael; Hontalas, Philip J.; Reiher, Peter L.; Weiland, Frederick P.

1991-01-01

User does not have to add any special logic to aid in synchronization. Time Warp Operating System (TWOS) computer program is special-purpose operating system designed to support parallel discrete-event simulation. Complete implementation of Time Warp mechanism. Supports only simulations and other computations designed for virtual time. Time Warp Simulator (TWSIM) subdirectory contains sequential simulation engine interface-compatible with TWOS. TWOS and TWSIM written in, and support simulations in, C programming language.

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

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)

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

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

Approximate albedo boundary conditions for energy multigroup X,Y-geometry discrete ordinates nuclear global calculations

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)

Shielding calculations in support of the Spallation Neutron Source (SNS) proton beam transport system

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

Use of exact albedo conditions in numerical methods for one-dimensional one-speed discrete ordinates eigenvalue problems

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)

Fast parallel approach for 2-D DHT-based real-valued discrete Gabor transform.

Science.gov (United States)

Tao, Liang; Kwan, Hon Keung

2009-12-01

Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.

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)

A curvature theory for discrete surfaces based on mesh parallelity

KAUST Repository

Bobenko, Alexander Ivanovich

2009-12-18

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces\\' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.

Solution of the one-dimensional time-dependent discrete ordinates problem in a slab by the spectral and LTSN methods

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

Energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators

Science.gov (United States)

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.

Ordinance concerning the filing of transport of nuclear fuel materials

International Nuclear Information System (INIS)

1979-01-01

The ordinance is defined under the law for the regulations of nuclear source materials, nuclear fuel materials and reactors and the order for execution of the law. Any person who reports the transport of nuclear fuel materials shall file four copies of a notification according to the form attached to the public safety commission of the prefecture in charge of the dispatching place. When the transportation extends over the area in charge of another public safety commission, the commission which has received the notice shall report without delay date and route of the transport, kind and quantity of nuclear fuel materials and other necessary matters to the commission concerned and hear from the latter opinions on the items informed. The designation by the ordinance includes speed of the vehicle loaded with nuclear fuel materials, disposition of an accompanying car, arrangement of the line of the loaded vehicle and accompanying and other escorting cars, location of the parking, place of unloading and temporary storage, etc. Reports concerning troubles and measures taken shall be filed in ten days to the public safety commission which has received the notification, when accidents occur on the way, such as: theft or loss of nuclear fuel materials; traffic accident; irregular leaking of nuclear fuel materials and personal trouble by the transport. (Okada, K.)

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

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

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

Multirate-based fast parallel algorithms for 2-D DHT-based real-valued discrete Gabor transform.

Science.gov (United States)

Tao, Liang; Kwan, Hon Keung

2012-07-01

Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.

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)

A curvature theory for discrete surfaces based on mesh parallelity

KAUST Repository

Bobenko, Alexander Ivanovich; Pottmann, Helmut; Wallner, Johannes

2009-01-01

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable

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 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

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

A response matrix method for slab-geometry discrete ordinates adjoint calculations in energy-dependent source-detector problems

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)

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

Science.gov (United States)

Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W

2017-09-26

The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.

Parallel discrete event simulation: A shared memory approach

Science.gov (United States)

Reed, Daniel A.; Malony, Allen D.; Mccredie, Bradley D.

1987-01-01

With traditional event list techniques, evaluating a detailed discrete event simulation model can often require hours or even days of computation time. Parallel simulation mimics the interacting servers and queues of a real system by assigning each simulated entity to a processor. By eliminating the event list and maintaining only sufficient synchronization to insure causality, parallel simulation can potentially provide speedups that are linear in the number of processors. A set of shared memory experiments is presented using the Chandy-Misra distributed simulation algorithm to simulate networks of queues. Parameters include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential simulation of most queueing network models.

Radiative transfer modelling in combusting systems using discrete ordinates method on three-dimensional unstructured grids; Modelisation des transferts radiatifs en combustion par methode aux ordonnees discretes sur des maillages non structures tridimensionnels

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)

Radiation (Safety Control) Ordinance 1978

International Nuclear Information System (INIS)

1978-01-01

This Ordinance provides for the control, regulation, possession, use and transport of radioactive substance and irradiating apparatus. The Director of Health is responsible for administration of the Ordinance, which contains detailed provisions concerning the terms and conditions of licences, duties of licensees, medical examinations, maximum radiation doses, precautions to be taken to avoid exceeding such doses. The Ordinance also lays down a system of record-keeping and registration as well as packaging specifications for the transport of radioactive substances. (NEA) [fr

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

The linear characteristic method for spatially discretizing the discrete ordinates equations in (x,y)-geometry

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

Optimized Parallel Discrete Event Simulation (PDES) for High Performance Computing (HPC) Clusters

National Research Council Canada - National Science Library

Abu-Ghazaleh, Nael

2005-01-01

The aim of this project was to study the communication subsystem performance of state of the art optimistic simulator Synchronous Parallel Environment for Emulation and Discrete-Event Simulation (SPEEDES...

Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks

Science.gov (United States)

Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.

2013-12-01

Modeling of flow and solute transport in discrete fracture networks is an important approach for understanding the migration of contaminants in impermeable hard rocks such as granite, where fractures provide dominant flow and transport pathways. The discrete fracture network (DFN) model attempts to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. An integrated DFN meshing [1], flow, and particle tracking [2] simulation capability that enables accurate flow and particle tracking simulation on large DFNs has recently been developed. The new capability has been used in numerical experiments on advective transport in large DFNs with tens of thousands of fractures and millions of computational cells. The modeling procedure starts from the fracture network generation using a stochastic model derived from site data. A high-quality computational mesh is then generated [1]. Flow is then solved using the highly parallel PFLOTRAN [3] code. PFLOTRAN uses the finite volume approach, which is locally mass conserving and thus eliminates mass balance problems during particle tracking. The flow solver provides the scalar fluxes on each control volume face. From the obtained fluxes the Darcy velocity is reconstructed for each node in the network [4]. Velocities can then be continuously interpolated to any point in the domain of interest, thus enabling random walk particle tracking. In order to describe the flow field on fractures intersections, the control volume cells on intersections are split into four planar polygons, where each polygon corresponds to a piece of a fracture near the intersection line. Thus

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)

A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere. I - Theory. II - Application

Science.gov (United States)

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.

EPRI-LATTICE: a multigroup neutron transport code for light water reactor lattice physics calculations

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

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.)

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.

Parallel discrete event simulation using shared memory

Science.gov (United States)

Reed, Daniel A.; Malony, Allen D.; Mccredie, Bradley D.

1988-01-01

With traditional event-list techniques, evaluating a detailed discrete-event simulation-model can often require hours or even days of computation time. By eliminating the event list and maintaining only sufficient synchronization to ensure causality, parallel simulation can potentially provide speedups that are linear in the numbers of processors. A set of shared-memory experiments, using the Chandy-Misra distributed-simulation algorithm, to simulate networks of queues is presented. Parameters of the study include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential-simulation of most queueing network models.

Second Ordinance amending the Radiation Protection Ordinance

International Nuclear Information System (INIS)

1989-01-01

The amendment of the Radiation Protection Ordinance brings about the following changes: (1) Introduction of the concept of effective dose, reduction of limits for partial body dose, adoption of the radiotoxicity values of radionuclides as established by the EC Basis Standards; (2) introduction of a working-life-related dose limit of 400 mSv; (3) supplementing provisions for the protection of the population, particularly by the standard procedure for radioecological impact assessment and determination of dose factors; (4) supplementing provisions on the use of radioactive substances in medicine and medical research; (5) supplementing provisions on health physics monitoring; (6) provisions for improving the supervision and controls in the transport of radioactive substances; (7) definition of activities and their assignment to the provisions of the Radiation Protection Ordinance; (8) revision of the waste management provisions of the Radiation Protection Ordinance. (HP) [de

Parallel discrete-event simulation of FCFS stochastic queueing networks

Science.gov (United States)

Nicol, David M.

1988-01-01

Physical systems are inherently parallel. Intuition suggests that simulations of these systems may be amenable to parallel execution. The parallel execution of a discrete-event simulation requires careful synchronization of processes in order to ensure the execution's correctness; this synchronization can degrade performance. Largely negative results were recently reported in a study which used a well-known synchronization method on queueing network simulations. Discussed here is a synchronization method (appointments), which has proven itself to be effective on simulations of FCFS queueing networks. The key concept behind appointments is the provision of lookahead. Lookahead is a prediction on a processor's future behavior, based on an analysis of the processor's simulation state. It is shown how lookahead can be computed for FCFS queueing network simulations, give performance data that demonstrates the method's effectiveness under moderate to heavy loads, and discuss performance tradeoffs between the quality of lookahead, and the cost of computing lookahead.

Angular discretization errors in transport theory

International Nuclear Information System (INIS)

Nelson, P.; Yu, F.

1992-01-01

Elements of the information-based complexity theory are computed for several types of information and associated algorithms for angular approximations in the setting of a on-dimensional model problem. For point-evaluation information, the local and global radii of information are computed, a (trivial) optimal algorithm is determined, and the local and global error of a discrete ordinates algorithm are shown to be infinite. For average cone-integral information, the local and global radii of information are computed, the local and global error tends to zero as the underlying partition is indefinitely refined. A central algorithm for such information and an optimal partition (of given cardinality) are described. It is further shown that the analytic first-collision source method has zero error (for the purely absorbing model problem). Implications of the restricted problem domains suitable for the various types of information are discussed

A more efficient implementation of the discrete-ordinates method for an approximate model of particle transport in a duct

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.

Comparison of Generated Parallel Capillary Arrays to Three-Dimensional Reconstructed Capillary Networks in Modeling Oxygen Transport in Discrete Microvascular Volumes

Science.gov (United States)

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

Radiation protection Ordinance

International Nuclear Information System (INIS)

1976-06-01

This Ordinance lays down the licensing system for activities in Switzerland involving possible exposure to radiation, with the exception of nuclear installations, fuels and radioactive waste which, under the 1959 Atomic Energy Act, are subject to licensing. The Ordinance applies to the production, handling, use, storage, transport, disposal, import and export of radioactive substances and devices and articles containing them; and generally to any activity involving hazards caused by ionizing radiation. The Federal Public Health Office is the competent authority for granting licences. Provision is also made for the administrative conditions to be complied with for obtaining such licences as well as for technical measures required when engaged in work covered by the Ordinance. This consolidated version of the Ordinance contains all the successive amendments up to 26 September 1988. (NEA) [fr

Investigation of radiation effects in Hiroshima and Nagasaki using a general Monte Carlo-discrete ordinates coupling scheme

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

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)

Evaluation of a new preconditioning algorithm based on the 3-D even-parity simplified SN equations for discrete ordinates in parallel environments

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)

SPEEDES - A multiple-synchronization environment for parallel discrete-event simulation

Science.gov (United States)

Steinman, Jeff S.

1992-01-01

Synchronous Parallel Environment for Emulation and Discrete-Event Simulation (SPEEDES) is a unified parallel simulation environment. It supports multiple-synchronization protocols without requiring users to recompile their code. When a SPEEDES simulation runs on one node, all the extra parallel overhead is removed automatically at run time. When the same executable runs in parallel, the user preselects the synchronization algorithm from a list of options. SPEEDES currently runs on UNIX networks and on the California Institute of Technology/Jet Propulsion Laboratory Mark III Hypercube. SPEEDES also supports interactive simulations. Featured in the SPEEDES environment is a new parallel synchronization approach called Breathing Time Buckets. This algorithm uses some of the conservative techniques found in Time Bucket synchronization, along with the optimism that characterizes the Time Warp approach. A mathematical model derived from first principles predicts the performance of Breathing Time Buckets. Along with the Breathing Time Buckets algorithm, this paper discusses the rules for processing events in SPEEDES, describes the implementation of various other synchronization protocols supported by SPEEDES, describes some new ones for the future, discusses interactive simulations, and then gives some performance results.

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

Comparison of the auxiliary function method and the discrete-ordinate method for solving the radiative transfer equation for light scattering.

Science.gov (United States)

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.

Few-Group Transport Analysis of the Core-Reflector Problem in Fast Reactor Cores via Equivalent Group Condensation and Local/Global Iteration

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

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

The cost of conservative synchronization in parallel discrete event simulations

Science.gov (United States)

Nicol, David M.

1990-01-01

The performance of a synchronous conservative parallel discrete-event simulation protocol is analyzed. The class of simulation models considered is oriented around a physical domain and possesses a limited ability to predict future behavior. A stochastic model is used to show that as the volume of simulation activity in the model increases relative to a fixed architecture, the complexity of the average per-event overhead due to synchronization, event list manipulation, lookahead calculations, and processor idle time approach the complexity of the average per-event overhead of a serial simulation. The method is therefore within a constant factor of optimal. The analysis demonstrates that on large problems--those for which parallel processing is ideally suited--there is often enough parallel workload so that processors are not usually idle. The viability of the method is also demonstrated empirically, showing how good performance is achieved on large problems using a thirty-two node Intel iPSC/2 distributed memory multiprocessor.

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)

Numerical computation of discrete differential scattering cross sections for Monte Carlo charged particle transport

International Nuclear Information System (INIS)

Walsh, Jonathan A.; Palmer, Todd S.; Urbatsch, Todd J.

2015-01-01

Highlights: • Generation of discrete differential scattering angle and energy loss cross sections. • Gauss–Radau quadrature utilizing numerically computed cross section moments. • Development of a charged particle transport capability in the Milagro IMC code. • Integration of cross section generation and charged particle transport capabilities. - Abstract: We investigate a method for numerically generating discrete scattering cross sections for use in charged particle transport simulations. We describe the cross section generation procedure and compare it to existing methods used to obtain discrete cross sections. The numerical approach presented here is generalized to allow greater flexibility in choosing a cross section model from which to derive discrete values. Cross section data computed with this method compare favorably with discrete data generated with an existing method. Additionally, a charged particle transport capability is demonstrated in the time-dependent Implicit Monte Carlo radiative transfer code, Milagro. We verify the implementation of charged particle transport in Milagro with analytic test problems and we compare calculated electron depth–dose profiles with another particle transport code that has a validated electron transport capability. Finally, we investigate the integration of the new discrete cross section generation method with the charged particle transport capability in Milagro.

An inherently parallel method for solving discretized diffusion equations

International Nuclear Information System (INIS)

Eccleston, B.R.; Palmer, T.S.

1999-01-01

A Monte Carlo approach to solving linear systems of equations is being investigated in the context of the solution of discretized diffusion equations. While the technique was originally devised decades ago, changes in computer architectures (namely, massively parallel machines) have driven the authors to revisit this technique. There are a number of potential advantages to this approach: (1) Analog Monte Carlo techniques are inherently parallel; this is not necessarily true to today's more advanced linear equation solvers (multigrid, conjugate gradient, etc.); (2) Some forms of this technique are adaptive in that they allow the user to specify locations in the problem where resolution is of particular importance and to concentrate the work at those locations; and (3) These techniques permit the solution of very large systems of equations in that matrix elements need not be stored. The user could trade calculational speed for storage if elements of the matrix are calculated on the fly. The goal of this study is to compare the parallel performance of Monte Carlo linear solvers to that of a more traditional parallelized linear solver. The authors observe the linear speedup that they expect from the Monte Carlo algorithm, given that there is no domain decomposition to cause significant communication overhead. Overall, PETSc outperforms the Monte Carlo solver for the test problem. The PETSc parallel performance improves with larger numbers of unknowns for a given number of processors. Parallel performance of the Monte Carlo technique is independent of the size of the matrix and the number of processes. They are investigating modifications to the scheme to accommodate matrix problems with positive off-diagonal elements. They are also currently coding an on-the-fly version of the algorithm to investigate the solution of very large linear systems

Determination of point isotropic buildup factors of gamma rays including incoherent and coherent scattering for aluminum, iron, lead, and water by discrete ordinates method

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

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)

Radiation Ordinance 1983 (No. 58 of 1983) (Australian Capital Territory)

International Nuclear Information System (INIS)

1983-01-01

This Ordinance provides for the safe use, transportation and disposal of radioactive materials and irradiating apparatus. It repeals the Fluoroscopes Ordinance of 1958. Radioactive materials whose radioactivity does not exceed levels as set out in a Schedule to the Ordinance are exempted from application of the Ordinance. (NEA) [fr

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

On the use of diffusion synthetic acceleration in parallel 3D neutral particle transport calculations

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

Group-theoretical aspects of the discrete sine-Gordon equation

International Nuclear Information System (INIS)

Orfanidis, S.J.

1980-01-01

The group-theoretical interpretation of the sine-Gordon equation in terms of connection forms on fiber bundles is extended to the discrete case. Solutions of the discrete sine-Gordon equation induce surfaces on a lattice in the SU(2) group space. The inverse scattering representation, expressing the parallel transport of fibers, is implemented by means of finite rotations. Discrete Baecklund transformations are realized as gauge transformations. The three-dimensional inverse scattering representation is used to derive a discrete nonlinear sigma model, and the corresponding Baecklund transformation and Pohlmeyer's R transformation are constructed

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

Synchronous Parallel System for Emulation and Discrete Event Simulation

Science.gov (United States)

Steinman, Jeffrey S. (Inventor)

2001-01-01

A synchronous parallel system for emulation and discrete event simulation having parallel nodes responds to received messages at each node by generating event objects having individual time stamps, stores only the changes to the state variables of the simulation object attributable to the event object and produces corresponding messages. The system refrains from transmitting the messages and changing the state variables while it determines whether the changes are superseded, and then stores the unchanged state variables in the event object for later restoral to the simulation object if called for. This determination preferably includes sensing the time stamp of each new event object and determining which new event object has the earliest time stamp as the local event horizon, determining the earliest local event horizon of the nodes as the global event horizon, and ignoring events whose time stamps are less than the global event horizon. Host processing between the system and external terminals enables such a terminal to query, monitor, command or participate with a simulation object during the simulation process.

Computational programs for shielding calculation with transport of one dimensional and monoenergetic SN

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

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

One-, two- and three-dimensional transport codes using multi-group double-differential form cross sections

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)

Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation

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

General Purpose Fortran Program for Discrete-Ordinate-Method Radiative Transfer in Scattering and Emitting Layered Media: An Update of DISORT

Science.gov (United States)

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.

The parallel algorithm for the 2D discrete wavelet transform

Science.gov (United States)

Barina, David; Najman, Pavel; Kleparnik, Petr; Kula, Michal; Zemcik, Pavel

2018-04-01

The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists of a small number of operations, it is preferred for processing using single-core CPUs. However, considering a parallel processing using multi-core processors, this scheme is inappropriate due to a large number of steps. On such architectures, the number of steps corresponds to the number of points that represent the exchange of data. Consequently, these points often form a performance bottleneck. Our approach appropriately rearranges calculations inside the transform, and thereby reduces the number of steps. In other words, we propose a new scheme that is friendly to parallel environments. When evaluating on multi-core CPUs, we consistently overcome the original lifting scheme. The evaluation was performed on 61-core Intel Xeon Phi and 8-core Intel Xeon processors.

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)

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.

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

Optimization and Openmp Parallelization of a Discrete Element Code for Convex Polyhedra on Multi-Core Machines

Science.gov (United States)

Chen, Jian; Matuttis, Hans-Georg

2013-02-01

We report our experiences with the optimization and parallelization of a discrete element code for convex polyhedra on multi-core machines and introduce a novel variant of the sort-and-sweep neighborhood algorithm. While in theory the whole code in itself parallelizes ideally, in practice the results on different architectures with different compilers and performance measurement tools depend very much on the particle number and optimization of the code. After difficulties with the interpretation of the data for speedup and efficiency are overcome, respectable parallelization speedups could be obtained.

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

Application of direct discrete method (DDM) to multigroup neutron transport problems

International Nuclear Information System (INIS)

Vosoughi, Naser; Salehi, Ali Akbar; Shahriari, Majid

2003-01-01

The Direct Discrete Method (DDM), which produced excellent results for one-group neutron transport problems, has been developed for multigroup energy. A multigroup neutron transport discrete equation has been produced for a cylindrical shape fuel element with and without associated coolant regions with two boundary conditions. The calculations are illustrated for two-group energy by graphs showing the fast and thermal fluxes. The validity of the results are tested against the results obtained by the ANISN code. (author)

Parallel discrete event simulation

NARCIS (Netherlands)

Overeinder, B.J.; Hertzberger, L.O.; Sloot, P.M.A.; Withagen, W.J.

1991-01-01

In simulating applications for execution on specific computing systems, the simulation performance figures must be known in a short period of time. One basic approach to the problem of reducing the required simulation time is the exploitation of parallelism. However, in parallelizing the simulation

Anomalous transport in discrete arcs and simulation of double layers in a model auroral circuit

Science.gov (United States)

Smith, Robert A.

1987-01-01

The evolution and long-time stability of a double layer in a discrete auroral arc requires that the parallel current in the arc, which may be considered uniform at the source, be diverted within the arc to charge the flanks of the U-shaped double-layer potential structure. A simple model is presented in which this current re-distribution is effected by anomalous transport based on electrostatic lower hybrid waves driven by the flank structure itself. This process provides the limiting constraint on the double-layer potential. The flank charging may be represented as that of a nonlinear transmission. A simplified model circuit, in which the transmission line is represented by a nonlinear impedance in parallel with a variable resistor, is incorporated in a 1-d simulation model to give the current density at the DL boundaries. Results are presented for the scaling of the DL potential as a function of the width of the arc and the saturation efficiency of the lower hybrid instability mechanism.

Anomalous transport in discrete arcs and simulation of double layers in a model auroral circuit

International Nuclear Information System (INIS)

Smith, R.A.

1987-01-01

The evolution and long-time stability of a double layer (DL) in a discrete auroral arc requires that the parallel current in the arc, which may be considered uniform at the source, be diverted within the arc to charge the flanks of the U-shaped double layer potential structure. A simple model is presented in which this current redistribution is effected by anomalous transport based on electrostatic lower hybrid waves driven by the flank structure itself. This process provides the limiting constraint on the double layer potential. The flank charging may be represented as that of a nonlinear transmission line. A simplified model circuit, in which the transmission line is represented by a nonlinear impedance in parallel with a variable resistor, is incorporated in a one-dimensional simulation model to give the current density at the DL boundaries. Results are presented for the scaling of the DL potential as a function of the width of the arc and the saturation efficiency of the lower hybrid instability mechanism

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

Analytical reconstruction schemes for coarse-mesh spectral nodal solution of slab-geometry SN transport problems

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)

A framework for grand scale parallelization of the combined finite discrete element method in 2d

Science.gov (United States)

Lei, Z.; Rougier, E.; Knight, E. E.; Munjiza, A.

2014-09-01

Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.

An analytical approach for a nodal formulation of a two-dimensional fixed-source neutron transport problem in heterogeneous medium

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.

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

New ordinances

International Nuclear Information System (INIS)

Reuter, H.

1980-01-01

Based on extensive preliminary work of the responsible Federal Minister of Labour and Social Affairs, the 'Ordinance to Replace Ordinances under Article 24 of the Irading and Industrial Code' has been issued by the Federal Government on February 27, 1980. This new ordinance also contains the new versions of the Steam Boiler Ordinance, the Pressure Gas Ordinance, the Lift Ordinance, the Ordinance on Electrical Installations in Rooms with High Explosion Hazards, the Acetylene Ordinance, and the Ordinance on Combustible Liquids. Accordingly, these new ordinances all have the same date of issue. Coming into force on July 1, 1980, they will replace six ordinances for plants to be licensed. The same applies to the pertinent general administrative regulations. (orig.) [de

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

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.

Ordinance of the Prime Minister's Office concerning reports on transport of radioisotopes

International Nuclear Information System (INIS)

1981-01-01

This rule is established under the provisions of the law on the prevention of radiation injuries by radioisotopes and the enforcement ordinance for this law, and to execute the law. Radioisotopes or the goods contaminated by radioisotopes which require reports are the same as those defined in the enforcement regulation for the law. Persons who intend to report on the transport of radioisotopes under the law shall submit two copies of reports in the form specified in this rule to the public safety commissions of prefectures which exercise jurisdiction over the dispatching places of these radioisotopes. The indication matters defined in this rule include speed of the vehicles loaded with radioisotopes, the disposition of escort cars, the formation of these vehicles, cars and other vehicles which accompany to transport, parking areas, the places of loading and unloading, etc. When the transport reported is related to the areas which are under the jurisdiction of other public safety commissions, those commissions which have received the reports shall inform without delay to the commissions concerned the date of transport, course, the kinds and quantities of radioisotopes and other necessary matters. The examinations of transport are made according to the contents of the reports submitted as to whether the transport was made as notified. Reports may be collected on the circumstances of transport outside works or enterprises and the personal injuries by the transport concerned, etc. (Okada, K.)

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

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)

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

Transport modelling for ergodic configurations

International Nuclear Information System (INIS)

Runov, A.; Kasilov, S.V.; McTaggart, N.; Schneider, R.; Bonnin, X.; Zagorski, R.; Reiter, D.

2004-01-01

The effect of ergodization, either by additional coils like in TEXTOR-dynamic ergodic divertor (DED) or by intrinsic plasma effects like in W7-X, defines the need for transport models that are able to describe the ergodic configuration properly. A prerequisite for this is the concept of local magnetic coordinates allowing a correct discretization with minimized numerical errors. For these coordinates the appropriate full metric tensor has to be known. To study the transport in complex edge geometries (in particular for W7-X) two possible methods are used. First, a finite-difference discretization of the transport equations on a custom-tailored grid in local magnetic coordinates is used. This grid is generated by field-line tracing to guarantee an exact discretization of the dominant parallel transport (thus also minimizing the numerical diffusion problem). The perpendicular fluxes are then interpolated in a plane (a toroidal cut), where the interpolation problem for a quasi-isotropic system has to be solved by a constrained Delaunay triangulation (keeping the structural information for magnetic surfaces if they exist) and discretization. All toroidal terms are discretized by finite differences. Second, a Monte Carlo transport model originally developed for the modelling of the DED configuration of TEXTOR is used. A generalization and extension of this model was necessary to be able to handle W7-X. The model solves the transport equations with Monte Carlo techniques making use of mappings of local magnetic coordinates. The application of this technique to W7-X in a limiter-like configuration is presented. The decreasing dominance of parallel transport with respect to radial transport for electron heat, ion heat and particle transport results in increasingly steep profiles for the respective quantities within the islands. (author)

The discrete spectrum in azimuthally dependent transport theory

International Nuclear Information System (INIS)

Garcia, R.D.M.; Siewert, C.E.

1989-01-01

The discrete spectrum for each component of a Fourier decomposition of the azimuthally dependent transport equation is analyzed. For a non-multiplying medium described by an L th -order scattering law, the problem of determining the zeros of the dispersion function for the m th Fourier component is formulated in terms of Sturm sequences. In particular, a straightforward application of the Sturm-sequence property is used to compute the number of discrete eigenvalue pairs κ m and to show that either κ m = γ m or κ m = γ m + 1, where γ m denotes the number of zeros of the Chandrasekhar polynomial g m L+1 (ξ) which are greater than unity. It is also shown how Sturm sequences can be used to construct effective algorithms to compute and to refine estimates of the discrete eigenvalues. Results are presented for a test problem. (author) [pt

A generalized nodal finite element formalism for discrete ordinates equations in slab geometry Part I: Theory in the continuous moment case

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

3D-radiative transfer in terrestrial atmosphere: An efficient parallel numerical procedure

Science.gov (United States)

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

Anomalous transport in discrete arcs and simulation of double layers in a model auroral circuit

International Nuclear Information System (INIS)

Smith, R.A.

1987-01-01

The evolution and long-time stability of a double layer in a discrete auroral arc requires that the parallel current in the arc, which may be considered uniform at the source, be diverted within the arc to change the flanks of the U-shaped double-layer potential structure. A simple model is presented in which this current re-distribution is effected by anomalous transport based on electrostatic lower hybrid waves driven by the flank structure itself. This process provides the limiting constraint on the double-layer potential. The flank charging may be represented as that of a nonlinear transmission line. A simplified model circuit, in which the transmission line is represented by a nonlinear impedance in parallel with a variable resistor, is incorporated in a 1-d simulation model to give the current density at the DL boundaries. Results are presented for the scaling of the DL potential as a function of the width of the arc and the saturation efficiency of the lower hybrid instability mechanism. (author)

Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes; Solucion de la ecuacion de transporte de Boltzmann-Fokker-Planck usando esquemas nodales exponenciales

Energy Technology Data Exchange (ETDEWEB)

Ortega J, R.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: roj@correo.azc.uam.mx

2003-07-01

There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S{sub 4} with expansions of the dispersion cross sections until P{sub 3} order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

Coarse-mesh rebalance methods compatible with the spherical harmonic fictitious source in neutron transport calculations

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)

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

Amendments to ordinances in Radiation Protection Law; Novellierung der strahlenschutzrechtlichen Verordnungen

Energy Technology Data Exchange (ETDEWEB)

Heller, W.

2007-05-15

The last major reform of the German Radiation Protection Ordinance took place on July 26, 2001. The 'First Ordinance Amending Ordinances in Radiation Protection Law' now proposed is to cover primarily the necessary changes and supplements resulting from experience in the execution of the ordinances. They mainly relate to these issues: (1) the scope of application of the Radiation Protection Ordinance and of the x-ray Ordinance in medical research (2) the scope of application of the Radiation Protection Ordinance and the -ray Ordinance in unjustified types of activities (3) electronic communication ('e-government') (4) changes in the provisions about permits and announcements in the Radiation Protection Ordinance (5) new clearance levels in the Radiation Protection Ordinance (6) cross-border transports of 'NORM' materials (7) other changes in the scope of application of the Radiation Protection Ordinance (8) other changes in the x-ray area. (orig.)

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

ANAUSN - a one-dimensional multigroup SN transport theory module for the AUS reactor neutronics system

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 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

Discrete nodal integral transport-theory method for multidimensional reactor physics and shielding calculations

International Nuclear Information System (INIS)

Lawrence, R.D.; Dorning, J.J.

1980-01-01

A coarse-mesh discrete nodal integral transport theory method has been developed for the efficient numerical solution of multidimensional transport problems of interest in reactor physics and shielding applications. The method, which is the discrete transport theory analogue and logical extension of the nodal Green's function method previously developed for multidimensional neutron diffusion problems, utilizes the same transverse integration procedure to reduce the multidimensional equations to coupled one-dimensional equations. This is followed by the conversion of the differential equations to local, one-dimensional, in-node integral equations by integrating back along neutron flight paths. One-dimensional and two-dimensional transport theory test problems have been systematically studied to verify the superior computational efficiency of the new method

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%

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

Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes

International Nuclear Information System (INIS)

Ortega J, R.; Valle G, E. del

2003-01-01

There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S 4 with expansions of the dispersion cross sections until P 3 order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

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

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

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

Ordinance on the Carriage of Dangerous Goods by Rail (GGVE). 2. rev. and enl. ed.

International Nuclear Information System (INIS)

Ridder, K.; Katholnig, F.

1993-01-01

The book presents the legislative texts and other legal provisions concerning the transport of dangerous goods by rail: (1) Act on the transport of dangerous goods, full text. (2) Ordinance on the carriage of dangerous goods by rail (GGVE) - GGVE skeleton ordinance; Annex to the skeleton ordinance. (3) Documents - GGVE implementing regulations RE 001; R 002; Ordinance on exeptions GGVE; Extracts from IAEA recommendations concerning safe transport of radioactive materials; catalogue of fines pertaining to section 10 GGVE. (4) Alphabetical list of materials for GGVE/RID and GGVS/ADR. Index terms printed in deep black at the margin of pages allow quick access to the text passages of interest, and there is a subject index for retrieval over the entire book. (orig./HP) [de

Coupling of a discrete ordinate 3-D radiant heat transfer model with the PHOENICS fluid mechanics software; Couplage d`un modele radiatif tridimensionnel aux ordonnees discretes au logiciel de mecanique des fluides phoenics

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.

Coupling of a discrete ordinate 3-D radiant heat transfer model with the PHOENICS fluid mechanics software; Couplage d`un modele radiatif tridimensionnel aux ordonnees discretes au logiciel de mecanique des fluides phoenics

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.

Introduction of Parallel GPGPU Acceleration Algorithms for the Solution of Radiative Transfer

Science.gov (United States)

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.

Implementation of the kinetics in the transport code AZTRAN; Implementacion de la cinetica en el codigo de transporte AZTRAN

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)

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)

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

Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

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

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%

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

Discrete event simulation of Maglev transport considering traffic waves

Directory of Open Access Journals (Sweden)

Moo Hyun Cha

2014-10-01

Full Text Available A magnetically levitated vehicle (Maglev system is under commercialization as a new transportation system in Korea. The Maglev is operated by an unmanned automatic control system. Therefore, the plan of train operation should be carefully established and validated in advance. In general, when making a train operation plan, statistically predicted traffic data is used. However, a traffic wave often occurs in real train service, and demand-driven simulation technology is required to review a train operation plan and service quality considering traffic waves. We propose a method and model to simulate Maglev operation considering continuous demand changes. For this purpose, we employed a discrete event model that is suitable for modeling the behavior of railway passenger transportation. We modeled the system hierarchically using discrete event system specification (DEVS formalism. In addition, through implementation and an experiment using the DEVSim++ simulation environment, we tested the feasibility of the proposed model. Our experimental results also verified that our demand-driven simulation technology can be used for a priori review of train operation plans and strategies.

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....

Ordinance of 30 June 1976 on radiation protection

International Nuclear Information System (INIS)

1976-01-01

This Ordinance on radiation protection lays down the licensing system for activities in Switzerland involving possible exposure to radiation, with the exception of nuclear installations, fuels and radioactive waste which, under the 1959 Atomic Energy Act, are subject to licensing. The Ordinance applies to the production, handling, use, storage, transport, disposal, import and export of radioactive substances and devices and articles containing them; and generally to any activity involving hazards caused by ionizing radiation. The Federal Public Health Service is the competent authority for granting licences. Provision is also made for the administrative conditions to be complied with for obtaining such licences as well as for technical measures required when engaged in work covered by the Ordinance. (NEA) [fr

Parallel Transport with Sheath and Collisional Effects in Global Electrostatic Turbulent Transport in FRCs

Science.gov (United States)

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.

Some results on the neutron transport and the coupling of equations; Quelques resultats sur le transport neutronique et le couplage d`equations

Energy Technology Data Exchange (ETDEWEB)

Bal, G. [Electricite de France (EDF), Direction des Etudes et Recherches, 92 - Clamart (France)

1997-12-31

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author). 34 refs.

Parallelization of a Monte Carlo particle transport simulation code

Science.gov (United States)

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.

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.

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

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)

Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

Science.gov (United States)

Arteaga, Santiago Egido

1998-12-01

The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the

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)

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

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.

Understanding decimal proportions: discrete representations, parallel access, and privileged processing of zero.

Science.gov (United States)

Varma, Sashank; Karl, Stacy R

2013-05-01

Much of the research on mathematical cognition has focused on the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, with considerably less attention paid to more abstract number classes. The current research investigated how people understand decimal proportions--rational numbers between 0 and 1 expressed in the place-value symbol system. The results demonstrate that proportions are represented as discrete structures and processed in parallel. There was a semantic interference effect: When understanding a proportion expression (e.g., "0.29"), both the correct proportion referent (e.g., 0.29) and the incorrect natural number referent (e.g., 29) corresponding to the visually similar natural number expression (e.g., "29") are accessed in parallel, and when these referents lead to conflicting judgments, performance slows. There was also a syntactic interference effect, generalizing the unit-decade compatibility effect for natural numbers: When comparing two proportions, their tenths and hundredths components are processed in parallel, and when the different components lead to conflicting judgments, performance slows. The results also reveal that zero decimals--proportions ending in zero--serve multiple cognitive functions, including eliminating semantic interference and speeding processing. The current research also extends the distance, semantic congruence, and SNARC effects from natural numbers to decimal proportions. These findings inform how people understand the place-value symbol system, and the mental implementation of mathematical symbol systems more generally. Copyright © 2013 Elsevier Inc. All rights reserved.

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

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

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)

GRAVE: An Interactive Geometry Construction and Visualization Software System for the TORT Nuclear Radiation Transport Code

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

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

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

The influence of collisional and anomalous radial diffusion on parallel ion transport in edge plasmas

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

Spatial and Angular Moment Analysis of Continuous and Discretized Transport Problems

International Nuclear Information System (INIS)

Brantley, Patrick S.; Larsen, Edward W.

2000-01-01

A new theoretical tool for analyzing continuous and discretized transport equations is presented. This technique is based on a spatial and angular moment analysis of the analytic transport equation, which yields exact expressions for the 'center of mass' and 'squared radius of gyration' of the particle distribution. Essentially the same moment analysis is applied to discretized particle transport problems to determine numerical expressions for the center of mass and squared radius of gyration. Because this technique makes no assumption about the optical thickness of the spatial cells or about the amount of absorption in the system, it is applicable to problems that cannot be analyzed by a truncation analysis or an asymptotic diffusion limit analysis. The spatial differencing schemes examined (weighted- diamond, lumped linear discontinuous, and multiple balance) yield a numerically consistent expression for computing the squared radius of gyration plus an error term that depends on the mesh spacing, quadrature constants, and material properties of the system. The numerical results presented suggest that the relative accuracy of spatial differencing schemes for different types of problems can be assessed by comparing the magnitudes of these error terms

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)

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

Some results on the neutron transport and the coupling of equations

International Nuclear Information System (INIS)

Bal, G.

1997-01-01

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author)

Comparison of discrete ordinate and Monte Carlo simulations of polarized radiative transfer in two coupled slabs with different refractive indices.

Science.gov (United States)

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.

Two-dimensional DORT discrete ordinates X-Y geometry neutron flux calculations for the Halden Heavy Boiling Water Reactor core configurations

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.

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)

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)

Radiation transport analyses in support of the SNS Target Station Neutron Beam Line Shutters Title I Design

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

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)

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.)

Application of discrete ordinates and Monte Carlo methods to transport of photons from environmental sources

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

Monte Carlo Transport for Electron Thermal Transport

Science.gov (United States)

Chenhall, Jeffrey; Cao, Duc; Moses, Gregory

2015-11-01

The iSNB (implicit Schurtz Nicolai Busquet multigroup electron thermal transport method of Cao et al. is adapted into a Monte Carlo transport method in order to better model the effects of non-local behavior. The end goal is a hybrid transport-diffusion method that combines Monte Carlo Transport with a discrete diffusion Monte Carlo (DDMC). The hybrid method will combine the efficiency of a diffusion method in short mean free path regions with the accuracy of a transport method in long mean free path regions. The Monte Carlo nature of the approach allows the algorithm to be massively parallelized. Work to date on the method will be presented. This work was supported by Sandia National Laboratory - Albuquerque and the University of Rochester Laboratory for Laser Energetics.

Deteksi Pemalsuan Citra dengan Teknik Copy-Move Menggunakan Metode Ordinal Measure dari Koefisien Discrete Cosine Transform

Directory of Open Access Journals (Sweden)

Zulfan

2016-07-01

Full Text Available This article discusses a new method for the detection of forgery images generated by copy-move technique. Copy-move technique is one of image forgery techniques which taking a particular object from its original image and add it on that image for the purpose of increasing the number of or changing the same object in the original image. This study aims to detect the forged image generated by the copy-move techniques and copy-move forged image that has been modified by the rotation operation and histogram equalization. Detection feature used is Ordinal Measure of Discrete Cosine Transform coefficient (OM-DCT. Detection starts with division of the image into a block size of BXB (B = 16x16, 32x32 and 64x64 and two-dimensional DCT was performed to each of blocks. The feature distance from the original to the fake image, was calculated by the Euclidian distance and each feature has a distance of less than or equal to the threshold value (T according to the observations will be marked as a forged part. The results show that there are blocks detected on the copy-move image, whether on the unmodified copy-move forge image or those which modified by the rotation operation and histogram equalization. The number of blocks that are found in the copy-move object varies according to the size of the detection block used.

Three-Dimensional Full Core Power Calculations for Pressurized Water Reactors

International Nuclear Information System (INIS)

Evans, Thomas M.; Davidson, Gregory G.; Slaybaugh, Rachel N.

2010-01-01

We have implemented a new multilevel parallel decomposition in the Denovo discrete ordinates radiation transport code. In concert with Krylov subspace iterative solvers, the multilevel decomposition allows concurrency over energy in addition to space-angle. The original space-angle partitioning in Denovo placed an eective limit on the scalability of the transport solver that was highly dependent on the problem size. The added phase-space concurrency combined with the high-performance Krylov solvers has enabled weak scaling to 100K cores on the Jaguar XT5 supercomputer. Furthermore, the multilevel decomposition provides enough concurrency to scale to exascale computing and beyond.

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)

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.

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

Parallelization of MCNP Monte Carlo neutron and photon transport code in parallel virtual machine and message passing interface

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)

Time-dependent Perpendicular Transport of Energetic Particles for Different Turbulence Configurations and Parallel Transport Models

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.

The German Radiation Protection Ordinance (StrlSchV). 3. ed.

International Nuclear Information System (INIS)

Hinrichs, O.

1992-01-01

The German Radiation Protection Ordinance constitutes the central statutory instrument containing the main protective provisions for all fields of application of radioactive materials and ionizing radiation, with the exception of the field covered by the X-ray Ordinance. The current text of the Ordinance is that promulgated on 30.06.1989 with the subsequent amendments, as last amended through the Unification Treaty (Einigungsvertrag) of 23.09.1990. The Radiation Protection Ordinance was adopted on the basis of the German Nuclear Energy Act (Atomgesetz), which contains, inter alia, the necessary empowerments to issue statutory ordinances. Further fields containing relevant protective provisions are, above all, the law of dangerous substances (which concerns the transport of radioactive materials), the law of pharmaceutical products and the law of foodstuffs. The whole regulatory package is a part of EC and Euratom law. The limit values of the Euratom Directives were transposed into the Radiation Protection Ordinance. In order to reduce the bulk of the Ordinance, the legislator has only included the limit values for the most important radionuclides, and has made provision for the separate promulgation of the other limit values. In order to enhance the practical use of the book, the provisions governing the radiation pass, which are regulated in a separate administrative instruction, are also reproduced. (orig./HSCH) [de

Parallel, but Dissociable, Processing in Discrete Corticostriatal Inputs Encodes Skill Learning.

Science.gov (United States)

Kupferschmidt, David A; Juczewski, Konrad; Cui, Guohong; Johnson, Kari A; Lovinger, David M

2017-10-11

Changes in cortical and striatal function underlie the transition from novel actions to refined motor skills. How discrete, anatomically defined corticostriatal projections function in vivo to encode skill learning remains unclear. Using novel fiber photometry approaches to assess real-time activity of associative inputs from medial prefrontal cortex to dorsomedial striatum and sensorimotor inputs from motor cortex to dorsolateral striatum, we show that associative and sensorimotor inputs co-engage early in action learning and disengage in a dissociable manner as actions are refined. Disengagement of associative, but not sensorimotor, inputs predicts individual differences in subsequent skill learning. Divergent somatic and presynaptic engagement in both projections during early action learning suggests potential learning-related in vivo modulation of presynaptic corticostriatal function. These findings reveal parallel processing within associative and sensorimotor circuits that challenges and refines existing views of corticostriatal function and expose neuronal projection- and compartment-specific activity dynamics that encode and predict action learning. Published by Elsevier Inc.

Application of space-angle synthesis to two-dimensional neutral-particle transport problems of weapon physics

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

Solution to the transport equation with anisotropic dispersion in a BWR type assembly using the AZTRAN code; Solucion de la ecuacion de transporte con dispersion anisotropica en un ensamble tipo BWR usando el codigo AZTRAN

Energy Technology Data Exchange (ETDEWEB)

Chepe P, M. [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico); Xolocostli M, J. V.; Gomez T, A. M. [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico); Del Valle G, E., E-mail: liaison.web@gmail.com [IPN, Escuela Superior de Fisica y Matematicas, Av. IPN s/n, Col. San Pedro Zacatenco, 07730 Ciudad de Mexico (Mexico)

2016-09-15

Due to the current computing power, the deterministic codes for analyzing nuclear reactors that have been used for several years are becoming more relevant, since much more precise solution techniques can be used; the last century would have been very difficult, since memory and processor capacities were very limited or had high prices on the components. In this work we analyze the effect of the anisotropic dispersion of the effective dispersion section, compared to the isotropic dispersion. The anisotropy implementation was carried out in the AZTRAN transport code, which is part of the AZTLAN platform for nuclear reactors analysis (in development). The AZTRAN code solves the Boltzmann transport equation in one, two and three dimensions at steady state, using the multi-group technique for energy discretization, the RTN-0 nodal method in spatial discretization and for angular discretization the discrete ordinates without considering anisotropy originally. The effect of the anisotropy dispersion on the effective multiplication factor and the axial and radial power on a fuel assembly BWR type are analyzed. (Author)

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

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)

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 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

Coupled electron-photon radiation transport

International Nuclear Information System (INIS)

Lorence, L.; Kensek, R.P.; Valdez, G.D.; Drumm, C.R.; Fan, W.C.; Powell, J.L.

2000-01-01

Massively-parallel computers allow detailed 3D radiation transport simulations to be performed to analyze the response of complex systems to radiation. This has been recently been demonstrated with the coupled electron-photon Monte Carlo code, ITS. To enable such calculations, the combinatorial geometry capability of ITS was improved. For greater geometrical flexibility, a version of ITS is under development that can track particles in CAD geometries. Deterministic radiation transport codes that utilize an unstructured spatial mesh are also being devised. For electron transport, the authors are investigating second-order forms of the transport equations which, when discretized, yield symmetric positive definite matrices. A novel parallelization strategy, simultaneously solving for spatial and angular unknowns, has been applied to the even- and odd-parity forms of the transport equation on a 2D unstructured spatial mesh. Another second-order form, the self-adjoint angular flux transport equation, also shows promise for electron transport

Linear triangle finite element formulation for multigroup neutron transport analysis with anisotropic scattering

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.

Linear triangle finite element formulation for multigroup neutron transport analysis with anisotropic scattering

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

UK Natural Analogue Co-Ordinating Group: first annual progress report

International Nuclear Information System (INIS)

Hooker, P.J.; Chapman, N.A.

1987-11-01

The British Geological Survey is reponsible for co-ordinating the Department of the Environment's programme of natural analogue studies of radionuclide migration, a research programme that involved both UK and overseas sites. Co-ordination is achieved through the UK Natural Analogue Co-ordinating Group (NACG) which was established in October 1986. It has met three times to date and its function is to ensure that the different research projects have an integrated purpose aimed at improving and applying our understanding of natural geochemical processes in a way that will increase our confidence in long-term modelling predictions. Improved modelling prediction of radionuclide transport in the geosphere will directly benefit the performance and safety assessments of proposed radioactive waste repositories. (author)

Rain Scattering and Co-ordinate Distance Calculation

Directory of Open Access Journals (Sweden)

M. Hajny

1998-12-01

Full Text Available Calculations of scattered field on the rain objects are based on using of Multiple MultiPole (MMP numerical method. Both bi-static scattering function and bi-static scattering cross section are calculated in the plane parallel to Earth surface. The co-ordination area was determined using the simple model of scattering volume [1]. Calculation for frequency 9.595 GHz and antenna elevation of 25° was done. Obtained results are compared with calculation in accordance to ITU-R recommendation.

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)

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 ...

Fast parallel molecular algorithms for DNA-based computation: solving the elliptic curve discrete logarithm problem over GF2.

Science.gov (United States)

Li, Kenli; Zou, Shuting; Xv, Jin

2008-01-01

Elliptic curve cryptographic algorithms convert input data to unrecognizable encryption and the unrecognizable data back again into its original decrypted form. The security of this form of encryption hinges on the enormous difficulty that is required to solve the elliptic curve discrete logarithm problem (ECDLP), especially over GF(2(n)), n in Z+. This paper describes an effective method to find solutions to the ECDLP by means of a molecular computer. We propose that this research accomplishment would represent a breakthrough for applied biological computation and this paper demonstrates that in principle this is possible. Three DNA-based algorithms: a parallel adder, a parallel multiplier, and a parallel inverse over GF(2(n)) are described. The biological operation time of all of these algorithms is polynomial with respect to n. Considering this analysis, cryptography using a public key might be less secure. In this respect, a principal contribution of this paper is to provide enhanced evidence of the potential of molecular computing to tackle such ambitious computations.

Solution of the Neutron transport equation in hexagonal geometry using strongly discontinuous nodal schemes; Solucion de la Ecuacion de transporte de neutrones en geometria hexagonal usando esquemas nodales fuertemente discontinuos

Energy Technology Data Exchange (ETDEWEB)

Mugica R, C.A.; Valle G, E. del [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: cmugica@ipn.mx

2005-07-01

In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD{sub 5,3} and WD{sub 12,8} (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD{sub 5,3} and WD{sub 12,8} were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD{sub 3} and SD{sub 8} (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)

Solution to the transport equation with anisotropic dispersion in a BWR type assembly using the AZTRAN code

International Nuclear Information System (INIS)

Chepe P, M.; Xolocostli M, J. V.; Gomez T, A. M.; Del Valle G, E.

2016-09-01

Due to the current computing power, the deterministic codes for analyzing nuclear reactors that have been used for several years are becoming more relevant, since much more precise solution techniques can be used; the last century would have been very difficult, since memory and processor capacities were very limited or had high prices on the components. In this work we analyze the effect of the anisotropic dispersion of the effective dispersion section, compared to the isotropic dispersion. The anisotropy implementation was carried out in the AZTRAN transport code, which is part of the AZTLAN platform for nuclear reactors analysis (in development). The AZTRAN code solves the Boltzmann transport equation in one, two and three dimensions at steady state, using the multi-group technique for energy discretization, the RTN-0 nodal method in spatial discretization and for angular discretization the discrete ordinates without considering anisotropy originally. The effect of the anisotropy dispersion on the effective multiplication factor and the axial and radial power on a fuel assembly BWR type are analyzed. (Author)

Parallel computing for homogeneous diffusion and transport equations in neutronics; Calcul parallele pour les equations de diffusion et de transport homogenes en neutronique

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)

Running Parallel Discrete Event Simulators on Sierra

Energy Technology Data Exchange (ETDEWEB)

Barnes, P. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Jefferson, D. R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-12-03

In this proposal we consider porting the ROSS/Charm++ simulator and the discrete event models that run under its control so that they run on the Sierra architecture and make efficient use of the Volta GPUs.

A NEW MONTE CARLO METHOD FOR TIME-DEPENDENT NEUTRINO RADIATION TRANSPORT

International Nuclear Information System (INIS)

Abdikamalov, Ernazar; Ott, Christian D.; O'Connor, Evan; Burrows, Adam; Dolence, Joshua C.; Löffler, Frank; Schnetter, Erik

2012-01-01

Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them potentially interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the Implicit Monte Carlo photon transport scheme of Fleck and Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, Implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents a robust approach for use in neutrino transport calculations in core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.

A NEW MONTE CARLO METHOD FOR TIME-DEPENDENT NEUTRINO RADIATION TRANSPORT

Energy Technology Data Exchange (ETDEWEB)

Abdikamalov, Ernazar; Ott, Christian D.; O' Connor, Evan [TAPIR, California Institute of Technology, MC 350-17, 1200 E California Blvd., Pasadena, CA 91125 (United States); Burrows, Adam; Dolence, Joshua C. [Department of Astrophysical Sciences, Princeton University, Peyton Hall, Ivy Lane, Princeton, NJ 08544 (United States); Loeffler, Frank; Schnetter, Erik, E-mail: abdik@tapir.caltech.edu [Center for Computation and Technology, Louisiana State University, 216 Johnston Hall, Baton Rouge, LA 70803 (United States)

2012-08-20

Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them potentially interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the Implicit Monte Carlo photon transport scheme of Fleck and Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, Implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents a robust approach for use in neutrino transport calculations in core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.

Reactivity perturbation formulation for a discontinuous Galerkin-based transport solver and its use with adaptive mesh refinement

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)

Development of three-dimensional neoclassical transport simulation code with high performance Fortran on a vector-parallel computer

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)

Applying Multivariate Discrete Distributions to Genetically Informative Count Data.

Science.gov (United States)

Kirkpatrick, Robert M; Neale, Michael C

2016-03-01

We present a novel method of conducting biometric analysis of twin data when the phenotypes are integer-valued counts, which often show an L-shaped distribution. Monte Carlo simulation is used to compare five likelihood-based approaches to modeling: our multivariate discrete method, when its distributional assumptions are correct, when they are incorrect, and three other methods in common use. With data simulated from a skewed discrete distribution, recovery of twin correlations and proportions of additive genetic and common environment variance was generally poor for the Normal, Lognormal and Ordinal models, but good for the two discrete models. Sex-separate applications to substance-use data from twins in the Minnesota Twin Family Study showed superior performance of two discrete models. The new methods are implemented using R and OpenMx and are freely available.

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

Development and implementation of a set of numerical quadratures SQN and EQN type in the transport code AZTRAN

International Nuclear Information System (INIS)

Chepe P, M.; Xolocostli M, J. V.; Gomez T, A. M.; Del Valle G, E.

2015-09-01

The deterministic transport codes for analysis of nuclear reactors have been used for several years already, these codes have evolved in terms of the methodology used and the degree of accuracy, because at the present time has more computer power. In this paper, the transport code used considers the classical technique of multi-group for discretization energy, for space discretization uses the nodal methods, while for the angular discretization the discrete ordinates method is used; so that presents the development and implementation of a set of numerical quadratures of SQ N type symmetrical with the same weight for each angular direction and these are compared with the quadratures of EQ N type. The two sets of numerical quadratures were implemented in the program AZTRAN to a problem with isotropic medium in XYZ geometry, in steady state using the nodal method RTN-0 (Raviart-Thomas-Nedelec). The analyzed results correspond to the effective multiplication factor k eff and neutron angular flux with approximations from S 4 to S 16 . (Author)

X-ray Ordinance

International Nuclear Information System (INIS)

Kramer, R.; Zerlett, G.

1983-01-01

This commentary, presented as volume 2 of the Deutsches Strahlenschutzrecht (German legislation on radiation protection) deals with the legal provisions of the ordinance on the protection against harmful effects of X-radiation (X-ray Ordinance - RoeV), of March 1, 1973 (announced in BGBl.I, page 173), as amended by the ordinance on the protection against harmful effects of ionizing radiation, of October 13, 1976 (announced in BGBl. I, page 2905). Thus volume 2 completes the task started with volume 1, namely to present a comprehensive view and account of the body of laws governing radiation protection, a task which was thought useful as developments in the FRG led to regulations being split up into the X-ray Ordinance, and the Radiation Protection Ordinance. In order to present a well-balanced commentary on the X-ray Ordinance, it was necessary to discuss the provisions both from the legal and the medical point of view. This edition takes into account the Fourth Public Notice of the BMA (Fed. Min. of Labour and Social Affairs) concerning the implementation of the X-ray Ordinance of January 4, 1982, as well as court decisions and literature published in this field, until September 1982. In addition, the judgment of the Federal Constitutional Court, dated October 19, 1982, concerning the voidness of the law on government liability, and two decisions by the Federal High Court, dated November 23, 1982, concerning the right to have insight into medical reports - of great significance in practice - have been considered. This commentary therefore is up to date with current developments. (orig.) [de

Verification & Validation of High-Order Short-Characteristics-Based Deterministic Transport Methodology on Unstructured Grids

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.

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)

Ordinance on the Protection against X-Radiation Hazards (X-Ray Ordinance)

International Nuclear Information System (INIS)

1987-01-01

The ordinance refers to X-ray equipment and to stray radiation sources which generate X-radiation of at least 5 keV by means of accelerated electrons, and for this purpose apply an acceleration energy not exceeding 3 MeV. The ordinance does not apply to stray radiation sources which are used for the generation of ionizing particle radiation and thus are subject to the provisions of the Radiation Protection Ordinance. (orig./PW) [de

IAEA co-ordinated research programme on the transport of low specific activity materials and surface contaminated objects

International Nuclear Information System (INIS)

Gray, I.L.S.

2000-01-01

The International Atomic Energy Agency (IAEA) prepares regulations for the safe transport of radioactive material, and periodically revised editions of these are published. These regulations are adopted by individual countries across the world and by international organisations concerned with transport. Whilst it is desirable to have a stable framework of regulatory requirements, there is also a need to take account of technical advances and operational experience and revise the regulations. From time to time Co-ordinated Research Programmes (CRP) are established to investigate particular areas of the regulations that are giving concern. In 1996 the IAEA Standing Advisory Group on the Transport of Radioactive Material (SAGSTRAM) concluded that the requirements for classification, packaging and transport of low specific activity (LSA) material and surface contaminated objects (SCO) did not always have a strong radiation protection basis. Accordingly SAGSTRAM established a CRP with an overall objective to develop a dose-based approach for establishing LSA/SCO requirements. Six countries are participating in this CRP. Brazil, Canada, France, Germany, United Kingdom and United States. Each country is carrying out work that is outlined in agreements with the IAEA, with the work aimed at meeting the specific objective of the agreement and also contributing to achieving the overall objective of the CRP. Completion of the CRP usually involves the preparation of an IAEA TECDOC by a Consultant Services Meeting (CSM), and this TECDOC will summarise the work performed under the CRP and include any recommendations made by the CRP. Following the establishment of the CRP in 1997, the first Research Co-ordination Meeting (RCM) was held in December 1997. The second RCM was held in March 1999, with the final RCM planned for the end of 2000. The work being carried out by Brazil and Canada is focused upon the transport of uranium and thorium ores, and is a mixture of theoretical and

Solution of the Neutron transport equation in hexagonal geometry using strongly discontinuous nodal schemes

International Nuclear Information System (INIS)

Mugica R, C.A.; Valle G, E. del

2005-01-01

In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD 5,3 and WD 12,8 (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD 5,3 and WD 12,8 were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD 3 and SD 8 (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)

An S_N Algorithm for Modern Architectures

Energy Technology Data Exchange (ETDEWEB)

Baker, Randal Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2016-08-29

LANL discrete ordinates transport packages are required to perform large, computationally intensive time-dependent calculations on massively parallel architectures, where even a single such calculation may need many months to complete. While KBA methods scale out well to very large numbers of compute nodes, we are limited by practical constraints on the number of such nodes we can actually apply to any given calculation. Instead, we describe a modified KBA algorithm that allows realization of the reductions in solution time offered by both the current, and future, architectural changes within a compute node.

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)

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

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

Mathematics and computational methods development in U.S. department of energy-sponsored research (nuclear energy research initiative and nuclear engineering education research). 4. Development of an Expert System for Generation of an Effective Mesh Distribution for the SN Method

International Nuclear Information System (INIS)

Patchimpattapong, Apisit; Haghighat, Alireza

2001-01-01

The discrete ordinates (S N ) method is widely used to obtain numerical solutions of the transport equation. The method calls for discretization of spatial, energy, and angular variables. To generate an 'effective' spatial mesh distribution, one has to consider various factors including particle mean free path (mfp), material and source discontinuities, and problem objectives. This becomes more complicated if we consider the effect of numerics such as differencing schemes, parallel processing strategies, and computation resources. As a result, one may often over/under-mesh depending upon limitations on accuracy, computing resources, and time allotted. To overcome the foregoing issues, we are developing an expert system for input preparation of the discrete ordinates (S N ) method. This project is a part of an ongoing project sponsored by Nuclear Engineering Education Research. Our expert system consists of two parts: (a) an algorithm for generation of a mesh distribution for a serial calculation and (b) an algorithm for extension to parallel computing, which accounts for parallelization parameters including granularity, load balancing, parallel algorithms, and possible architectural issues. Thus far, we have developed a stand-alone algorithm for generation of an 'effective' mesh distribution for a serial calculation. The algorithm has been successfully tested with the Parallel Environment Neutral-Particle Transport (PENTRAN) code system. In this paper, we discuss the structure of our algorithm and present its use for simulating the VENUS-3 experimental facility. To date, we have developed and tested part 1 of this system. This part comprises of four steps: creation of a geometric model and coarse meshes, calculation of un-collided flux, selection of differencing schemes, and generation of fine-mesh distribution. For the un-collided flux calculation, we have developed a parallel code called PENFC. It is capable of calculating un-collided and first-collision fluxes

The Second Ordinance for Amendment of the Radiation Protection Ordinance

International Nuclear Information System (INIS)

Czajka, D.

1989-01-01

This Second Ordinance for Amendment of the Radiation Protection Ordinance has modified the most important legal provisions supplementing the Atomic Energy Act. But looking closer at the revised version of the Ordinance, many an amendment turns out to be just a new facade on the old brickwork. The article critically reviews the most important amendments, stating that the main principles have remained untouched, and discussing the modification of limiting values, the definition of regulatory scopes, the new meaning of the term 'wastes containing nuclear fuel', and the regulatory scope of provisions governing radioactive substances and their medical applications. (orig./RST) [de

Parallel Implementation of the Discrete Green's Function Formulation of the FDTD Method on a Multicore Central Processing Unit

Directory of Open Access Journals (Sweden)

T. Stefański

2014-12-01

Full Text Available Parallel implementation of the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD method was developed on a multicore central processing unit. DGF-FDTD avoids computations of the electromagnetic field in free-space cells and does not require domain termination by absorbing boundary conditions. Computed DGF-FDTD solutions are compatible with the FDTD grid enabling the perfect hybridization of FDTD with the use of time-domain integral equation methods. The developed implementation can be applied to simulations of antenna characteristics. For the sake of example, arrays of Yagi-Uda antennas were simulated with the use of parallel DGF-FDTD. The efficiency of parallel computations was investigated as a function of the number of current elements in the FDTD grid. Although the developed method does not apply the fast Fourier transform for convolution computations, advantages stemming from the application of DGF-FDTD instead of FDTD can be demonstrated for one-dimensional wire antennas when simulation results are post-processed by the near-to-far-field transformation.

Boron transport in plants: co-ordinated regulation of transporters

Science.gov (United States)

Miwa, Kyoko; Fujiwara, Toru

2010-01-01

Background The essentiality of boron (B) for plant growth was established >85 years ago. In the last decade, it has been revealed that one of the physiological roles of B is cross-linking the pectic polysaccharide rhamnogalacturonan II in primary cell walls. Borate cross-linking of pectic networks serves both for physical strength of cell walls and for cell adhesion. On the other hand, high concentrations of B are toxic to plant growth. To avoid deficiency and toxicity problems, it is important for plants to maintain their tissue B concentrations within an optimum range by regulating transport processes. Boron transport was long believed to be a passive, unregulated process, but the identification of B transporters has suggested that plants sense and respond to the B conditions and regulate transporters to maintain B homeostasis. Scope Transporters responsible for efficient B uptake by roots, xylem loading and B distribution among leaves have been described. These transporters are required under B limitation for efficient acquisition and utilization of B. Transporters important for tolerating high B levels in the environment have also been identified, and these transporters export B from roots back to the soil. Two types of transporters are involved in these processes: NIPs (nodulin-26-like intrinsic proteins), boric acid channels, and BORs, B exporters. It is demonstrated that the expression of genes encoding these transporters is finely regulated in response to B availability in the environment to ensure tissue B homeostasis. Furthermore, plants tolerant to stress produced by low B or high B in the environment can be generated through altered expression of these transporters. Conclusions The identification of the first B transporter led to the discovery that B transport was a process mediated not only by passive diffusion but also by transporters whose activity was regulated in response to B conditions. Now it is evident that plants sense internal and external B

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

Concatenating algorithms for parallel numerical simulations coupling radiation hydrodynamics with neutron transport

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)

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)

Development and implementation of a set of numerical quadratures SQ{sub N} and EQ{sub N} type in the transport code AZTRAN; Desarrollo e implementacion de un conjunto de cuadraturas numericas de tipo SQ{sub N} y EQ{sub N} en el codigo de transporte AZTRAN

Energy Technology Data Exchange (ETDEWEB)

Chepe P, M. [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico); Xolocostli M, J. V.; Gomez T, A. M. [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico); Del Valle G, E., E-mail: liaison.web@gmail.com [IPN, Escuela Superior de Fisica y Matematicas, Av. IPN s/n, Col. Lindavista, 07738 Ciudad de Mexico (Mexico)

2015-09-15

The deterministic transport codes for analysis of nuclear reactors have been used for several years already, these codes have evolved in terms of the methodology used and the degree of accuracy, because at the present time has more computer power. In this paper, the transport code used considers the classical technique of multi-group for discretization energy, for space discretization uses the nodal methods, while for the angular discretization the discrete ordinates method is used; so that presents the development and implementation of a set of numerical quadratures of SQ{sub N} type symmetrical with the same weight for each angular direction and these are compared with the quadratures of EQ{sub N} type. The two sets of numerical quadratures were implemented in the program AZTRAN to a problem with isotropic medium in XYZ geometry, in steady state using the nodal method RTN-0 (Raviart-Thomas-Nedelec). The analyzed results correspond to the effective multiplication factor k{sub eff} and neutron angular flux with approximations from S{sub 4} to S{sub 16}. (Author)

Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations

Science.gov (United States)

Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen

2015-04-01

This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive

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

Preparation and crystal structure of carbonyltris (diethyldithiocarbamato) technetium (III): an unexpected source of co-ordinated carbon monoxide

International Nuclear Information System (INIS)

Baldas, J.; Bonnyman, J.; Pojer, P.M.; Williams, G.A.

1981-10-01

Tc(S 2 CNEt 2 ) 3 CO has been prepared by the reduction of NH 4 TcO 4 with formamidinesulphinic acid in the presence of NaS 2 CNEt 2 . It is suggested that the co-ordinated carbon monoxide is formed after co-ordination of formamidinesulphinic acid, or some decomposition product, with technetium. The crystal structure of Tc(S 2 CNEt 2 ) 3 CO has been determined by single-crystal X-ray diffraction methods at 17 deg. C. Diffractometry has provided significant Bragg intensities for 2045 independent reflections and the structure has been refined by full-matrix least-squares methods to R 0.049. The compound is isostructural with the rhenium analogue and consists of discrete Tc(S 2 CNEt 2 ) 3 CO molecules, each containing a terminal linear CO group. The technetium atom has a seven co-ordinate environment which is best described as a distorted pentagonal bipyramid

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))

Radioactive whey concentrate - a case to apply section 3 of the Radiation Protection Ordinance

International Nuclear Information System (INIS)

Sauer, G.W.; Zypries, B.

1988-01-01

According to the authors, section 4 StrlSchV does not apply, the case has to be handled applying section 3 StrlSchV (Radiation Protection Ordinance). This means that the storage, treatment and disposal of the radioactive whey concentrate is subject to licensing. Disposal as radioactive waste, however, will require a licence only if the limit given in section 4 IV, No. 2 lit. e, the 10 -4 -fold of the allowed radioactivity per gramme (i.e. 3700 Bq/kg) is exceeded. The averaged radioactivity data measured do exceed this limit. Only the transport of the radioactive whey concentrate does not fall under the provisions of the ordinances on road transport or rail transport of hazardons substances, as the limit given there is 74 Bq/g of specific activity. (orig./HP) [de

Solution algorithms for a PN-1 - Equivalent SN angular discretization of the transport equation in one-dimensional spherical coordinates

International Nuclear Information System (INIS)

Warsa, J. S.; Morel, J. E.

2007-01-01

Angular discretizations of the S N transport equation in curvilinear coordinate systems may result in a streaming-plus-removal operator that is dense in the angular variable or that is not lower-triangular. We investigate numerical solution algorithms for such angular discretizations using relationships given by Chandrasekhar to compute the angular derivatives in the one-dimensional S N transport equation in spherical coordinates with Gauss quadrature. This discretization makes the S N transport equation P N-1 - equivalent, but it also makes the sweep operator dense at every spatial point because the N angular derivatives are expressed in terms of the N angular fluxes. To avoid having to invert the sweep operator directly, we must work with the angular fluxes to solve the equations iteratively. We show how we can use approximations to the sweep operator to precondition the full P N-1 equivalent S N equations. We show that these pre-conditioners affect the operator enough such that convergence of a Krylov iterative method improves. (authors)

Ordinal measures for iris recognition.

Science.gov (United States)

Sun, Zhenan; Tan, Tieniu

2009-12-01

Images of a human iris contain rich texture information useful for identity authentication. A key and still open issue in iris recognition is how best to represent such textural information using a compact set of features (iris features). In this paper, we propose using ordinal measures for iris feature representation with the objective of characterizing qualitative relationships between iris regions rather than precise measurements of iris image structures. Such a representation may lose some image-specific information, but it achieves a good trade-off between distinctiveness and robustness. We show that ordinal measures are intrinsic features of iris patterns and largely invariant to illumination changes. Moreover, compactness and low computational complexity of ordinal measures enable highly efficient iris recognition. Ordinal measures are a general concept useful for image analysis and many variants can be derived for ordinal feature extraction. In this paper, we develop multilobe differential filters to compute ordinal measures with flexible intralobe and interlobe parameters such as location, scale, orientation, and distance. Experimental results on three public iris image databases demonstrate the effectiveness of the proposed ordinal feature models.

Synchronous Parallel Emulation and Discrete Event Simulation System with Self-Contained Simulation Objects and Active Event Objects

Science.gov (United States)

Steinman, Jeffrey S. (Inventor)

1998-01-01

The present invention is embodied in a method of performing object-oriented simulation and a system having inter-connected processor nodes operating in parallel to simulate mutual interactions of a set of discrete simulation objects distributed among the nodes as a sequence of discrete events changing state variables of respective simulation objects so as to generate new event-defining messages addressed to respective ones of the nodes. The object-oriented simulation is performed at each one of the nodes by assigning passive self-contained simulation objects to each one of the nodes, responding to messages received at one node by generating corresponding active event objects having user-defined inherent capabilities and individual time stamps and corresponding to respective events affecting one of the passive self-contained simulation objects of the one node, restricting the respective passive self-contained simulation objects to only providing and receiving information from die respective active event objects, requesting information and changing variables within a passive self-contained simulation object by the active event object, and producing corresponding messages specifying events resulting therefrom by the active event objects.

Sub-cell balanced nodal expansion methods using S4 eigenfunctions for multi-group SN transport problems in slab geometry

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)

A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

KAUST Repository

El-Amin, Mohamed F.; Kou, Jisheng; Sun, Shuyu

2017-01-01

Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy's law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.

A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

KAUST Repository

El-Amin, Mohamed F.

2017-06-06

Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy\\'s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.

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

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

Albedo boundary conditions for global calculations of thermal nuclear reactors with the model of discrete ordinates to two energy groups

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)

Neutronics analysis of the International Thermonuclear Experimental Reactor (ITER) MCNP ''Benchmark CAD Model'' with the ATTILA discrete ordinance code

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.)

Simulating Ordinal Data

Science.gov (United States)

Ferrari, Pier Alda; Barbiero, Alessandro

2012-01-01

The increasing use of ordinal variables in different fields has led to the introduction of new statistical methods for their analysis. The performance of these methods needs to be investigated under a number of experimental conditions. Procedures to simulate from ordinal variables are then required. In this article, we deal with simulation from…

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...

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)

User's manual for ONEDANT: a code package for one-dimensional, diffusion-accelerated, neutral-particle transport

International Nuclear Information System (INIS)

O'Dell, R.D.; Brinkley, F.W. Jr.; Marr, D.R.

1982-02-01

ONEDANT is designed for the CDC-7600, but the program has been implemented and run on the IBM-370/190 and CRAY-I computers. ONEDANT solves the one-dimensional multigroup transport equation in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous (k/sub eff/ and eigenvalue search) 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. ONEDANT numerically solves the one-dimensional, multigroup form of the neutral-particle, steady-state form of the Boltzmann transport equation. The discrete-ordinates approximation is used for treating the angular variation of the particle distribution and the diamond-difference scheme is used for phase space discretization. Negative fluxes are eliminated by a local set-to-zero-and-correct algorithm. A standard inner (within-group) iteration, outer (energy-group-dependent source) iteration technique is used. Both inner and outer iterations are accelerated using the diffusion synthetic acceleration method

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.

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.

Co-ordinated traffic control in freeway corridors : A proposed evaluation approach

NARCIS (Netherlands)

Hoogendoorn, S.P.; Bovy, P.H.L.; Van der Zijpp, N.J.

1997-01-01

In the course of the Telematics implications Programme Transport of the European Commission Fourth Framework Research Programme much attention is devoted to evaluation and demonstration. This report is part of the DACCORD project TR1017, devoted to the development and application of co-ordinated