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

Multidimensional electron-photon transport with standard discrete ordinates codes

International Nuclear Information System (INIS)

Drumm, C.R.

1995-01-01

A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electronphoton transport problems

The 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

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.

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

Meshes optimized for discrete exterior calculus (DEC).

Energy Technology Data Exchange (ETDEWEB)

Mousley, Sarah C. [Univ. of Illinois, Urbana-Champaign, IL (United States); Deakin, Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Knupp, Patrick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, Scott A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-12-01

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximation of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.

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

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

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)

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

Time dependence linear transport III convergence of the discrete ordinate method

International Nuclear Information System (INIS)

Wilson, D.G.

1983-01-01

In this paper the uniform pointwise convergence of the discrete ordinate method for weak and strong solutions of the time dependent, linear transport equation posed in a multidimensional, rectangular parallelepiped with partially reflecting walls is established. The first result is that a sequence of discrete ordinate solutions converges uniformly on the quadrature points to a solution of the continuous problem provided that the corresponding sequence of truncation errors for the solution of the continuous problem converges to zero in the same manner. The second result is that continuity of the solution with respect to the velocity variables guarantees that the truncation erros in the quadrature formula go the zero and hence that the discrete ordinate approximations converge to the solution of the continuous problem as the discrete ordinate become dense. An existence theory for strong solutions of the the continuous problem follows as a result

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.

Multidimensional electron-photon transport with standard discrete ordinates codes

International Nuclear Information System (INIS)

Drumm, C.R.

1997-01-01

A method is described for generating electron cross sections that are comparable with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electron-photon transport problems. The key to the method is a simultaneous solution of the continuous-slowing-down (CSD) portion and elastic-scattering portion of the scattering source by the Goudsmit-Saunderson theory. The resulting multigroup-Legendre cross sections are much smaller than the true scattering cross sections that they represent. Under certain conditions, the cross sections are guaranteed positive and converge with a low-order Legendre expansion

Multidimensional electron-photon transport with standard discrete ordinates codes

International Nuclear Information System (INIS)

Drumm, C.R.

1997-01-01

A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages to using an established discrete ordinates solver, e.g., immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and synthetic radiation environments. The cross sections have been successfully used in the DORT, TWODANT, and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electron-photon transport problems. The key to the method is a simultaneous solution of the continuous-slowing-down and elastic-scattering portions of the scattering source by the Goudsmit-Saunderson theory. The resulting multigroup-Legendre cross sections are much smaller than the true scattering cross sections that they represent. Under certain conditions, the cross sections are guaranteed positive and converge with a low-order Legendre expansion

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.

2016-02-11

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

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

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

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

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...

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

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)

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

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)

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)

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.

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)

Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations

International Nuclear Information System (INIS)

Bonelle, Jerome

2014-01-01

This thesis presents a new class of spatial discretization schemes on polyhedral meshes, called Compatible Discrete Operator (CDO) schemes and their application to elliptic and Stokes equations In CDO schemes, preserving the structural properties of the continuous equations is the leading principle to design the discrete operators. De Rham maps define the degrees of freedom according to the physical nature of fields to discretize. CDO schemes operate a clear separation between topological relations (balance equations) and constitutive relations (closure laws). Topological relations are related to discrete differential operators, and constitutive relations to discrete Hodge operators. A feature of CDO schemes is the explicit use of a second mesh, called dual mesh, to build the discrete Hodge operator. Two families of CDO schemes are considered: vertex-based schemes where the potential is located at (primal) mesh vertices, and cell-based schemes where the potential is located at dual mesh vertices (dual vertices being in one-to-one correspondence with primal cells). The CDO schemes related to these two families are presented and their convergence is analyzed. A first analysis hinges on an algebraic definition of the discrete Hodge operator and allows one to identify three key properties: symmetry, stability, and P0-consistency. A second analysis hinges on a definition of the discrete Hodge operator using reconstruction operators, and the requirements on these reconstruction operators are identified. In addition, CDO schemes provide a unified vision on a broad class of schemes proposed in the literature (finite element, finite element, mimetic schemes... ). Finally, the reliability and the efficiency of CDO schemes are assessed on various test cases and several polyhedral meshes. (author)

Discrete Ordinates Method-Like Computation with Group Condensation and Angle Collapsing in Transport Theory

International Nuclear Information System (INIS)

Won, Jong Hyuck; Cho, Nam Zin

2010-01-01

In group condensation for transport method, it is well-known that angle-dependent total cross section is generated. To remove this difficulty on angledependent total cross section, we normally perform the group condensation on total cross section by using scalar flux weight as used in neutron diffusion method. In this study, angle-dependent total cross section is directly applied to the discrete ordinates method. In addition, angle collapsing concept is introduced based on equivalence to reduce calculational burden of transport computation. We also show numerical results for a heterogeneous 1-D slab problem with local/global iteration, in which fine-group discrete ordinates calculation is used in local problem while few-group angle collapsed discrete ordinates calculation is used in global problem iteratively

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)

Variable discrete ordinates method for radiation transfer in plane-parallel semi-transparent media with variable refractive index

Science.gov (United States)

Sarvari, S. M. Hosseini

2017-09-01

The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.

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 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

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

A parallel algorithm for solving the multidimensional within-group discrete ordinates equations with spatial domain decomposition - 104

International Nuclear Information System (INIS)

Zerr, R.J.; Azmy, Y.Y.

2010-01-01

A spatial domain decomposition with a parallel block Jacobi solution algorithm has been developed based on the integral transport matrix formulation of the discrete ordinates approximation for solving the within-group transport equation. The new methodology abandons the typical source iteration scheme and solves directly for the fully converged scalar flux. Four matrix operators are constructed based upon the integral form of the discrete ordinates equations. A single differential mesh sweep is performed to construct these operators. The method is parallelized by decomposing the problem domain into several smaller sub-domains, each treated as an independent problem. The scalar flux of each sub-domain is solved exactly given incoming angular flux boundary conditions. Sub-domain boundary conditions are updated iteratively, and convergence is achieved when the scalar flux error in all cells meets a pre-specified convergence criterion. The method has been implemented in a computer code that was then employed for strong scaling studies of the algorithm's parallel performance via a fixed-size problem in tests ranging from one domain up to one cell per sub-domain. Results indicate that the best parallel performance compared to source iterations occurs for optically thick, highly scattering problems, the variety that is most difficult for the traditional SI scheme to solve. Moreover, the minimum execution time occurs when each sub-domain contains a total of four cells. (authors)

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

International Nuclear Information System (INIS)

FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov

2002-01-01

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

CERN Document Server

Fan, W C; Powell, J L

2002-01-01

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

Coarse-mesh discretized low-order quasi-diffusion equations for subregion averaged scalar fluxes

International Nuclear Information System (INIS)

Anistratov, D. Y.

2004-01-01

In this paper we develop homogenization procedure and discretization for the low-order quasi-diffusion equations on coarse grids for core-level reactor calculations. The system of discretized equations of the proposed method is formulated in terms of the subregion averaged group scalar fluxes. The coarse-mesh solution is consistent with a given fine-mesh discretization of the transport equation in the sense that it preserves a set of average values of the fine-mesh transport scalar flux over subregions of coarse-mesh cells as well as the surface currents, and eigenvalue. The developed method generates numerical solution that mimics the large-scale behavior of the transport solution within assemblies. (authors)

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)

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

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)

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.

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

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

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

Experiences in the parallelization of the discrete ordinates method using OpenMP and MPI

Energy Technology Data Exchange (ETDEWEB)

Pautz, A. [TUV Hannover/Sachsen-Anhalt e.V. (Germany); Langenbuch, S. [Gesellschaft fur Anlagen- und Reaktorsicherheit (GRS) mbH (Germany)

2003-07-01

The method of Discrete Ordinates is in principle parallelizable to a high degree, since the transport 'mesh sweeps' are mutually independent for all angular directions. However, in the well-known production code Dort such a type of angular domain decomposition has to be done on a spatial line-byline basis, causing the parallelism in the code to be very fine-grained. The construction of scalar fluxes and moments requires a large effort for inter-thread or inter-process communication. We have implemented two different parallelization approaches in Dort: firstly, we have used a shared-memory model suitable for SMP (Symmetric Multiprocessor) machines based on the standard OpenMP. The second approach uses the well-known Message Passing Interface (MPI) to establish communication between parallel processes running in a distributed-memory environment. We investigate the benefits and drawbacks of both models and show first results on performance and scaling behaviour of the parallel Dort code. (authors)

Experiences in the parallelization of the discrete ordinates method using OpenMP and MPI

International Nuclear Information System (INIS)

Pautz, A.; Langenbuch, S.

2003-01-01

The method of Discrete Ordinates is in principle parallelizable to a high degree, since the transport 'mesh sweeps' are mutually independent for all angular directions. However, in the well-known production code Dort such a type of angular domain decomposition has to be done on a spatial line-byline basis, causing the parallelism in the code to be very fine-grained. The construction of scalar fluxes and moments requires a large effort for inter-thread or inter-process communication. We have implemented two different parallelization approaches in Dort: firstly, we have used a shared-memory model suitable for SMP (Symmetric Multiprocessor) machines based on the standard OpenMP. The second approach uses the well-known Message Passing Interface (MPI) to establish communication between parallel processes running in a distributed-memory environment. We investigate the benefits and drawbacks of both models and show first results on performance and scaling behaviour of the parallel Dort code. (authors)

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

Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

Energy Technology Data Exchange (ETDEWEB)

Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.

2006-01-01

Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.

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

A constrained Delaunay discretization method for adaptively meshing highly discontinuous geological media

Science.gov (United States)

Wang, Yang; Ma, Guowei; Ren, Feng; Li, Tuo

2017-12-01

A constrained Delaunay discretization method is developed to generate high-quality doubly adaptive meshes of highly discontinuous geological media. Complex features such as three-dimensional discrete fracture networks (DFNs), tunnels, shafts, slopes, boreholes, water curtains, and drainage systems are taken into account in the mesh generation. The constrained Delaunay triangulation method is used to create adaptive triangular elements on planar fractures. Persson's algorithm (Persson, 2005), based on an analogy between triangular elements and spring networks, is enriched to automatically discretize a planar fracture into mesh points with varying density and smooth-quality gradient. The triangulated planar fractures are treated as planar straight-line graphs (PSLGs) to construct piecewise-linear complex (PLC) for constrained Delaunay tetrahedralization. This guarantees the doubly adaptive characteristic of the resulted mesh: the mesh is adaptive not only along fractures but also in space. The quality of elements is compared with the results from an existing method. It is verified that the present method can generate smoother elements and a better distribution of element aspect ratios. Two numerical simulations are implemented to demonstrate that the present method can be applied to various simulations of complex geological media that contain a large number of discontinuities.

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)

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)

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

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

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

Influence of an SN solver in a fine-mesh neutronics/thermal-hydraulics framework

International Nuclear Information System (INIS)

Jareteg, Klas; Vinai, Paolo; Demaziere, Christophe; Sasic, Srdjan

2015-01-01

In this paper a study on the influence of a neutron discrete ordinates (S N ) solver within a fine-mesh neutronic/thermal-hydraulic methodology is presented. The methodology consists of coupling a neutronic solver with a single-phase fluid solver, and it is aimed at computing the two fields on a three-dimensional (3D) sub-pin level. The cross-sections needed for the neutron transport equations are pre-generated using a Monte Carlo approach. The coupling is resolved in an iterative manner with full convergence of both fields. A conservative transfer of the full 3D information is achieved, allowing for a proper coupling between the neutronic and the thermal-hydraulic meshes on the finest calculated scales. The discrete ordinates solver is benchmarked against a Monte Carlo reference solution for a two-dimensional (2D) system. The results confirm the need of a high number of ordinates, giving a satisfactory accuracy in k eff and scalar flux profile applying S 16 for 16 energy groups. The coupled framework is used to compare the S N implementation and a solver based on the neutron diffusion approximation for a full 3D system of a quarter of a symmetric, 7x7 array in an infinite lattice setup. In this case, the impact of the discrete ordinates solver shows to be significant for the coupled system, as demonstrated in the calculations of the temperature distributions. (author)

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.

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.

Numerical convergence of discrete exterior calculus on arbitrary surface meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2018-01-01

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special

Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

Science.gov (United States)

Thompson, David; Tong, Xiaoling; Arnoldus, Qiuhan; Collins, Eric; McLaurin, David; Luke, Edward; Bidwell, Colin S.

2013-01-01

Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

Numerical convergence of discrete exterior calculus on arbitrary surface meshes

KAUST Repository

Mohamed, Mamdouh S.

2018-02-13

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially for curved surfaces. This paper presents numerical evidence demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.

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)

Parallel ray tracing for one-dimensional discrete ordinate computations

International Nuclear Information System (INIS)

Jarvis, R.D.; Nelson, P.

1996-01-01

The ray-tracing sweep in discrete-ordinates, spatially discrete numerical approximation methods applied to the linear, steady-state, plane-parallel, mono-energetic, azimuthally symmetric, neutral-particle transport equation can be reduced to a parallel prefix computation. In so doing, the often severe penalty in convergence rate of the source iteration, suffered by most current parallel algorithms using spatial domain decomposition, can be avoided while attaining parallelism in the spatial domain to whatever extent desired. In addition, the reduction implies parallel algorithm complexity limits for the ray-tracing sweep. The reduction applies to all closed, linear, one-cell functional (CLOF) spatial approximation methods, which encompasses most in current popular use. Scalability test results of an implementation of the algorithm on a 64-node nCube-2S hypercube-connected, message-passing, multi-computer are described. (author)

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.

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

DOT-IV two-dimensional discrete ordinates transport code with space-dependent mesh and quadrature

International Nuclear Information System (INIS)

Rhoades, W.A.; Simpson, D.B.; Childs, R.L.; Engle, W.W. Jr.

1979-01-01

DOT IV is designed to allow very large problems to be solved on a wide range of computers and memory arrangements. New flexibility in both space-mesh and directional-quadrature specification is allowed. For example, the radial mesh in an R-Z problem can vary with axial position. The directional quadrature can vary with both space and energy group. Several features improve performance on both deep penetration and criticality problems. The program has been checked and used extensively on several types of computers. All of the features have been insured operable except the following two, which must not be used: criticality searches and P/sub L/ variable by group or material. Diffusion theory problems must not use internal or external boundary sources, variable mesh, or variable quadrature. A diffusion iteration cannot produce internal boundary source output or ''angular flux tape.'' The P 1 module is very limited. The special geometries, INGEOM greater than or equal to 10, have not been completely checked and are not guaranteed. 7 figures, 1 table

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

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.

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)

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)

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

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

Parallel performance of the angular versus spatial domain decomposition for discrete ordinates transport methods

International Nuclear Information System (INIS)

Fischer, J.W.; Azmy, Y.Y.

2003-01-01

A previously reported parallel performance model for Angular Domain Decomposition (ADD) of the Discrete Ordinates method for solving multidimensional neutron transport problems is revisited for further validation. Three communication schemes: native MPI, the bucket algorithm, and the distributed bucket algorithm, are included in the validation exercise that is successfully conducted on a Beowulf cluster. The parallel performance model is comprised of three components: serial, parallel, and communication. The serial component is largely independent of the number of participating processors, P, while the parallel component decreases like 1/P. These two components are independent of the communication scheme, in contrast with the communication component that typically increases with P in a manner highly dependent on the global reduced algorithm. Correct trends for each component and each communication scheme were measured for the Arbitrarily High Order Transport (AHOT) code, thus validating the performance models. Furthermore, extensive experiments illustrate the superiority of the bucket algorithm. The primary question addressed in this research is: for a given problem size, which domain decomposition method, angular or spatial, is best suited to parallelize Discrete Ordinates methods on a specific computational platform? We address this question for three-dimensional applications via parallel performance models that include parameters specifying the problem size and system performance: the above-mentioned ADD, and a previously constructed and validated Spatial Domain Decomposition (SDD) model. We conclude that for large problems the parallel component dwarfs the communication component even on moderately large numbers of processors. The main advantages of SDD are: (a) scalability to higher numbers of processors of the order of the number of computational cells; (b) smaller memory requirement; (c) better performance than ADD on high-end platforms and large number of

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)

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)

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

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 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

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

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

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)

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

Improvement of neutronic calculations on a Masurca core using adaptive mesh refinement capabilities

International Nuclear Information System (INIS)

Fournier, D.; Archier, P.; Le Tellier, R.; Suteau, C.

2011-01-01

The simulation of 3D cores with homogenized assemblies in transport theory remains time and memory consuming for production calculations. With a multigroup discretization for the energy variable and a discrete ordinate method for the angle, a system of about 10"4 coupled hyperbolic transport equations has to be solved. For these equations, we intend to optimize the spatial discretization. In the framework of the SNATCH solver used in this study, the spatial problem is dealt with by using a structured hexahedral mesh and applying a Discontinuous Galerkin Finite Element Method (DGFEM). This paper shows the improvements due to the development of Adaptive Mesh Refinement (AMR) methods. As the SNATCH solver uses a hierarchical polynomial basis, p−refinement is possible but also h−refinement thanks to non conforming capabilities. Besides, as the flux spatial behavior is highly dependent on the energy, we propose to adapt differently the spatial discretization according to the energy group. To avoid dealing with too many meshes, some energy groups are joined and share the same mesh. The different energy-dependent AMR strategies are compared to each other but also with the classical approach of a conforming and highly refined spatial mesh. This comparison is carried out on different quantities such as the multiplication factor, the flux or the current. The gain in time and memory is shown for 2D and 3D benchmarks coming from the ZONA2B experimental core configuration of the MASURCA mock-up at CEA Cadarache. (author)

Some efficient Lagrangian mesh finite elements encoded in ZEPHYR for two dimensional transport calculations

International Nuclear Information System (INIS)

Mordant, Maurice.

1981-04-01

To solve a multigroup stationary neutron transport equation in two-dimensional geometries (X-Y), (R-O) or (R-Z) generally on uses discrete ordinates and rectangular meshes. The way to do it is then well known, well documented and somewhat obvious. If one needs to treat awkward geometries or distorted meshes, things are not so easy and the way to do it is no longer straightforward. We have studied this problem at Limeil Nuclear Center and as an alternative to Monte Carlo methods and code we have implemented in ZEPHYR code at least two efficient finite element solutions for Lagrangian meshes involving any kind of triangles and quadrilaterals

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)

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

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.

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.

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 influence of boundary conditions on resonant frequencies of cavities in 3-D FDTD algorithm using non-orthogonal co-ordinates

Energy Technology Data Exchange (ETDEWEB)

Zhao, L.; Tong, L.S. [Southeast Univ., Nanjing (China). Research Inst. of Electronics; Carter, R.G. [Lancaster Univ. (United Kingdom). Engineering Dept.

1994-09-01

The 3-dimensional finite-difference time-domain method in non-orthogonal co-ordinates (non-standard FDTD) is used to calculate the frequencies of resonators. The numerical boundary conditions of the method are presented. The Influences of boundary conditions and discrete meshes on the numerical accuracy are investigated. The authors present the nonstandard FDTD method using the boundary-orthogonal mesh and equivalent dielectric constant so that the error is reduced from 8.66% to 3.0% for the cylindrical cavity loaded by a dielectric button.

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)

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

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)

Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations

International Nuclear Information System (INIS)

Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.

2005-01-01

In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects

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

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.

Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

International Nuclear Information System (INIS)

Feng, Bao-Feng; Chen, Junchao; Chen, Yong; Maruno, Ken-ichi; Ohta, Yasuhiro

2015-01-01

In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well. (paper)

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

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.

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.

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.

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.

A discrete ordinate response matrix method for massively parallel computers

International Nuclear Information System (INIS)

Hanebutte, U.R.; Lewis, E.E.

1991-01-01

A discrete ordinate response matrix method is formulated for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices which result from the diamond-differenced equations are utilized in a factored form which minimizes memory requirements and significantly reduces the required number of algorithm utilizes massive parallelism by assigning each spatial node to a processor. The algorithm is accelerated effectively by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red/black iterations. The method has been implemented on a 16k Connection Machine-2, and S 8 and S 16 solutions have been obtained for fixed-source benchmark problems in X--Y geometry

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

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

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

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.

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.

Discretization of the Joule heating term for plasma discharge fluid models in unstructured meshes

International Nuclear Information System (INIS)

Deconinck, T.; Mahadevan, S.; Raja, L.L.

2009-01-01

The fluid (continuum) approach is commonly used for simulation of plasma phenomena in electrical discharges at moderate to high pressures (>10's mTorr). The description comprises governing equations for charged and neutral species transport and energy equations for electrons and the heavy species, coupled to equations for the electromagnetic fields. The coupling of energy from the electrostatic field to the plasma species is modeled by the Joule heating term which appears in the electron and heavy species (ion) energy equations. Proper numerical discretization of this term is necessary for accurate description of discharge energetics; however, discretization of this term poses a special problem in the case of unstructured meshes owing to the arbitrary orientation of the faces enclosing each cell. We propose a method for the numerical discretization of the Joule heating term using a cell-centered finite volume approach on unstructured meshes with closed convex cells. The Joule heating term is computed by evaluating both the electric field and the species flux at the cell center. The dot product of these two vector quantities is computed to obtain the Joule heating source term. We compare two methods to evaluate the species flux at the cell center. One is based on reconstructing the fluxes at the cell centers from the fluxes at the face centers. The other recomputes the flux at the cell center using the common drift-diffusion approximation. The reconstructed flux scheme is the most stable method and yields reasonably accurate results on coarse meshes.

Analysis of Massively Parallel Discrete-Ordinates Transport Sweep Algorithms with Collisions

International Nuclear Information System (INIS)

Bailey, T.S.; Falgout, R.D.

2008-01-01

We present theoretical scaling models for a variety of discrete-ordinates sweep algorithms. In these models, we pay particular attention to the way each algorithm handles collisions. A collision is defined as a processor having multiple angles with ready to be swept during one stage of the sweep. The models also take into account how subdomains are assigned to processors and how angles are grouped during the sweep. We describe a data driven algorithm that resolves collisions efficiently during the sweep as well as other algorithms that have been designed to avoid collisions completely. Our models are validated using the ARGES and AMTRAN transport codes. We then use the models to study and predict scaling trends in all of the sweep algorithms

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.

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

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Development of parallel 3D discrete ordinates transport program on JASMIN framework

International Nuclear Information System (INIS)

Cheng, T.; Wei, J.; Shen, H.; Zhong, B.; Deng, L.

2015-01-01

A parallel 3D discrete ordinates radiation transport code JSNT-S is developed, aiming at simulating real-world radiation shielding and reactor physics applications in a reasonable time. Through the patch-based domain partition algorithm, the memory requirement is shared among processors and a space-angle parallel sweeping algorithm is developed based on data-driven algorithm. Acceleration methods such as partial current rebalance are implemented. The correctness is proved through the VENUS-3 and other benchmark models. In the radiation shielding calculation of the Qinshan-II reactor pressure vessel model with 24.3 billion DoF, only 88 seconds is required and the overall parallel efficiency of 44% is achieved on 1536 CPU cores. (author)

A 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.

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

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)

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)

A massively parallel discrete ordinates response matrix method for neutron transport

International Nuclear Information System (INIS)

Hanebutte, U.R.; Lewis, E.E.

1992-01-01

In this paper a discrete ordinates response matrix method is formulated with anisotropic scattering for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices that result from the diamond-differenced equations are utilized in a factored form that minimizes memory requirements and significantly reduces the number of arithmetic operations required per node. The red-black solution algorithm utilizes massive parallelism by assigning each spatial node to one or more processors. The algorithm is accelerated by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red-black iterations. The method is implemented on a 16K Connection Machine-2, and S 8 and S 16 solutions are obtained for fixed-source benchmark problems in x-y geometry

Polyhedral meshing as an innovative approach to computational domain discretization of a cyclone in a fluidized bed CLC unit

Directory of Open Access Journals (Sweden)

Sosnowski Marcin

2017-01-01

Full Text Available Chemical Looping Combustion (CLC is a technology that allows the separation of CO2, which is generated by the combustion of fossil fuels. The majority of process designs currently under investigation are systems of coupled fluidized beds. Advances in the development of power generation system using CLC cannot be introduced without using numerical modelling as a research tool. The primary and critical activity in numerical modelling is the computational domain discretization. It influences the numerical diffusion as well as convergence of the model and therefore the overall accuracy of the obtained results. Hence an innovative approach of computational domain discretization using polyhedral (POLY mesh is proposed in the paper. This method reduces both the numerical diffusion of the mesh as well as the time cost of preparing the model for subsequent calculation. The major advantage of POLY mesh is that each individual cell has many neighbours, so gradients can be much better approximated in comparison to commonly-used tetrahedral (TET mesh. POLYs are also less sensitive to stretching than TETs which results in better numerical stability of the model. Therefore detailed comparison of numerical modelling results concerning subsection of CLC system using tetrahedral and polyhedral mesh is covered in the paper.

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.

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

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

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

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)

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)

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

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

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

PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils

Science.gov (United States)

Johnson, Scott; Walton, Otis; Settgast, Randolph

2013-01-01

PowderSim is a calculation tool that combines a discrete-element method (DEM) module, including calibrated interparticle-interaction relationships, with a mesh-free, continuum, SPH (smoothed-particle hydrodynamics) based module that utilizes enhanced, calibrated, constitutive models capable of mimicking both large deformations and the flow behavior of regolith simulants and lunar regolith under conditions anticipated during in situ resource utilization (ISRU) operations. The major innovation introduced in PowderSim is to use a mesh-free method (SPH-based) with a calibrated and slightly modified critical-state soil mechanics constitutive model to extend the ability of the simulation tool to also address full-scale engineering systems in the continuum sense. The PowderSim software maintains the ability to address particle-scale problems, like size segregation, in selected regions with a traditional DEM module, which has improved contact physics and electrostatic interaction models.

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.

Development and comparison of different spatial numerical schemes for the radiative transfer equation resolution using three-dimensional unstructured meshes

International Nuclear Information System (INIS)

Capdevila, R.; Perez-Segarra, C.D.; Oliva, A.

2010-01-01

In the present work four different spatial numerical schemes have been developed with the aim of reducing the false-scattering of the numerical solutions obtained with the discrete ordinates (DOM) and the finite volume (FVM) methods. These schemes have been designed specifically for unstructured meshes by means of the extrapolation of nodal values of intensity on the studied radiative direction. The schemes have been tested and compared in several 3D benchmark test cases using both structured orthogonal and unstructured grids.

Application of the TWODANT code system to pressure vessel dosimetry calculations

International Nuclear Information System (INIS)

Parsons, D.K.; Alcouffe, R.E.; Marr, D.R.; Urban, W.T.

1993-01-01

The TWODANT code system has recently been enhanced to include TWODANT/GQ and THREEDANT. TWODANT/GQ solves the two-dimensional form of the discrete ordinates approximation to the transport equation on a generalized quadrilateral mesh. This geometric capability is very general and allows nearly exact representations of X-Y or R-Z geometries. THREEDANT solves the three-dimensional form of the discrete ordinates equations. In addition to the conventional coarse-mesh material zone input, THREEDANT can also be linked to a three-dimensional nested-region mesh generation code called FRAC-IN-THE-BOX. THREEDANT can thus model a much wider variety of geometric shapes than any other discrete ordinates code. These enhanced geometric modeling capabilities are applied here to the analysis of the VENUS PWR Mock-Up Facility

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

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

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

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

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

Science.gov (United States)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

An extended step characteristic method for solving the transport equation in general geometries

International Nuclear Information System (INIS)

DeHart, M.D.; Pevey, R.E.; Parish, T.A.

1994-01-01

A method for applying the discrete ordinates method to solve the Boltzmann transport equation on arbitrary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the geometrical shape of a mesh element characteristic of a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. By using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. Results for a number of test problems have been compared with solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well as numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN-II computer programs

A 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)

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)

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)

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.

Do patients prefer mesh or anterior colporrhaphy for primary correction of anterior vaginal wall prolapse: a labelled discrete choice experiment

NARCIS (Netherlands)

Notten, K. J. B.; Essers, B. A.; Weemhoff, M.; Rutten, A. G. H.; Donners, J. J. A. E.; van Gestel, I.; Kruitwagen, R. F. M. P.; Roovers, J. P. W. R.; Dirksen, C. D.

2015-01-01

We investigated patients' preferences for anterior colporrhaphy or mesh surgery as surgical correction of anterior vaginal wall prolapse. Labelled discrete choice experiment. Three Dutch teaching hospitals. Women with anterior vaginal wall prolapse Pelvic Organ Prolapse Quantification stage 2 or

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

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)

Vertex Normals and Face Curvatures of Triangle Meshes

KAUST Repository

Sun, Xiang; Jiang, Caigui; Wallner, Johannes; Pottmann, Helmut

2016-01-01

This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals

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.)

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)

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)

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.

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

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

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.

The quasidiffusion method for transport problems on unstructured meshes

Science.gov (United States)

Wieselquist, William A.

2009-06-01

In this work, we develop a quasidiffusion (QD) method for solving radiation transport problems on unstructured quadrilateral meshes in 2D Cartesian geometry, for example hanging-node meshes from adaptive mesh refinement (AMR) applications or skewed quadrilateral meshes from radiation hydrodynamics with Lagrangian meshing. The main result of the work is a new low-order quasidiffusion (LOQD) discretization on arbitrary quadrilaterals and a strategy for the efficient iterative solution which uses Krylov methods and incomplete LU factorization (ILU) preconditioning. The LOQD equations are a non-symmetric set of first-order PDEs that in second-order form resembles convection- diffusion with a diffusion tensor, with the difference that the LOQD equations contain extra cross-derivative terms. Our finite volume (FV) discretization of the LOQD equations is compared with three LOQD discretizations from literature. We then present a conservative, short characteristics discretization based on subcell balances (SCSB) that uses polynomial exponential moments to achieve robust behavior in various limits (e.g. small cells and voids) and is second- order accurate in space. A linear representation of the isotropic component of the scattering source based on face-average and cell-average scalar fluxes is also proposed and shown to be effective in some problems. In numerical tests, our QD method with linear scattering source representation shows some advantages compared to other transport methods. We conclude with avenues for future research and note that this QD method may easily be extended to arbitrary meshes in 3D Cartesian geometry.

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

Vertex Normals and Face Curvatures of Triangle Meshes

KAUST Repository

Sun, Xiang

2016-08-12

This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ʼnormal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.

Direct Discrete Method for Neutronic Calculations

International Nuclear Information System (INIS)

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

2002-01-01

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)

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)

Multiphase flow of immiscible fluids on unstructured moving meshes

DEFF Research Database (Denmark)

Misztal, Marek Krzysztof; Erleben, Kenny; Bargteil, Adam

2012-01-01

In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization op...

Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes

DEFF Research Database (Denmark)

Misztal, Marek Krzysztof; Erleben, Kenny; Bargteil, Adam

2013-01-01

In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization op...

Current density and continuity in discretized models

International Nuclear Information System (INIS)

Boykin, Timothy B; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schroedinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying discrete models, students can encounter conceptual difficulties with the representation of the current and its divergence because different finite-difference expressions, all of which reduce to the current density in the continuous limit, measure different physical quantities. Understanding these different discrete currents is essential and requires a careful analysis of the current operator, the divergence of the current and the continuity equation. Here we develop point forms of the current and its divergence valid for an arbitrary mesh and basis. We show that in discrete models currents exist only along lines joining atomic sites (or mesh points). Using these results, we derive a discrete analogue of the divergence theorem and demonstrate probability conservation in a purely localized-basis approach.

Sierra toolkit computational mesh conceptual model

International Nuclear Information System (INIS)

Baur, David G.; Edwards, Harold Carter; Cochran, William K.; Williams, Alan B.; Sjaardema, Gregory D.

2010-01-01

The Sierra Toolkit computational mesh is a software library intended to support massively parallel multi-physics computations on dynamically changing unstructured meshes. This domain of intended use is inherently complex due to distributed memory parallelism, parallel scalability, heterogeneity of physics, heterogeneous discretization of an unstructured mesh, and runtime adaptation of the mesh. Management of this inherent complexity begins with a conceptual analysis and modeling of this domain of intended use; i.e., development of a domain model. The Sierra Toolkit computational mesh software library is designed and implemented based upon this domain model. Software developers using, maintaining, or extending the Sierra Toolkit computational mesh library must be familiar with the concepts/domain model presented in this report.

Discrete Fracture Modeling of 3D Heterogeneous Enhanced Coalbed Methane Recovery with Prismatic Meshing

Directory of Open Access Journals (Sweden)

Yongbin Zhang

2015-06-01

Full Text Available In this study, a 3D multicomponent multiphase simulator with a new fracture characterization technique is developed to simulate the enhanced recovery of coalbed methane. In this new model, the diffusion source from the matrix is calculated using the traditional dual-continuum approach, while in the Darcy flow scale, the Discrete Fracture Model (DFM is introduced to explicitly represent the flow interaction between cleats and large-scale fractures. For this purpose, a general formulation is proposed to model the multicomponent multiphase flow through the fractured coal media. The S&D model and a revised P&M model are incorporated to represent the geomechanical effects. Then a finite volume based discretization and solution strategies are constructed to solve the general ECBM equations. The prismatic meshing algorism is used to construct the grids for 3D reservoirs with complex fracture geometry. The simulator is validated with a benchmark case in which the results show close agreement with GEM. Finally, simulation of a synthetic heterogeneous 3D coal reservoir modified from a published literature is performed to evaluate the production performance and the effects of injected gas composition, well pattern and gas buoyancy.

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.

Discrete geometric structures for architecture

KAUST Repository

Pottmann, Helmut

2010-06-13

The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This

Geometrically Consistent Mesh Modification

KAUST Repository

Bonito, A.

2010-01-01

A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

An optimization-based framework for anisotropic simplex mesh adaptation

Science.gov (United States)

Yano, Masayuki; Darmofal, David L.

2012-09-01

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a discretization and any element-wise, localizable error estimate, our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom. Utilizing mesh-metric duality, we consider a continuous optimization problem of the Riemannian metric tensor field that provides an anisotropic description of element sizes. First, our method performs a series of local solves to survey the behavior of the local error function. This information is then synthesized using an affine-invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field. Finally, we perform gradient descent in the metric space to drive the mesh toward optimality. The method is first demonstrated to produce optimal anisotropic meshes minimizing the L2 projection error for a pair of canonical problems containing a singularity and a singular perturbation. The effectiveness of the framework is then demonstrated in the context of output-based adaptation for the advection-diffusion equation using a high-order discontinuous Galerkin discretization and the dual-weighted residual (DWR) error estimate. The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.

MHD simulations on an unstructured mesh

International Nuclear Information System (INIS)

Strauss, H.R.; Park, W.

1996-01-01

We describe work on a full MHD code using an unstructured mesh. MH3D++ is an extension of the PPPL MH3D resistive full MHD code. MH3D++ replaces the structured mesh and finite difference / fourier discretization of MH3D with an unstructured mesh and finite element / fourier discretization. Low level routines which perform differential operations, solution of PDEs such as Poisson's equation, and graphics, are encapsulated in C++ objects to isolate the finite element operations from the higher level code. The high level code is the same, whether it is run in structured or unstructured mesh versions. This allows the unstructured mesh version to be benchmarked against the structured mesh version. As a preliminary example, disruptions in DIIID reverse shear equilibria are studied numerically with the MH3D++ code. Numerical equilibria were first produced starting with an EQDSK file containing equilibrium data of a DIII-D L-mode negative central shear discharge. Using these equilibria, the linearized equations are time advanced to get the toroidal mode number n = 1 linear growth rate and eigenmode, which is resistively unstable. The equilibrium and linear mode are used to initialize 3D nonlinear runs. An example shows poloidal slices of 3D pressure surfaces: initially, on the left, and at an intermediate time, on the right

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.

BOT3P5.2, 3D Mesh Generator and Graphical Display of Geometry for Radiation Transport Codes, Display of Results

International Nuclear Information System (INIS)

Orsi, Roberto; Bidaud, Adrien

2007-01-01

1 - Description of program or function: BOT3P was originally conceived as a set of standard FORTRAN 77 language programs in order to give the users of the DORT and TORT deterministic transport codes some useful diagnostic tools to prepare and check their input data files. Later versions extended the possibility to produce the geometrical, material distribution and fixed neutron source data to other deterministic transport codes such as TWODANT/THREEDANT of the DANTSYS system, PARTISN and, potentially, to any transport code through BOT3P binary output files that can be easily interfaced (see, for example, the Russian two-dimensional (2D) and three-dimensional (3D) discrete ordinates neutron, photon and charged particle transport codes KASKAD-S-2.5 and KATRIN-2.0). As from Version 5.1 BOT3P contained important additions specifically addressed to radiation transport analysis for medical applications. BOT3P-5.2 contains new graphics capabilities. Some of them enable users to select space sub-domains of the total mesh grid in order to improve the zoom simulation of the geometry, both in 2D cuts and in 3D. Moreover the new BOT3P module (PDTM) may improve the interface of BOT3P geometrical models to transport analysis codes. The following programs are included in the BOT3P software package: GGDM, DDM, GGTM, DTM2, DTM3, RVARSCL, COMPARE, MKSRC, CATSM, DTET, and PDTM. The main features of these different programs are described. 2 - Methods: GGDM and GGTM work similarly from the logical point of view. Since the 3D case is more general, the following description refers to GGTM. All the co-ordinate values that characterise the geometrical scheme at the basis of the 3D transport code geometrical and material model are read, sorted and all stored if different from the neighbouring ones more than an input tolerance established by the user. These co-ordinates are always present in the fine-mesh boundary arrays independently of the mesh grid refinement options, because they

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

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.

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.

Discretization-dependent model for weakly connected excitable media

Science.gov (United States)

Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

2018-03-01

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

Unstructured Adaptive Meshes: Bad for Your Memory?

Science.gov (United States)

Biswas, Rupak; Feng, Hui-Yu; VanderWijngaart, Rob

2003-01-01

This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

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

Obtuse triangle suppression in anisotropic meshes

KAUST Repository

Sun, Feng; Choi, Yi King; Wang, Wen Ping; Yan, Dongming; Liu, Yang; Lé vy, Bruno L.

2011-01-01

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

Obtuse triangle suppression in anisotropic meshes

KAUST Repository

Sun, Feng

2011-12-01

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

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

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.)

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)

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)

Domain Discretization and Circle Packings

DEFF Research Database (Denmark)

Dias, Kealey

A circle packing is a configuration of circles which are tangent with one another in a prescribed pattern determined by a combinatorial triangulation, where the configuration fills a planar domain or a two-dimensional surface. The vertices in the triangulation correspond to centers of circles...... to domain discretization problems such as triangulation and unstructured mesh generation techniques. We wish to ask ourselves the question: given a cloud of points in the plane (we restrict ourselves to planar domains), is it possible to construct a circle packing preserving the positions of the vertices...... and constrained meshes having predefined vertices as constraints. A standard method of two-dimensional mesh generation involves conformal mapping of the surface or domain to standardized shapes, such as a disk. Since circle packing is a new technique for constructing discrete conformal mappings, it is possible...

New non-structured discretizations for fluid flows with reinforced incompressibility

International Nuclear Information System (INIS)

Heib, S.

2003-01-01

This work deals with the discretization of Stokes and Navier-Stokes equations modeling the flow of incompressible fluids on 2-D or 3-D non-structured meshes. Triangles and tetrahedrons are used for 2-D and 3-D meshes, respectively. The developments and calculations are performed with the code Priceles (fast CEA-EdF industrial platform for large Eddy simulation). This code allows to perform simulations both on structured and non-structured meshes. A finite-volume resolution method is used: a finite difference volume (FDV) method is used for the structured meshes and a finite element volume (FEV) method is used for the non-structured meshes. The finite element used in the beginning of this work has several defects. Starting from this situation, the discretization is improved by adding modifications to this element and the new elements introduced are analyzed theoretically. In parallel to these analyses, the new discretizations are implemented in order to test them numerically and to confirm the theoretical analyses. The first chapter presents the physical and mathematical modeling used in this work. The second chapter treats of the discretization of Stokes equations and presents the FEV resolution method. Chapter 3 presents a first attempt of improvement of this finite element and leads to the proposal of a new element which is presented in details. The problem encountered with the new discretization leads to a modification presented in chapter 4. This new discretization gives all the expected convergence results and sometimes shows super-convergence properties. Chapter 5 deals with the study and discretization of the Navier-Stokes equations. The study of the filtered Navier-Stokes equations, used for large Eddy simulations, requires to give a particular attention to the discretization of the diffusive terms. Then, the convective terms are considered. The effects of the convective terms in the initial discretization and in the improved method are compared. The use of

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

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

MHD simulations on an unstructured mesh

International Nuclear Information System (INIS)

Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Sugiyama, L.E.

1998-01-01

Two reasons for using an unstructured computational mesh are adaptivity, and alignment with arbitrarily shaped boundaries. Two codes which use finite element discretization on an unstructured mesh are described. FEM3D solves 2D and 3D RMHD using an adaptive grid. MH3D++, which incorporates methods of FEM3D into the MH3D generalized MHD code, can be used with shaped boundaries, which might be 3D

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.

COGEDIF - automatic TORT and DORT input generation from MORSE combinatorial geometry models

International Nuclear Information System (INIS)

Castelli, R.A.; Barnett, D.A.

1992-01-01

COGEDIF is an interactive utility which was developed to automate the preparation of two and three dimensional geometrical inputs for the ORNL-TORT and DORT discrete ordinates programs from complex three dimensional models described using the MORSE combinatorial geometry input description. The program creates either continuous or disjoint mesh input based upon the intersections of user defined meshing planes and the MORSE body definitions. The composition overlay of the combinatorial geometry is used to create the composition mapping of the discretized geometry based upon the composition found at the centroid of each of the mesh cells. This program simplifies the process of using discrete orthogonal mesh cells to represent non-orthogonal geometries in large models which require mesh sizes of the order of a million cells or more. The program was specifically written to take advantage of the new TORT disjoint mesh option which was developed at ORNL

MeshVoro: A Three-Dimensional Voronoi Mesh Building Tool for the TOUGH Family of Codes

Energy Technology Data Exchange (ETDEWEB)

Freeman, C. M.; Boyle, K. L.; Reagan, M.; Johnson, J.; Rycroft, C.; Moridis, G. J.

2013-09-30

Few tools exist for creating and visualizing complex three-dimensional simulation meshes, and these have limitations that restrict their application to particular geometries and circumstances. Mesh generation needs to trend toward ever more general applications. To that end, we have developed MeshVoro, a tool that is based on the Voro (Rycroft 2009) library and is capable of generating complex threedimensional Voronoi tessellation-based (unstructured) meshes for the solution of problems of flow and transport in subsurface geologic media that are addressed by the TOUGH (Pruess et al. 1999) family of codes. MeshVoro, which includes built-in data visualization routines, is a particularly useful tool because it extends the applicability of the TOUGH family of codes by enabling the scientifically robust and relatively easy discretization of systems with challenging 3D geometries. We describe several applications of MeshVoro. We illustrate the ability of the tool to straightforwardly transform a complex geological grid into a simulation mesh that conforms to the specifications of the TOUGH family of codes. We demonstrate how MeshVoro can describe complex system geometries with a relatively small number of grid blocks, and we construct meshes for geometries that would have been practically intractable with a standard Cartesian grid approach. We also discuss the limitations and appropriate applications of this new technology.

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

Comparison of discrete Hodge star operators for surfaces

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

We investigate the performance of various discrete Hodge star operators for discrete exterior calculus (DEC) using circumcentric and barycentric dual meshes. The performance is evaluated through the DEC solution of Darcy and incompressible Navier

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)

Kinetic solvers with adaptive mesh in phase space

Science.gov (United States)

Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.

2013-12-01

An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a “tree of trees” (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.

Dynamic Mesh Adaptation for Front Evolution Using Discontinuous Galerkin Based Weighted Condition Number Mesh Relaxation

Energy Technology Data Exchange (ETDEWEB)

Greene, Patrick T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schofield, Samuel P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nourgaliev, Robert [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-06-21

A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.

Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids

International Nuclear Information System (INIS)

Ragusa, Jean C.

2015-01-01

In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Current Density and Continuity in Discretized Models

Science.gov (United States)

Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…

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.

Mesh Association by Projection along Smoothed-Normal-Vector Fields : Association of Closed Manifolds

NARCIS (Netherlands)

Van Brummelen, E.H.

2006-01-01

The necessity to associate two geometrically distinct meshes arises in many engineering applications. Current mesh-association algorithms are generally unsuitable for the high-order geometry representations associated with high-order finite-element discretizations. In the present work we therefore

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

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)

Moving mesh generation with a sequential approach for solving PDEs

DEFF Research Database (Denmark)

In moving mesh methods, physical PDEs and a mesh equation derived from equidistribution of an error metrics (so-called the monitor function) are simultaneously solved and meshes are dynamically concentrated on steep regions (Lim et al., 2001). However, the simultaneous solution procedure...... a simple and robust moving mesh algorithm in one or multidimension. In this study, we propose a sequential solution procedure including two separate parts: prediction step to obtain an approximate solution to a next time level (integration of physical PDEs) and regriding step at the next time level (mesh...... generation and solution interpolation). Convection terms, which appear in physical PDEs and a mesh equation, are discretized by a WENO (Weighted Essentially Non-Oscillatory) scheme under the consrvative form. This sequential approach is to keep the advantages of robustness and simplicity for the static...

Ordering schemes for parallel processing of certain mesh problems

International Nuclear Information System (INIS)

O'Leary, D.

1984-01-01

In this work, some ordering schemes for mesh points are presented which enable algorithms such as the Gauss-Seidel or SOR iteration to be performed efficiently for the nine-point operator finite difference method on computers consisting of a two-dimensional grid of processors. Convergence results are presented for the discretization of u /SUB xx/ + u /SUB yy/ on a uniform mesh over a square, showing that the spectral radius of the iteration for these orderings is no worse than that for the standard row by row ordering of mesh points. Further applications of these mesh point orderings to network problems, more general finite difference operators, and picture processing problems are noted

Finite Element in Angle Unit Sphere Meshing for Charged Particle Transport.

Energy Technology Data Exchange (ETDEWEB)

Ortega, Mario Ivan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Drumm, Clifton R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-10-01

Finite element in angle formulations of the charged particle transport equation require the discretization of the unit sphere. In Sceptre, a three-dimensional surface mesh of a sphere is transformed into a two-dimensional mesh. Projection of a sphere onto a two-dimensional surface is well studied with map makers spending the last few centuries attempting to create maps that preserve proportion and area. Using these techniques, various meshing schemes for the unit sphere were investigated.

The slice balance approach (SBA): a characteristic-based, multiple balance SN approach on unstructured polyhedral meshes

International Nuclear Information System (INIS)

Grove, R.E.

2005-01-01

The Slice Balance Approach (SBA) is an approach for solving geometrically-complex, neutral-particle transport problems within a multi-group discrete ordinates (S N ) framework. The salient feature is an angle-dependent spatial decomposition. We approximate general surfaces with arbitrary polygonal faces and mesh the geometry with arbitrarily-shaped polyhedral cells. A cell-local spatial decomposition divides cells into angle-dependent slices for each S N direction. This subdivision follows from a characteristic-based view of the transport problem. Most balance-based characteristic methods use it implicitly; we use it explicitly and exploit its properties. Our mathematical approach is a multiple balance approach using exact spatial moments balance equations on cells and slices along with auxiliary relations on slices. We call this the slice balance approach; it is a characteristic-based multiple balance approach. The SBA is intentionally general and can extend differencing schemes to arbitrary 2-D and 3-D meshes. This work contributes to development of general-geometry deterministic transport capability to complement Monte Carlo capability for large, geometrically-complex transport problems. The purpose of this paper is to describe the SBA. We describe the spatial decomposition and mathematical framework and highlight a few interesting properties. We sketch the derivation of two solution schemes, a step characteristic scheme and a diamond-difference-like scheme, to illustrate the approach and we present interesting results for a 2-D problem. (author)

A general boundary capability embedded in an orthogonal mesh

International Nuclear Information System (INIS)

Hewett, D.W.; Yu-Jiuan Chen

1995-01-01

The authors describe how they hold onto orthogonal mesh discretization when dealing with curved boundaries. Special difference operators were constructed to approximate numerical zones split by the domain boundary; the operators are particularly simple for this rectangular mesh. The authors demonstrated that this simple numerical approach, termed Dynamic Alternating Direction Implicit, turned out to be considerably more efficient than more complex grid-adaptive algorithms that were tried previously

Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

Science.gov (United States)

Baxes, Gregory A. (Inventor); Linger, Timothy C. (Inventor)

2011-01-01

Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

Science.gov (United States)

Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe

2009-08-01

In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.

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

An Efficient Mesh Generation Method for Fractured Network System Based on Dynamic Grid Deformation

Directory of Open Access Journals (Sweden)

Shuli Sun

2013-01-01

Full Text Available Meshing quality of the discrete model influences the accuracy, convergence, and efficiency of the solution for fractured network system in geological problem. However, modeling and meshing of such a fractured network system are usually tedious and difficult due to geometric complexity of the computational domain induced by existence and extension of fractures. The traditional meshing method to deal with fractures usually involves boundary recovery operation based on topological transformation, which relies on many complicated techniques and skills. This paper presents an alternative and efficient approach for meshing fractured network system. The method firstly presets points on fractures and then performs Delaunay triangulation to obtain preliminary mesh by point-by-point centroid insertion algorithm. Then the fractures are exactly recovered by local correction with revised dynamic grid deformation approach. Smoothing algorithm is finally applied to improve the quality of mesh. The proposed approach is efficient, easy to implement, and applicable to the cases of initial existing fractures and extension of fractures. The method is successfully applied to modeling of two- and three-dimensional discrete fractured network (DFN system in geological problems to demonstrate its effectiveness and high efficiency.

Go with the Flow. Moving meshes and solution monitoring for compressible flow simulation

NARCIS (Netherlands)

van Dam, A.

2009-01-01

The simulation of time-dependent physical problems, such as flows of some kind, places high demands on the domain discretization in order to obtain high accuracy of the numerical solution. We present a moving mesh method in which the mesh points automatically move towards regions where high spatial

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

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.

Integrable discretizations of the short pulse equation

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

2010-01-01

In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.

An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids

Energy Technology Data Exchange (ETDEWEB)

Rieben, R N; White, D A; Wallin, B K; Solberg, J M

2006-06-12

We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.

A novel method of the image processing on irregular triangular meshes

Science.gov (United States)

Vishnyakov, Sergey; Pekhterev, Vitaliy; Sokolova, Elizaveta

2018-04-01

The paper describes a novel method of the image processing based on irregular triangular meshes implementation. The triangular mesh is adaptive to the image content, least mean square linear approximation is proposed for the basic interpolation within the triangle. It is proposed to use triangular numbers to simplify using of the local (barycentric) coordinates for the further analysis - triangular element of the initial irregular mesh is to be represented through the set of the four equilateral triangles. This allows to use fast and simple pixels indexing in local coordinates, e.g. "for" or "while" loops for access to the pixels. Moreover, representation proposed allows to use discrete cosine transform of the simple "rectangular" symmetric form without additional pixels reordering (as it is used for shape-adaptive DCT forms). Furthermore, this approach leads to the simple form of the wavelet transform on triangular mesh. The results of the method application are presented. It is shown that advantage of the method proposed is a combination of the flexibility of the image-adaptive irregular meshes with the simple form of the pixel indexing in local triangular coordinates and the using of the common forms of the discrete transforms for triangular meshes. Method described is proposed for the image compression, pattern recognition, image quality improvement, image search and indexing. It also may be used as a part of video coding (intra-frame or inter-frame coding, motion detection).

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

Discrete Curvature Theories and Applications

KAUST Repository

Sun, Xiang

2016-08-25

Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the

Discrete Green’s functions for propagators between complex objects in discrete space-time nonlinear electromagnetics

NARCIS (Netherlands)

Arnold, J.M.; Hon, de B.P.; Graglia, R.D.

2007-01-01

We propose a potential-based form of the FDTD scheme, with potentials driven by sources that are themselves simple dynamical systems. This formulation admits a radiative boundary condition for the discrete-mesh Maxwell's equations in a multiply connected exterior domain, which facilitates

Comparison of discrete Hodge star operators for surfaces

KAUST Repository

Mohamed, Mamdouh S.

2016-05-10

We investigate the performance of various discrete Hodge star operators for discrete exterior calculus (DEC) using circumcentric and barycentric dual meshes. The performance is evaluated through the DEC solution of Darcy and incompressible Navier–Stokes flows over surfaces. While the circumcentric Hodge operators may be favorable due to their diagonal structure, the barycentric (geometric) and the Galerkin Hodge operators have the advantage of admitting arbitrary simplicial meshes. Numerical experiments reveal that the barycentric and the Galerkin Hodge operators retain the numerical convergence order attained through the circumcentric (diagonal) Hodge operators. Furthermore, when the barycentric or the Galerkin Hodge operators are employed, a super-convergence behavior is observed for the incompressible flow solution over unstructured simplicial surface meshes generated by successive subdivision of coarser meshes. Insofar as the computational cost is concerned, the Darcy flow solutions exhibit a moderate increase in the solution time when using the barycentric or the Galerkin Hodge operators due to a modest decrease in the linear system sparsity. On the other hand, for the incompressible flow simulations, both the solution time and the linear system sparsity do not change for either the circumcentric or the barycentric and the Galerkin Hodge operators.

Scalable parallel prefix solvers for discrete ordinates transport

International Nuclear Information System (INIS)

Pautz, S.; Pandya, T.; Adams, M.

2009-01-01

The well-known 'sweep' algorithm for inverting the streaming-plus-collision term in first-order deterministic radiation transport calculations has some desirable numerical properties. However, it suffers from parallel scaling issues caused by a lack of concurrency. The maximum degree of concurrency, and thus the maximum parallelism, grows more slowly than the problem size for sweeps-based solvers. We investigate a new class of parallel algorithms that involves recasting the streaming-plus-collision problem in prefix form and solving via cyclic reduction. This method, although computationally more expensive at low levels of parallelism than the sweep algorithm, offers better theoretical scalability properties. Previous work has demonstrated this approach for one-dimensional calculations; we show how to extend it to multidimensional calculations. Notably, for multiple dimensions it appears that this approach is limited to long-characteristics discretizations; other discretizations cannot be cast in prefix form. We implement two variants of the algorithm within the radlib/SCEPTRE transport code library at Sandia National Laboratories and show results on two different massively parallel systems. Both the 'forward' and 'symmetric' solvers behave similarly, scaling well to larger degrees of parallelism then sweeps-based solvers. We do observe some issues at the highest levels of parallelism (relative to the system size) and discuss possible causes. We conclude that this approach shows good potential for future parallel systems, but the parallel scalability will depend heavily on the architecture of the communication networks of these systems. (authors)

In-plane material continuity for the discrete material optimization method

DEFF Research Database (Denmark)

Sørensen, Rene; Lund, Erik

2015-01-01

When performing discrete material optimization of laminated composite structures, the variation of the in-plane material continuity is typically governed by the size of the finite element discretization. For a fine mesh, this can lead to designs that cannot be manufactured due to the complexity...

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.

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.

Effectiveness of a consistently formulated diffusion-synthetic acceleration differencing approach

International Nuclear Information System (INIS)

Khalil, H.

1988-01-01

A consistently formulated differencing approach is applied to the diffusion-synthetic acceleration of discrete ordinates calculations based on various spatial differencing schemes. The diffusion ''coupling'' equations derived for each scheme are contrasted to conventional coupling relations and are shown to permit derivation of either point- or box-centered diffusion difference equations. The resulting difference equations are shown to be mathematically equivalent, in slab geometry, to equations derived by applying Larsen's four-step procedure to the S/sub 2/ equations. Fourier stability analysis of the acceleration method applied to slab model problems is used to demonstrate that, for any S/sub n/ differencing scheme (a) the upper bound on the spectral radius of the method occurs in the fine-mesh limit and equals that of the spatially continuous case (0.22466), and (b) the spectral radius decreases with increasing mesh size to an asymptotic value <0.13135. This model problem performance is somewhat superior to that of Larsen's approach, for which the spectral radius is bounded by 0.25 in the wide-mesh limit. Numerical results of multidimensional, heterogeneous, scattering-dominated problems are also presented to demonstrate the rapid convergence of accelerated discrete ordinates calculations using various spatial differencing schemes

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

Computing discrete signed distance fields from triangle meshes

DEFF Research Database (Denmark)

Bærentzen, Jakob Andreas; Aanæs, Henrik

2002-01-01

A method for generating a discrete, signed 3D distance field is proposed. Distance fields are used in a number of contexts. In particular the popular level set method is usually initialized by a distance field. The main focus of our work is on simplifying the computation of the sign when generating...

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

Science.gov (United States)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

A Novel Mesh Quality Improvement Method for Boundary Elements

Directory of Open Access Journals (Sweden)

Hou-lin Liu

2012-01-01

Full Text Available In order to improve the boundary mesh quality while maintaining the essential characteristics of discrete surfaces, a new approach combining optimization-based smoothing and topology optimization is developed. The smoothing objective function is modified, in which two functions denoting boundary and interior quality, respectively, and a weight coefficient controlling boundary quality are taken into account. In addition, the existing smoothing algorithm can improve the mesh quality only by repositioning vertices of the interior mesh. Without destroying boundary conformity, bad elements with all their vertices on the boundary cannot be eliminated. Then, topology optimization is employed, and those elements are converted into other types of elements whose quality can be improved by smoothing. The practical application shows that the worst elements can be eliminated and, with the increase of weight coefficient, the average quality of boundary mesh can also be improved. Results obtained with the combined approach are compared with some common approach. It is clearly shown that it performs better than the existing approach.

Generation of hybrid meshes for the simulation of petroleum reservoirs; Generation de maillages hybrides pour la simulation de reservoirs petroliers

Energy Technology Data Exchange (ETDEWEB)

Balaven-Clermidy, S.

2001-12-01

Oil reservoir simulations study multiphase flows in porous media. These flows are described and evaluated through numerical schemes on a discretization of the reservoir domain. In this thesis, we were interested in this spatial discretization and a new kind of hybrid mesh has been proposed where the radial nature of flows in the vicinity of wells is directly taken into account in the geometry. Our modular approach described wells and their drainage area through radial circular meshes. These well meshes are inserted in a structured reservoir mesh (a Corner Point Geometry mesh) made up with hexahedral cells. Finally, in order to generate a global conforming mesh, proper connections are realized between the different kinds of meshes through unstructured transition ones. To compute these transition meshes that we want acceptable in terms of finite volume methods, an automatic method based on power diagrams has been developed. Our approach can deal with a homogeneous anisotropic medium and allows the user to insert vertical or horizontal wells as well as secondary faults in the reservoir mesh. Our work has been implemented, tested and validated in 2D and 2D1/2. It can also be extended in 3D when the geometrical constraints are simplicial ones: points, segments and triangles. (author)

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

Improved mesh based photon sampling techniques for neutron activation analysis

International Nuclear Information System (INIS)

Relson, E.; Wilson, P. P. H.; Biondo, E. D.

2013-01-01

The design of fusion power systems requires analysis of neutron activation of large, complex volumes, and the resulting particles emitted from these volumes. Structured mesh-based discretization of these problems allows for improved modeling in these activation analysis problems. Finer discretization of these problems results in large computational costs, which drives the investigation of more efficient methods. Within an ad hoc subroutine of the Monte Carlo transport code MCNP, we implement sampling of voxels and photon energies for volumetric sources using the alias method. The alias method enables efficient sampling of a discrete probability distribution, and operates in 0(1) time, whereas the simpler direct discrete method requires 0(log(n)) time. By using the alias method, voxel sampling becomes a viable alternative to sampling space with the 0(1) approach of uniformly sampling the problem volume. Additionally, with voxel sampling it is straightforward to introduce biasing of volumetric sources, and we implement this biasing of voxels as an additional variance reduction technique that can be applied. We verify our implementation and compare the alias method, with and without biasing, to direct discrete sampling of voxels, and to uniform sampling. We study the behavior of source biasing in a second set of tests and find trends between improvements and source shape, material, and material density. Overall, however, the magnitude of improvements from source biasing appears to be limited. Future work will benefit from the implementation of efficient voxel sampling - particularly with conformal unstructured meshes where the uniform sampling approach cannot be applied. (authors)

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.

Parallel paving: An algorithm for generating distributed, adaptive, all-quadrilateral meshes on parallel computers

Energy Technology Data Exchange (ETDEWEB)

Lober, R.R.; Tautges, T.J.; Vaughan, C.T.

1997-03-01

Paving is an automated mesh generation algorithm which produces all-quadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial algorithm in its operation. Parallel paving is the extension of serial paving into parallel environments to perform the same meshing functions as conventional paving only on distributed, discretized models. This extension allows large, adaptive, parallel finite element simulations to take advantage of paving`s meshing capabilities for h-remap remeshing. A significantly modified version of the CUBIT mesh generation code has been developed to host the parallel paving algorithm and demonstrate its capabilities on both two dimensional and three dimensional surface geometries and compare the resulting parallel produced meshes to conventionally paved meshes for mesh quality and algorithm performance. Sandia`s {open_quotes}tiling{close_quotes} dynamic load balancing code has also been extended to work with the paving algorithm to retain parallel efficiency as subdomains undergo iterative mesh refinement.

A two-dimensional method of manufactured solutions benchmark suite based on variations of Larsen's benchmark with escalating order of smoothness of the exact solution

International Nuclear Information System (INIS)

Schunert, Sebastian; Azmy, Yousry Y.

2011-01-01

The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally ne mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization error associated with the reference solution is not small compared to the discretization error associated with the mesh under scrutiny. Typically this situation occurs if the mesh of interest is only a couple of refinement levels away from the reference solution or if the order of accuracy of the numerical method (and hence the reference as well) is lower than expected. In this work we present a Method of Manufactured Solutions (MMS) benchmark suite with variable order of smoothness of the underlying exact solution for two-dimensional Cartesian geometries which provides analytical solutions aver- aged over arbitrary orthogonal meshes for scattering and non-scattering media. It should be emphasized that the developed MMS benchmark suite rst eliminates the aforementioned limitation of ne mesh reference solutions since it secures knowledge of the underlying true solution and second that it allows for an arbitrary order of smoothness of the underlying ex- act solution. The latter is of importance because even for smooth parameters and boundary conditions the DO equations can feature exact solution with limited smoothness. Moreover, the degree of smoothness is crucial for both the order of accuracy and the magnitude of the discretization error for any spatial discretization scheme. (author)

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

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

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.

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

Pericles and Attila results for the C5G7 MOX benchmark problems

International Nuclear Information System (INIS)

Wareing, T.A.; McGhee, J.M.

2002-01-01

Recently the Nuclear Energy Agency has published a new benchmark entitled, 'C5G7 MOX Benchmark.' This benchmark is to test the ability of current transport codes to treat reactor core problems without spatial homogenization. The benchmark includes both a two- and three-dimensional problem. We have calculated results for these benchmark problems with our Pericles and Attila codes. Pericles is a one-,two-, and three-dimensional unstructured grid discrete-ordinates code and was used for the twodimensional benchmark problem. Attila is a three-dimensional unstructured tetrahedral mesh discrete-ordinate code and was used for the three-dimensional problem. Both codes use discontinuous finite element spatial differencing. Both codes use diffusion synthetic acceleration (DSA) for accelerating the inner iterations.

Semi-implicit surface tension formulation with a Lagrangian surface mesh on an Eulerian simulation grid

KAUST Repository

Schroeder, Craig

2012-02-01

We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels. © 2011.

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

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)

On Discrete Killing Vector Fields and Patterns on Surfaces

KAUST Repository

Ben-Chen, Mirela; Butscher, Adrian; Solomon, Justin; Guibas, Leonidas

2010-01-01

, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal

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

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

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)

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)

RINGMesh: A programming library for developing mesh-based geomodeling applications

Science.gov (United States)

Pellerin, Jeanne; Botella, Arnaud; Bonneau, François; Mazuyer, Antoine; Chauvin, Benjamin; Lévy, Bruno; Caumon, Guillaume

2017-07-01

RINGMesh is a C++ open-source programming library for manipulating discretized geological models. It is designed to ease the development of applications and workflows that use discretized 3D models. It is neither a geomodeler, nor a meshing software. RINGMesh implements functionalities to read discretized surface-based or volumetric structural models and to check their validity. The models can be then exported in various file formats. RINGMesh provides data structures to represent geological structural models, either defined by their discretized boundary surfaces, and/or by discretized volumes. A programming interface allows to develop of new geomodeling methods, and to plug in external software. The goal of RINGMesh is to help researchers to focus on the implementation of their specific method rather than on tedious tasks common to many applications. The documented code is open-source and distributed under the modified BSD license. It is available at https://www.ring-team.org/index.php/software/ringmesh.

Users manual for Opt-MS : local methods for simplicial mesh smoothing and untangling.

Energy Technology Data Exchange (ETDEWEB)

Freitag, L.

1999-07-20

Creating meshes containing good-quality elements is a challenging, yet critical, problem facing computational scientists today. Several researchers have shown that the size of the mesh, the shape of the elements within that mesh, and their relationship to the physical application of interest can profoundly affect the efficiency and accuracy of many numerical approximation techniques. If the application contains anisotropic physics, the mesh can be improved by considering both local characteristics of the approximate application solution and the geometry of the computational domain. If the application is isotropic, regularly shaped elements in the mesh reduce the discretization error, and the mesh can be improved a priori by considering geometric criteria only. The Opt-MS package provides several local node point smoothing techniques that improve elements in the mesh by adjusting grid point location using geometric, criteria. The package is easy to use; only three subroutine calls are required for the user to begin using the software. The package is also flexible; the user may change the technique, function, or dimension of the problem at any time during the mesh smoothing process. Opt-MS is designed to interface with C and C++ codes, ad examples for both two-and three-dimensional meshes are provided.

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

3D unstructured mesh discontinuous finite element hydro

International Nuclear Information System (INIS)

Prasad, M.K.; Kershaw, D.S.; Shaw, M.J.

1995-01-01

The authors present detailed features of the ICF3D hydrodynamics code used for inertial fusion simulations. This code is intended to be a state-of-the-art upgrade of the well-known fluid code, LASNEX. ICF3D employs discontinuous finite elements on a discrete unstructured mesh consisting of a variety of 3D polyhedra including tetrahedra, prisms, and hexahedra. The authors discussed details of how the ROE-averaged second-order convection was applied on the discrete elements, and how the C++ coding interface has helped to simplify implementing the many physics and numerics modules within the code package. The author emphasized the virtues of object-oriented design in large scale projects such as ICF3D

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

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.

Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing.

Science.gov (United States)

Elmoataz, Abderrahim; Lezoray, Olivier; Bougleux, Sébastien

2008-07-01

We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach considers the problem as a variational one, which consists of minimizing a weighted sum of two energy terms: a regularization one that uses a discrete weighted p-Dirichlet energy and an approximation one. This is the discrete analogue of recent continuous Euclidean nonlocal regularization functionals. The proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted p-Laplace operator, parameterized by the degree p of regularity, the graph structure and the graph weight function. These discrete processing methods provide a graph-based version of recently proposed semi-local or nonlocal processing methods used in image and mesh processing, such as the bilateral filter, the TV digital filter or the nonlocal means filter. It works with equal ease on regular 2-D and 3-D images, manifolds or any data. We illustrate the abilities of the approach by applying it to various types of images, meshes, manifolds, and data represented as graphs.

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

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

Opfront: mesh

DEFF Research Database (Denmark)

2015-01-01

Mesh generation and visualization software based on the CGAL library. Folder content: drawmesh Visualize slices of the mesh (surface/volumetric) as wireframe on top of an image (3D). drawsurf Visualize surfaces of the mesh (surface/volumetric). img2mesh Convert isosurface in image to volumetric m...... mesh (medit format). img2off Convert isosurface in image to surface mesh (off format). off2mesh Convert surface mesh (off format) to volumetric mesh (medit format). reduce Crop and resize 3D and stacks of images. data Example data to test the library on...

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

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…

Documentation for MeshKit - Reactor Geometry (&mesh) Generator

Energy Technology Data Exchange (ETDEWEB)

Jain, Rajeev [Argonne National Lab. (ANL), Argonne, IL (United States); Mahadevan, Vijay [Argonne National Lab. (ANL), Argonne, IL (United States)

2015-09-30

This report gives documentation for using MeshKit’s Reactor Geometry (and mesh) Generator (RGG) GUI and also briefly documents other algorithms and tools available in MeshKit. RGG is a program designed to aid in modeling and meshing of complex/large hexagonal and rectilinear reactor cores. RGG uses Argonne’s SIGMA interfaces, Qt and VTK to produce an intuitive user interface. By integrating a 3D view of the reactor with the meshing tools and combining them into one user interface, RGG streamlines the task of preparing a simulation mesh and enables real-time feedback that reduces accidental scripting mistakes that could waste hours of meshing. RGG interfaces with MeshKit tools to consolidate the meshing process, meaning that going from model to mesh is as easy as a button click. This report is designed to explain RGG v 2.0 interface and provide users with the knowledge and skills to pilot RGG successfully. Brief documentation of MeshKit source code, tools and other algorithms available are also presented for developers to extend and add new algorithms to MeshKit. RGG tools work in serial and parallel and have been used to model complex reactor core models consisting of conical pins, load pads, several thousands of axially varying material properties of instrumentation pins and other interstices meshes.

Simulation of geothermal water extraction in heterogeneous reservoirs using dynamic unstructured mesh optimisation

Science.gov (United States)

Salinas, P.; Pavlidis, D.; Jacquemyn, C.; Lei, Q.; Xie, Z.; Pain, C.; Jackson, M.

2017-12-01

It is well known that the pressure gradient into a production well increases with decreasing distance to the well. To properly capture the local pressure drawdown into the well a high grid or mesh resolution is required; moreover, the location of the well must be captured accurately. In conventional simulation models, the user must interact with the model to modify grid resolution around wells of interest, and the well location is approximated on a grid defined early in the modelling process.We report a new approach for improved simulation of near wellbore flow in reservoir scale models through the use of dynamic mesh optimisation and the recently presented double control volume finite element method. Time is discretized using an adaptive, implicit approach. Heterogeneous geologic features are represented as volumes bounded by surfaces. Within these volumes, termed geologic domains, the material properties are constant. Up-, cross- or down-scaling of material properties during dynamic mesh optimization is not required, as the properties are uniform within each geologic domain. A given model typically contains numerous such geologic domains. Wells are implicitly coupled with the domain, and the fluid flows is modelled inside the wells. The method is novel for two reasons. First, a fully unstructured tetrahedral mesh is used to discretize space, and the spatial location of the well is specified via a line vector, ensuring its location even if the mesh is modified during the simulation. The well location is therefore accurately captured, the approach allows complex well trajectories and wells with many laterals to be modelled. Second, computational efficiency is increased by use of dynamic mesh optimization, in which an unstructured mesh adapts in space and time to key solution fields (preserving the geometry of the geologic domains), such as pressure, velocity or temperature, this also increases the quality of the solutions by placing higher resolution where required

Anisotropic mesh adaptation for solution of finite element problems using hierarchical edge-based error estimates

Energy Technology Data Exchange (ETDEWEB)

Lipnikov, Konstantin [Los Alamos National Laboratory; Agouzal, Abdellatif [UNIV DE LYON; Vassilevski, Yuri [Los Alamos National Laboratory

2009-01-01

We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.

A point-centered diffusion differencing for unstructured meshes in 3-D

International Nuclear Information System (INIS)

Palmer, T.S.

1994-01-01

We describe a point-centered diffusion discretization for 3-D unstructured meshes of polyhedra. The method has several attractive qualities, including second-order accuracy and preservation of linear solutions. A potential drawback to the scheme is that the diffusion matrix is asymmetric, in general. Results of numerical test problems illustrate the behavior of the scheme

Numerical simulation of flow induced by a pitched blade turbine. Comparison of the sliding mesh technique and an averaged source term method

Energy Technology Data Exchange (ETDEWEB)

Majander, E.O.J.; Manninen, M.T. [VTT Energy, Espoo (Finland)

1996-12-31

The flow induced by a pitched blade turbine was simulated using the sliding mesh technique. The detailed geometry of the turbine was modelled in a computational mesh rotating with the turbine and the geometry of the reactor including baffles was modelled in a stationary co-ordinate system. Effects of grid density were investigated. Turbulence was modelled by using the standard k-{epsilon} model. Results were compared to experimental observations. Velocity components were found to be in good agreement with the measured values throughout the tank. Averaged source terms were calculated from the sliding mesh simulations in order to investigate the reliability of the source term approach. The flow field in the tank was then simulated in a simple grid using these source terms. Agreement with the results of the sliding mesh simulations was good. Commercial CFD-code FLUENT was used in all simulations. (author)

Numerical simulation of flow induced by a pitched blade turbine. Comparison of the sliding mesh technique and an averaged source term method

Energy Technology Data Exchange (ETDEWEB)

Majander, E O.J.; Manninen, M T [VTT Energy, Espoo (Finland)

1997-12-31

The flow induced by a pitched blade turbine was simulated using the sliding mesh technique. The detailed geometry of the turbine was modelled in a computational mesh rotating with the turbine and the geometry of the reactor including baffles was modelled in a stationary co-ordinate system. Effects of grid density were investigated. Turbulence was modelled by using the standard k-{epsilon} model. Results were compared to experimental observations. Velocity components were found to be in good agreement with the measured values throughout the tank. Averaged source terms were calculated from the sliding mesh simulations in order to investigate the reliability of the source term approach. The flow field in the tank was then simulated in a simple grid using these source terms. Agreement with the results of the sliding mesh simulations was good. Commercial CFD-code FLUENT was used in all simulations. (author)

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.

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

Science.gov (United States)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

Milestone Deliverable: FY18-Q1: Deploy production sliding mesh capability with linear solver benchmarking.

Energy Technology Data Exchange (ETDEWEB)

Domino, Stefan P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-12-01

This milestone was focused on deploying and verifying a “sliding-mesh interface,” and establishing baseline timings for blade-resolved simulations of a sub-MW-scale turbine. In the ExaWind project, we are developing both sliding-mesh and overset-mesh approaches for handling the rotating blades in an operating wind turbine. In the sliding-mesh approach, the turbine rotor and its immediate surrounding fluid are captured in a “disk” that is embedded in the larger fluid domain. The embedded fluid is simulated in a coordinate system that rotates with the rotor. It is important that the coupling algorithm (and its implementation) between the rotating and inertial discrete models maintains the accuracy of the numerical methods on either side of the interface, i.e., the interface is “design order.”

Atomic Energy Act and ordinances. 8. ed.

International Nuclear Information System (INIS)

Anon.

1978-01-01

The new issue of the text contains the Atomic Energy Act (AtG) in its new wording of the announcement of 31 Oct 76, the new wording of the ordinances put in effect in 1977: Atomic procedure ordinance (AtVfV), radiation protection ordinance (SSU), and atomic financial security ordinance (AtDeckV); furthermore the x-ray ordinance (RoeV) of 1978 in its wording which has been changed by the radiation protection ordinance. Also printed are the cost ordinance (AtKostV) of 1971, the food irradiation ordinance (LebensmBestrV) in the wording of 1975 and the medicine ordinance (ArzneimV) in the wording of 1971. An addition was made by adding to the liability laws the Paris agreement (PUE) on the liability towards third persons in the field of nuclear energy in the wording of the announcement of 5 Feb 76. (orig./HP) [de

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

Computational domain discretization in numerical analysis of flow within granular materials

Science.gov (United States)

Sosnowski, Marcin

2018-06-01

The discretization of computational domain is a crucial step in Computational Fluid Dynamics (CFD) because it influences not only the numerical stability of the analysed model but also the agreement of obtained results and real data. Modelling flow in packed beds of granular materials is a very challenging task in terms of discretization due to the existence of narrow spaces between spherical granules contacting tangentially in a single point. Standard approach to this issue results in a low quality mesh and unreliable results in consequence. Therefore the common method is to reduce the diameter of the modelled granules in order to eliminate the single-point contact between the individual granules. The drawback of such method is the adulteration of flow and contact heat resistance among others. Therefore an innovative method is proposed in the paper: single-point contact is extended to a cylinder-shaped volume contact. Such approach eliminates the low quality mesh elements and simultaneously introduces only slight distortion to the flow as well as contact heat transfer. The performed analysis of numerous test cases prove the great potential of the proposed method of meshing the packed beds of granular materials.

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

Topology reconstruction for B-Rep modeling from 3D mesh in reverse engineering applications

Science.gov (United States)

Bénière, Roseline; Subsol, Gérard; Gesquière, Gilles; Le Breton, François; Puech, William

2012-03-01

Nowadays, most of the manufactured objects are designed using CAD (Computer-Aided Design) software. Nevertheless, for visualization, data exchange or manufacturing applications, the geometric model has to be discretized into a 3D mesh composed of a finite number of vertices and edges. But, in some cases, the initial model may be lost or unavailable. In other cases, the 3D discrete representation may be modified, for example after a numerical simulation, and does not correspond anymore to the initial model. A reverse engineering method is then required to reconstruct a 3D continuous representation from the discrete one. In previous work, we have presented a new approach for 3D geometric primitive extraction. In this paper, to complete our automatic and comprehensive reverse engineering process, we propose a method to construct the topology of the retrieved object. To reconstruct a B-Rep model, a new formalism is now introduced to define the adjacency relations. Then a new process is used to construct the boundaries of the object. The whole process is tested on 3D industrial meshes and bring a solution to recover B-Rep models.

Parametric Quadrilateral Meshes for the Design and Optimization of Superconducting Magnets

CERN Document Server

Aleksa, Martin; Völlinger, Christine

2002-01-01

The program package ROXIE has been developed at CERN for the design and optimization of accelerator magnets. The necessity of extremely uniform fields in the superconducting accelerator magnets for LHC requires very accurate methods of field computation. For this purpose the coupled boundary-element / finite-element technique (BEM-FEM) is used. Quadrilateral higher order finite-element meshes are generated for the discretization of the iron domain (yoke) and stainless steel collars. A new mesh generator using geometrically optimized domain decomposition which was developed at the University of Stuttgart, Germany has been implemented into the ROXIE program providing fully automatic and user friendly mesh generation. The structure of the magnet cross-section can be modeled using parametric objects such as holes of different forms, elliptic, parabolic or hyperbolic arcs, notches, slots, .... For sensitivity analysis and parametric studies, point based morphing algorithms are applied to guarantee smooth adaptatio...

Electromagnetic forward modelling for realistic Earth models using unstructured tetrahedral meshes and a meshfree approach

Science.gov (United States)

Farquharson, C.; Long, J.; Lu, X.; Lelievre, P. G.

2017-12-01

Real-life geology is complex, and so, even when allowing for the diffusive, low resolution nature of geophysical electromagnetic methods, we need Earth models that can accurately represent this complexity when modelling and inverting electromagnetic data. This is particularly the case for the scales, detail and conductivity contrasts involved in mineral and hydrocarbon exploration and development, but also for the larger scale of lithospheric studies. Unstructured tetrahedral meshes provide a flexible means of discretizing a general, arbitrary Earth model. This is important when wanting to integrate a geophysical Earth model with a geological Earth model parameterized in terms of surfaces. Finite-element and finite-volume methods can be derived for computing the electric and magnetic fields in a model parameterized using an unstructured tetrahedral mesh. A number of such variants have been proposed and have proven successful. However, the efficiency and accuracy of these methods can be affected by the "quality" of the tetrahedral discretization, that is, how many of the tetrahedral cells in the mesh are long, narrow and pointy. This is particularly the case if one wants to use an iterative technique to solve the resulting linear system of equations. One approach to deal with this issue is to develop sophisticated model and mesh building and manipulation capabilities in order to ensure that any mesh built from geological information is of sufficient quality for the electromagnetic modelling. Another approach is to investigate other methods of synthesizing the electromagnetic fields. One such example is a "meshfree" approach in which the electromagnetic fields are synthesized using a mesh that is distinct from the mesh used to parameterized the Earth model. There are then two meshes, one describing the Earth model and one used for the numerical mathematics of computing the fields. This means that there are no longer any quality requirements on the model mesh, which

Approximation of scalar and vector transport problems on polyhedral meshes

International Nuclear Information System (INIS)

Cantin, Pierre

2016-01-01

This thesis analyzes, at the continuous and at the discrete level on polyhedral meshes, the scalar and the vector transport problems in three-dimensional domains. These problems are composed of a diffusive term, an advective term, and a reactive term. In the context of Friedrichs systems, the continuous problems are analyzed in Lebesgue graph spaces. The classical positivity assumption on the Friedrichs tensor is generalized so as to consider the case of practical interest where this tensor takes null or slightly negative values. A new scheme converging at the order 3/2 is devised for the scalar advection-reaction problem using scalar degrees of freedom attached to mesh vertices. Two new schemes considering as well scalar degrees of freedom attached to mesh vertices are devised for the scalar transport problem and are robust with respect to the dominant regime. The first scheme converges at the order 1/2 when advection effects are dominant and at the order 1 when diffusion effects are dominant. The second scheme improves the accuracy by converging at the order 3/2 when advection effects are dominant. Finally, a new scheme converging at the order 1/2 is devised for the vector advection-reaction problem considering only one scalar degree of freedom per mesh edge. The accuracy and the efficiency of all these schemes are assessed on various test cases using three-dimensional polyhedral meshes. (author)

Numerical simulation for quenching meshes with TONUS platform

International Nuclear Information System (INIS)

Bin, Chen; Hongxing, Yu

2009-01-01

For mitigation of hydrogen risks during severe accidents to protect the integrity of containment, PAR and ignitors are used in current advanced nuclear power plants. But multiple combustions induced by ignitors and consequent DDT phenomena are not practically eliminated. An innovative design call 'quenching meshes' is considered to confine hydrogen flame within one compartment by metallic meshes, so that hazardous flame propagation can be prevented. The numerical simulation results based on discretization of the full Navier-Stokes equations with global one-step reaction represented by Arrhenius laminar combustion model have shown the possibility of flame quenching 'numerically'. This is achieved via multiplication of the combustion rate expression by a Heaviside function having an ignition temperature as a parameter. Qualitative behavior of the computed flow shows that the flame velocity diminishes while passing through a quenching mesh, while qualitative analysis based on the energy balance reveals the mechanism of flame quenching. All the above analysis has been performed for a stoichiometric mixture and normal initial pressure and temperature for initial conditions. For further research we would like to suggest the investigation of the influence of the mixture composition, initial pressure and/or temperature on the quenching criteria

Mesh Excision: Is Total Mesh Excision Necessary?

Science.gov (United States)

Wolff, Gillian F; Winters, J Christian; Krlin, Ryan M

2016-04-01

Nearly 29% of women will undergo a secondary, repeat operation for pelvic organ prolapse (POP) symptom recurrence following a primary repair, as reported by Abbott et al. (Am J Obstet Gynecol 210:163.e1-163.e1, 2014). In efforts to decrease the rates of failure, graft materials have been utilized to augment transvaginal repairs. Following the success of using polypropylene mesh (PPM) for stress urinary incontinence (SUI), the use of PPM in the transvaginal repair of POP increased. However, in recent years, significant concerns have been raised about the safety of PPM mesh. Complications, some specific to mesh, such as exposures, erosion, dyspareunia, and pelvic pain, have been reported with increased frequency. In the current literature, there is not substantive evidence to suggest that PPM has intrinsic properties that warrant total mesh removal in the absence of complications. There are a number of complications that can occur after transvaginal mesh placement that do warrant surgical intervention after failure of conservative therapy. In aggregate, there are no high-quality controlled studies that clearly demonstrate that total mesh removal is consistently more likely to achieve pain reduction. In the cases of obstruction and erosion, it seems clear that definitive removal of the offending mesh is associated with resolution of symptoms in the majority of cases and reasonable practice. There are a number of complications that can occur with removal of mesh, and patients should be informed of this as they formulate a choice of treatment. We will review these considerations as we examine the clinical question of whether total versus partial removal of mesh is necessary for the resolution of complications following transvaginal mesh placement.

CDCC calculations with the Lagrange-mesh technique

International Nuclear Information System (INIS)

Druet, T.; Baye, D.; Descouvemont, P.; Sparenberg, J.-M.

2010-01-01

We apply the Lagrange-mesh technique to the Continuum Discretized Coupled Channel (CDCC) theory. The CDCC equations are solved with the R-matrix method, using Lagrange functions as variational basis. The choice of Lagrange functions is shown to be efficient and accurate for elastic scattering as well as for breakup reactions. We describe the general formalism for two-body projectiles, and apply it to the d+ 58 Ni collision at E d =80 MeV. Various numerical and physical aspects are discussed. Benchmark calculations on elastic scattering and breakup are presented.

Coarse mesh finite element method for boiling water reactor physics analysis

International Nuclear Information System (INIS)

Ellison, P.G.

1983-01-01

A coarse mesh method is formulated for the solution of Boiling Water Reactor physics problems using two group diffusion theory. No fuel assembly cross-section homogenization is required; water gaps, control blades and fuel pins of varying enrichments are treated explicitly. The method combines constrained finite element discretization with infinite lattice super cell trial functions to obtain coarse mesh solutions for which the only approximations are along the boundaries between fuel assemblies. The method is applied to bench mark Boiling Water Reactor problems to obtain both the eigenvalue and detailed flux distributions. The solutions to these problems indicate the method is useful in predicting detailed power distributions and eigenvalues for Boiling Water Reactor physics problems

Parametric Quadrilateral Meshes for the Design and Optimization of Superconducting Magnets

CERN Document Server

Aleksa, Martin; Völlinger, Christine

2000-01-01

The program package ROXIE [1] has been developed at CERN for the design and optimization of the superconducting magnets for the LHC.The necessity of extremely uniform (coil dominated) fields in accelerator magnets requires very accurate methods of .eld computation. For this purpose a coupled boundary-element/ finite-element technique (BEM-FEM) is used [2]. Quadrilateral higher order finite-elements are used for the discretization of the iron domain.This is necessary for the accurate modeling of the iron contours and is favorable for 3D meshes. A new quadrilateral mesh generator using geometrically optimized domain decomposition which was developed at the University of Stuttgart, Germany [3] has been implemented into the ROXIE program providing fully automatic and user friendly mesh generation.The frequent application of mathematical optimization techniques requires parametric models which are set-up using a feature-based approach.The structure of the magnet cross-section can be modeled using parametric object...

Quantization in rotating co-ordinates revisited

International Nuclear Information System (INIS)

Hussain, F.; Qadir, A.

1982-07-01

Recent work on quantization in rotating co-ordinates showed that no radiation would be seen by an observer rotating with a constant angular speed. This work used a Galilean-type co-ordinate transformation. We show that the same result holds for a Lorentz-type co-ordinate system, in spite of the fact that the metric has a co-ordinate singularity at rΩ = 1. Further, we are able to define positive and negative energy modes for a particular case of a non-static, non-stationary metric. (author)

Parallel octree-based hexahedral mesh generation for eulerian to lagrangian conversion.

Energy Technology Data Exchange (ETDEWEB)

Staten, Matthew L.; Owen, Steven James

2010-09-01

Computational simulation must often be performed on domains where materials are represented as scalar quantities or volume fractions at cell centers of an octree-based grid. Common examples include bio-medical, geotechnical or shock physics calculations where interface boundaries are represented only as discrete statistical approximations. In this work, we introduce new methods for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to ASC codes such as CTH and Alegra. New procedures for generating all-hexahedral finite element meshes from volume fraction data are introduced. A new primal-contouring approach is introduced for defining a geometric domain. New methods for refinement, node smoothing, resolving non-manifold conditions and defining geometry are also introduced as well as an extension of the algorithm to handle tetrahedral meshes. We also describe new scalable MPI-based implementations of these procedures. We describe a new software module, Sculptor, which has been developed for use as an embedded component of CTH. We also describe its interface and its use within the mesh generation code, CUBIT. Several examples are shown to illustrate the capabilities of Sculptor.

Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

Science.gov (United States)

Schwing, Alan Michael

For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable

An effective FEM-based approach for discrete 3D crack growth

DEFF Research Database (Denmark)

Nielsen, Morten Eggert; Lambertsen, Søren Heide; Pedersen, Erik B.

2015-01-01

A new geometric approach for discrete crack growth modeling is proposed and implemented in a commercial FEM software. The basic idea is to model the crack growth by removing volumes of material as the crack front advances. Thereby, adaptive meshing techniques, found in commercial software, is wel...

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

Adaptive Shape Functions and Internal Mesh Adaptation for Modelling Progressive Failure in Adhesively Bonded Joints

Science.gov (United States)

Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.

2014-01-01

Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.

Ordinal bivariate inequality

DEFF Research Database (Denmark)

Sonne-Schmidt, Christoffer Scavenius; Tarp, Finn; Østerdal, Lars Peter Raahave

This paper introduces a concept of inequality comparisons with ordinal bivariate categorical data. In our model, one population is more unequal than another when they have common arithmetic median outcomes and the first can be obtained from the second by correlationincreasing switches and/or median......-preserving spreads. For the canonical 2x2 case (with two binary indicators), we derive a simple operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood deprivation in Mozambique....

Notes on the Mesh Handler and Mesh Data Conversion

International Nuclear Information System (INIS)

Lee, Sang Yong; Park, Chan Eok

2009-01-01

At the outset of the development of the thermal-hydraulic code (THC), efforts have been made to utilize the recent technology of the computational fluid dynamics. Among many of them, the unstructured mesh approach was adopted to alleviate the restriction of the grid handling system. As a natural consequence, a mesh handler (MH) has been developed to manipulate the complex mesh data from the mesh generator. The mesh generator, Gambit, was chosen at the beginning of the development of the code. But a new mesh generator, Pointwise, was introduced to get more flexible mesh generation capability. An open source code, Paraview, was chosen as a post processor, which can handle unstructured as well as structured mesh data. Overall data processing system for THC is shown in Figure-1. There are various file formats to save the mesh data in the permanent storage media. A couple of dozen of file formats are found even in the above mentioned programs. A competent mesh handler should have the capability to import or export mesh data as many as possible formats. But, in reality, there are two aspects that make it difficult to achieve the competence. The first aspect to consider is the time and efforts to program the interface code. And the second aspect, which is even more difficult one, is the fact that many mesh data file formats are proprietary information. In this paper, some experience of the development of the format conversion programs will be presented. File formats involved are Gambit neutral format, Ansys-CFX grid file format, VTK legacy file format, Nastran format and CGNS

An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of elliptic interface problems and conjugate heat transfer problems

Science.gov (United States)

Sun, Huafei; Darmofal, David L.

2014-12-01

In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an output-based adaptive scheme. We first present a DG discretization with a dual-consistent output evaluation for elliptic interface problems on interface-conforming meshes, and then extend the method to handle multi-physics interface problems, in particular conjugate heat transfer (CHT) problems. The method is then applied to non-interface-conforming meshes using a cut-cell technique, where the interface definition is completely separate from the mesh generation process. No assumption is made on the interface shape (other than Lipschitz continuity). We then equip our strategy with an output-based adaptive scheme for an accurate output prediction. Through numerical examples, we demonstrate high-order convergence for elliptic interface problems and CHT problems with both smooth and non-smooth interface shapes.

Ordinance on protection from the harmful effects of X-radiation (X-ray Ordinance). As of January 8, 1987. 3. ed.

International Nuclear Information System (INIS)

Hinrichs, O.

1992-01-01

The German X-ray Ordinance (Roentgenverordnung) contains the main protective provisions applying to the field of X-ray equipment and sources of unwanted X radiation. It thus forms a complement to the German Radiation Protection Ordinance (Strahlenschutzverordnung). The X-ray Ordinance is based, as is the Radiation Protection Ordinance, on the German Nuclear Energy Act (Atomgesetz). It transposes the same Euratom Directives into national law, through which above all the limit values are defined. The current state of the X-ray Ordinance is that of the text promulgated on 8.01.1987 with the subsequent amendments, the last of which was adopted on 19.12.1990. The brochure also reproduces the Official Memorandum to the X-ray Ordinance, as this gives important indications for the legal construction of the Ordinance. (orig./HSCH) [de

Memory-Based Specification of Verbal Features for Classifying Animals into Super-Ordinate and Sub-Ordinate Categories

Directory of Open Access Journals (Sweden)

Takahiro Soshi

2017-09-01

Full Text Available Accumulating evidence suggests that category representations are based on features. Distinguishing features are considered to define categories, because of all-or-none responses for objects in different categories; however, it is unclear how distinguishing features actually classify objects at various category levels. The present study included 75 animals within three classes (mammal, bird, and fish, along with 195 verbal features. Healthy adults participated in memory-based feature-animal matching verification tests. Analyses included a hierarchical clustering analysis, support vector machine, and independent component analysis to specify features effective for classifications. Quantitative and qualitative comparisons for significant features were conducted between super-ordinate and sub-ordinate levels. The number of significant features was larger for super-ordinate than sub-ordinate levels. Qualitatively, the proportion of biological features was larger than cultural/affective features in both the levels, while the proportion of affective features increased at the sub-ordinate level. To summarize, the two types of features differentially function to establish category representations.

A spectral nodal method for discrete ordinates problems in x,y geometry

International Nuclear Information System (INIS)

Barros, R.C. de; Larsen, E.W.

1991-06-01

A new nodal method is proposed for the solution of S N problems in x- y-geometry. This method uses the Spectral Green's Function (SGF) scheme for solving the one-dimensional transverse-integrated nodal transport equations with no spatial truncation error. Thus, the only approximations in the x, y-geometry nodal method occur in the transverse leakage terms, as in diffusion theory. We approximate these leakage terms using a flat or constant approximation, and we refer to the resulting method as the SGF-Constant Nodal (SGF-CN) method. We show in numerical calculations that the SGF-CN method is much more accurate than other well-known transport nodal methods for coarse-mesh deep-penetration S N problems, even though the transverse leakage terms are approximated rather simply. (author)

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.

Ordinal Bivariate Inequality

DEFF Research Database (Denmark)

Sonne-Schmidt, Christoffer Scavenius; Tarp, Finn; Østerdal, Lars Peter Raahave

2016-01-01

This paper introduces a concept of inequality comparisons with ordinal bivariate categorical data. In our model, one population is more unequal than another when they have common arithmetic median outcomes and the first can be obtained from the second by correlation-increasing switches and....../or median-preserving spreads. For the canonical 2 × 2 case (with two binary indicators), we derive a simple operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood deprivation in Mozambique....

Tree Ordination as Invented Tradition

Directory of Open Access Journals (Sweden)

Avery Morrow

2012-01-01

Full Text Available The symbolic ordination of trees as monks in Thailand is widely perceived in Western scholarship to be proof of the power of Buddhism to spur ecological thought. However, a closer analysis of tree ordination demonstrates that it is not primarily about Buddhist teaching, but rather is an invented tradition based on the sanctity of Thai Buddhist symbols as well as those of spirit worship and the monarchy. Tree ordinations performed by non-Buddhist minorities in Thailand do not demonstrate a religious commitment but rather a political one.

Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

International Nuclear Information System (INIS)

Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

2017-01-01

A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.

Solution adaptive triangular meshes with application to the simulation of plasma equilibrium

International Nuclear Information System (INIS)

Erlebacher, G.

1984-01-01

A new discrete Laplace operator is constructed on a local mesh molecule, second order accurate on symmetric cell regions, based on local Taylor series expansions. This discrete Laplacian is then compared to the one commonly used in the literature. A truncation error analysis of gradient and Laplace operators calculated at triangle centroids reveals that the maximum bounds of their truncation errors are minimized on equilateral triangles, for a fixed triangle perimeter. A new adaptive strategy on arbitrary triangular grids is developed in which a uniform grid is defined with respect to the solution surface, as opposed to the x,y plane. Departures from mesh uniformity arises from a spacially dependent mean-curvature of the solution surface. The power of this new adaptive technique is applied to the problem of finding free-boundary plasma equilibria within the context of MHD. The geometry is toroidal, and axisymmetry in the toroidal direction is assumed. We are led to conclude that the grid should move, not towards regions of high curvature of magnetic flux, but rather towards regions of greater toroidal current density. This has a direct bearing on the accuracy with which the Grad-Shafranov equation is being approximated

Benchmark calculations on resonance absorption by 238U in a PWR pin-cell geometry

International Nuclear Information System (INIS)

Kruijf, W.J.M. de; Janssen, A.J.

1993-12-01

Very accurate Monte Carlo calculations with MCNP have been performed to serve as a reference for benchmark calculations on resonance absorption by 238 U in a typical PWR pin-cell geometry. Calculations with the energy-pointwise slowing down code ROLAIDS-CPM show that this code calculates the resonance absorption accurately. Calculations with the multigroup discrete ordinates code XSDRN show that accurate results can only be achieved with a very fine energy mesh. (orig.)

Detailed resonance absorption calculations with the Monte Carlo code MCNP and collision probability version of the slowing down code ROLAIDS

International Nuclear Information System (INIS)

Kruijf, W.J.M. de; Janssen, A.J.

1994-01-01

Very accurate Mote Carlo calculations with Monte Carlo Code have been performed to serve as reference for benchmark calculations on resonance absorption by U 238 in a typical PWR pin-cell geometry. Calculations with the energy-pointwise slowing down code calculates the resonance absorption accurately. Calculations with the multigroup discrete ordinates code XSDRN show that accurate results can only be achieved with a very fine energy mesh. (authors). 9 refs., 5 figs., 2 tabs

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Science.gov (United States)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Atomic Energy Law with ordinances. 9. ed.

International Nuclear Information System (INIS)

Anon.

1982-01-01

The revised edition of the text is due to a variety of major changes in, and amendments to, the German Atomic Energy Law. This book includes the current version of the Atomic Energy Law which has been changed several times, the 1982-version of the ordinace concerning procedures laid down in the Atomic Energy Law, the 1976 radiation protection ordinance together with recent amendments, the 1973 X-ray ordinance, the 1977 financial security ordinance laid down in the Atomic Energy Law, the 1981 ordinance concerning costs, the ordinance concerning performance in anticipation of ultimate disposal. The book is a compilation of the basic Atomic Energy Law which is needed mostly for imminent practical requirements. (orig./HSCH) [de

Mimetic finite difference method for the stokes problem on polygonal meshes

Energy Technology Data Exchange (ETDEWEB)

Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA

2009-01-01

Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.

Social Host Ordinances and Policies. Prevention Update

Science.gov (United States)

Higher Education Center for Alcohol, Drug Abuse, and Violence Prevention, 2011

2011-01-01

Social host liability laws (also known as teen party ordinances, loud or unruly gathering ordinances, or response costs ordinances) target the location in which underage drinking takes place. Social host liability laws hold noncommercial individuals responsible for underage drinking events on property they own, lease, or otherwise control. They…

Processing ordinality and quantity: the case of developmental dyscalculia.

Directory of Open Access Journals (Sweden)

Orly Rubinsten

Full Text Available In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1 the traditionally and well accepted numerical magnitude system but also (2 core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD. Participants made "ordered" or "non-ordered" judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1 and 3 numbers (symbolic task: Experiment 2. In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks, DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.

Processing ordinality and quantity: the case of developmental dyscalculia.

Science.gov (United States)

Rubinsten, Orly; Sury, Dana

2011-01-01

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made "ordered" or "non-ordered" judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.

Adaptive mesh refinement for a finite volume method for flow and transport of radionuclides in heterogeneous porous media

International Nuclear Information System (INIS)

Amaziane, Brahim; Bourgeois, Marc; El Fatini, Mohamed

2014-01-01

In this paper, we consider adaptive numerical simulation of miscible displacement problems in porous media, which are modeled by single phase flow equations. A vertex-centred finite volume method is employed to discretize the coupled system: the Darcy flow equation and the diffusion-convection concentration equation. The convection term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion-dispersion term is discretized by piecewise linear conforming finite elements. We introduce two kinds of indicators, both of them of residual type. The first one is related to time discretization and is local with respect to the time discretization: thus, at each time, it provides an appropriate information for the choice of the next time step. The second is related to space discretization and is local with respect to both the time and space variable and the idea is that at each time it is an efficient tool for mesh adaptivity. An error estimation procedure evaluates where additional refinement is needed and grid generation procedures dynamically create or remove fine-grid patches as resolution requirements change. The method was implemented in the software MELODIE, developed by the French Institute for Radiological Protection and Nuclear Safety (IRSN, Institut de Radioprotection et de Surete Nucleaire). The algorithm is then used to simulate the evolution of radionuclide migration from the waste packages through a heterogeneous disposal, demonstrating its capability to capture complex behavior of the resulting flow. (authors)

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

Finite difference discretization of semiconductor drift-diffusion equations for nanowire solar cells

Science.gov (United States)

Deinega, Alexei; John, Sajeev

2012-10-01

We introduce a finite difference discretization of semiconductor drift-diffusion equations using cylindrical partial waves. It can be applied to describe the photo-generated current in radial pn-junction nanowire solar cells. We demonstrate that the cylindrically symmetric (l=0) partial wave accurately describes the electronic response of a square lattice of silicon nanowires at normal incidence. We investigate the accuracy of our discretization scheme by using different mesh resolution along the radial direction r and compare with 3D (x, y, z) discretization. We consider both straight nanowires and nanowires with radius modulation along the vertical axis. The charge carrier generation profile inside each nanowire is calculated using an independent finite-difference time-domain simulation.

A Tissue Relevance and Meshing Method for Computing Patient-Specific Anatomical Models in Endoscopic Sinus Surgery Simulation

Science.gov (United States)

Audette, M. A.; Hertel, I.; Burgert, O.; Strauss, G.

This paper presents on-going work on a method for determining which subvolumes of a patient-specific tissue map, extracted from CT data of the head, are relevant to simulating endoscopic sinus surgery of that individual, and for decomposing these relevant tissues into triangles and tetrahedra whose mesh size is well controlled. The overall goal is to limit the complexity of the real-time biomechanical interaction while ensuring the clinical relevance of the simulation. Relevant tissues are determined as the union of the pathology present in the patient, of critical tissues deemed to be near the intended surgical path or pathology, and of bone and soft tissue near the intended path, pathology or critical tissues. The processing of tissues, prior to meshing, is based on the Fast Marching method applied under various guises, in a conditional manner that is related to tissue classes. The meshing is based on an adaptation of a meshing method of ours, which combines the Marching Tetrahedra method and the discrete Simplex mesh surface model to produce a topologically faithful surface mesh with well controlled edge and face size as a first stage, and Almost-regular Tetrahedralization of the same prescribed mesh size as a last stage.

Discrete modelling of drapery systems

Science.gov (United States)

Thoeni, Klaus; Giacomini, Anna

2016-04-01

Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...

Stable grid refinement and singular source discretization for seismic wave simulations

Energy Technology Data Exchange (ETDEWEB)

Petersson, N A; Sjogreen, B

2009-10-30

An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid, consisting of a set of structured rectangular component grids with hanging nodes on the grid refinement interface. Previously developed summation-by-parts properties are generalized to devise a stable second order accurate coupling of the solution across mesh refinement interfaces. The discretization of singular source terms of point force and point moment tensor type are also studied. Based on enforcing discrete moment conditions that mimic properties of the Dirac distribution and its gradient, previous single grid formulas are generalized to work in the vicinity of grid refinement interfaces. These source discretization formulas are shown to give second order accuracy in the solution, with the error being essentially independent of the distance between the source and the grid refinement boundary. Several numerical examples are given to illustrate the properties of the proposed method.

Application of preconditioned GMRES to the numerical solution of the neutron transport equation

International Nuclear Information System (INIS)

Patton, B.W.; Holloway, J.P.

2002-01-01

The generalized minimal residual (GMRES) method with right preconditioning is examined as an alternative to both standard and accelerated transport sweeps for the iterative solution of the diamond differenced discrete ordinates neutron transport equation. Incomplete factorization (ILU) type preconditioners are used to determine their effectiveness in accelerating GMRES for this application. ILU(τ), which requires the specification of a dropping criteria τ, proves to be a good choice for the types of problems examined in this paper. The combination of ILU(τ) and GMRES is compared with both DSA and unaccelerated transport sweeps for several model problems. It is found that the computational workload of the ILU(τ)-GMRES combination scales nonlinearly with the number of energy groups and quadrature order, making this technique most effective for problems with a small number of groups and discrete ordinates. However, the cost of preconditioner construction can be amortized over several calculations with different source and/or boundary values. Preconditioners built upon standard transport sweep algorithms are also evaluated as to their effectiveness in accelerating the convergence of GMRES. These preconditioners show better scaling with such problem parameters as the scattering ratio, the number of discrete ordinates, and the number of spatial meshes. These sweeps based preconditioners can also be cast in a matrix free form that greatly reduces storage requirements

A guide to practical radiation protection in medicine. X-Ray Ordinance. Radiation Protection Ordinance. Practice-oriented hints, comments, text compilation

International Nuclear Information System (INIS)

Fiebich, M.; Nischelsky, J.E.; Pfeiff, H.; Westermann, K.

2003-01-01

This loose-leaf collection has been compiled for users who have to implement the X-ray Ordinance and the Radiation Protection Ordinance at their place of work. It presents all acts, ordinances, safety guides, regulations and recommendations of relevance in connection with the above two ordinances, as well as practical instructions and the full text of technical codes. Radiation protection officers and other persons in charge of radiation protection will find the references, information and advice needed to solve problems encountered. (orig.) [de

The new German radiation protection ordinance

International Nuclear Information System (INIS)

Pfeffer, W.; Weimer, G.

2003-01-01

According to European law, the Basic Safety Standards (BSS) published by the European Council in 1996 and the Council Directive on health protection of individuals against dangers of ionising radiation in relation to medical exposure had to be transferred into national law within due time. In 2001 the new Ordinance for the Implementation of the Euratom Guidelines on Radiation Protection] was published, which replaces the old Radiation Protection Ordinance. The new German Ordinance adapts the European Directive to German law, covering the general principles but even giving more details in many fields of radiation protection. The BSS scope certainly is much broader than the prescriptions important for the field of radiation protection in nuclear power plants. According to the scope of this workshop on occupational exposure in nuclear power plants - and as the BSS most probably will be quite familiar to all of you - after a short general overview on relevant contents of the German Ordinance, this presentation will focus on the main issues important in the operation of NPP and especially on some areas which may give rise to necessary changes caused by the new Ordinance. (A.L.B.)

Tensile Behaviour of Welded Wire Mesh and Hexagonal Metal Mesh for Ferrocement Application

Science.gov (United States)

Tanawade, A. G.; Modhera, C. D.

2017-08-01

Tension tests were conducted on welded mesh and hexagonal Metal mesh. Welded Mesh is available in the market in different sizes. The two types are analysed viz. Ø 2.3 mm and Ø 2.7 mm welded mesh, having opening size 31.75 mm × 31.75 mm and 25.4 mm × 25.4 mm respectively. Tensile strength test was performed on samples of welded mesh in three different orientations namely 0°, 30° and 45° degrees with the loading axis and hexagonal Metal mesh of Ø 0.7 mm, having opening 19.05 × 19.05 mm. Experimental tests were conducted on samples of these meshes. The objective of this study was to investigate the behaviour of the welded mesh and hexagonal Metal mesh. The result shows that the tension load carrying capacity of welded mesh of Ø 2.7 mm of 0° orientation is good as compared to Ø2.3 mm mesh and ductility of hexagonal Metal mesh is good in behaviour.

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

Science.gov (United States)

Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

2018-05-01

Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

DEFF Research Database (Denmark)

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

2011-01-01

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal......, whereas the convergence of the coefficients happens only with respect to the "volumetric" Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise. We...... provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example....

Seeking new surgical predictors of mesh exposure after transvaginal mesh repair.

Science.gov (United States)

Wu, Pei-Ying; Chang, Chih-Hung; Shen, Meng-Ru; Chou, Cheng-Yang; Yang, Yi-Ching; Huang, Yu-Fang

2016-10-01

The purpose of this study was to explore new preventable risk factors for mesh exposure. A retrospective review of 92 consecutive patients treated with transvaginal mesh (TVM) in the urogynecological unit of our university hospital. An analysis of perioperative predictors was conducted in patients after vaginal repairs using a type 1 mesh. Mesh complications were recorded according to International Urogynecological Association (IUGA) definitions. Mesh-exposure-free durations were calculated by using the Kaplan-Meier method and compared between different closure techniques using log-rank test. Hazard ratios (HR) of predictors for mesh exposure were estimated by univariate and multivariate analyses using Cox proportional hazards regression models. The median surveillance interval was 24.1 months. Two late occurrences were found beyond 1 year post operation. No statistically significant correlation was observed between mesh exposure and concomitant hysterectomy. Exposure risks were significantly higher in patients with interrupted whole-layer closure in univariate analysis. In the multivariate analysis, hematoma [HR 5.42, 95 % confidence interval (CI) 1.26-23.35, P = 0.024), Prolift mesh (HR 5.52, 95 % CI 1.15-26.53, P = 0.033), and interrupted whole-layer closure (HR 7.02, 95 % CI 1.62-30.53, P = 0.009) were the strongest predictors of mesh exposure. Findings indicate the risks of mesh exposure and reoperation may be prevented by avoiding hematoma, large amount of mesh, or interrupted whole-layer closure in TVM surgeries. If these risk factors are prevented, hysterectomy may not be a relative contraindication for TVM use. We also provide evidence regarding mesh exposure and the necessity for more than 1 year of follow-up and preoperative counselling.

Co-ordinating Product Developing Activities

DEFF Research Database (Denmark)

Terkelsen, Søren Bendix

1996-01-01

The paper contains a presentation of research methods to be used in case studies in product development and a presentation on how to deal with Design Co-ordination according to litterature......The paper contains a presentation of research methods to be used in case studies in product development and a presentation on how to deal with Design Co-ordination according to litterature...

Discrete Feature Model (DFM) User Documentation

Energy Technology Data Exchange (ETDEWEB)

Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))

2008-06-15

software, the geometry of discrete features and their hydrologic properties are defined as a mesh composed of triangular, finite elements. Hydrologic boundary conditions arc prescribed as a simulation sequence, which permits specification of conditions ranging from simple, steady-state flow to complex situations where both the magnitude and type of boundary conditions may vary over time

Discrete Feature Model (DFM) User Documentation

International Nuclear Information System (INIS)

Geier, Joel

2008-06-01

geometry of discrete features and their hydrologic properties are defined as a mesh composed of triangular, finite elements. Hydrologic boundary conditions arc prescribed as a simulation sequence, which permits specification of conditions ranging from simple, steady-state flow to complex situations where both the magnitude and type of boundary conditions may vary over time

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.

Two-dimensional parasitic capacitance extraction for integrated circuit with dual discrete geometric methods

International Nuclear Information System (INIS)

Ren Dan; Ren Zhuoxiang; Qu Hui; Xu Xiaoyu

2015-01-01

Capacitance extraction is one of the key issues in integrated circuits and also a typical electrostatic problem. The dual discrete geometric method (DGM) is investigated to provide relative solutions in two-dimensional unstructured mesh space. The energy complementary characteristic and quick field energy computation thereof based on it are emphasized. Contrastive analysis between the dual finite element methods and the dual DGMs are presented both from theoretical derivation and through case studies. The DGM, taking the scalar potential as unknown on dual interlocked meshes, with simple form and good accuracy, is expected to be one of the mainstreaming methods in associated areas. (paper)

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

Overview of Existing Wind Energy Ordinances

Energy Technology Data Exchange (ETDEWEB)

Oteri, F.

2008-12-01

Due to increased energy demand in the United States, rural communities with limited or no experience with wind energy now have the opportunity to become involved in this industry. Communities with good wind resources may be approached by entities with plans to develop the resource. Although these opportunities can create new revenue in the form of construction jobs and land lease payments, they also create a new responsibility on the part of local governments to ensure that ordinances will be established to aid the development of safe facilities that will be embraced by the community. The purpose of this report is to educate and engage state and local governments, as well as policymakers, about existing large wind energy ordinances. These groups will have a collection of examples to utilize when they attempt to draft a new large wind energy ordinance in a town or county without existing ordinances.

Spatial Representation of Ordinal Information

Directory of Open Access Journals (Sweden)

Meng eZhang

2016-04-01

Full Text Available Right hand responds faster than left hand when shown larger numbers and vice-versa when shown smaller numbers (the SNARC effect. Accumulating evidence suggests that the SNARC effect may not be exclusive for numbers and can be extended to other ordinal sequences (e.g., months or letters in the alphabet as well. In this study, we tested the SNARC effect with a non-numerically ordered sequence: The Chinese notations for the color spectrum (Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Chinese color word sequence reserves relatively weak ordinal information, because each element color in the sequence normally appears in non-sequential contexts, making it ideal to test the spatial organization of sequential information that was stored in the long-term memory. This study found a reliable SNARC-like effect for Chinese color words (deciding whether the presented color word was before or after the reference color word green, suggesting that, without access to any quantitative information or exposure to any previous training, ordinal representation can still activate a sense of space. The results support that weak ordinal information without quantitative magnitude encoded in the long-term memory can activate spatial representation in a comparison task.

Spatial Representation of Ordinal Information.

Science.gov (United States)

Zhang, Meng; Gao, Xuefei; Li, Baichen; Yu, Shuyuan; Gong, Tianwei; Jiang, Ting; Hu, Qingfen; Chen, Yinghe

2016-01-01

Right hand responds faster than left hand when shown larger numbers and vice-versa when shown smaller numbers (the SNARC effect). Accumulating evidence suggests that the SNARC effect may not be exclusive for numbers and can be extended to other ordinal sequences (e.g., months or letters in the alphabet) as well. In this study, we tested the SNARC effect with a non-numerically ordered sequence: the Chinese notations for the color spectrum (Red, Orange, Yellow, Green, Blue, Indigo, and Violet). Chinese color word sequence reserves relatively weak ordinal information, because each element color in the sequence normally appears in non-sequential contexts, making it ideal to test the spatial organization of sequential information that was stored in the long-term memory. This study found a reliable SNARC-like effect for Chinese color words (deciding whether the presented color word was before or after the reference color word "green"), suggesting that, without access to any quantitative information or exposure to any previous training, ordinal representation can still activate a sense of space. The results support that weak ordinal information without quantitative magnitude encoded in the long-term memory can activate spatial representation in a comparison task.

Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations

Science.gov (United States)

Loseille, A.; Dervieux, A.; Alauzet, F.

2010-04-01

This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions. Consequently, a full and strong coupling between both is hard to achieve due to this apparent incompatibility. This paper shows how to achieve this coupling in three steps. First, a new a priori error estimate is proved in a formal framework adapted to goal-oriented mesh adaptation for output functionals. This estimate is based on a careful analysis of the contributions of the implicit error and of the interpolation error. Second, the error estimate is applied to the set of steady compressible Euler equations which are solved by a stabilized Galerkin finite element discretization. A goal-oriented error estimation is derived. It involves the interpolation error of the Euler fluxes weighted by the gradient of the adjoint state associated with the observed functional. Third, rewritten in the continuous mesh framework, the previous estimate is minimized on the set of continuous meshes thanks to a calculus of variations. The optimal continuous mesh is then derived analytically. Thus, it can be used as a metric tensor field to drive the mesh adaptation. From a numerical point of view, this method is completely automatic, intrinsically anisotropic, and does not depend on any a priori choice of variables to perform the adaptation. 3D examples of steady flows around supersonic and transsonic jets are presented to validate the current approach and to demonstrate its efficiency.

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

Science.gov (United States)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

The Role of Chronic Mesh Infection in Delayed-Onset Vaginal Mesh Complications or Recurrent Urinary Tract Infections: Results From Explanted Mesh Cultures.

Science.gov (United States)

Mellano, Erin M; Nakamura, Leah Y; Choi, Judy M; Kang, Diana C; Grisales, Tamara; Raz, Shlomo; Rodriguez, Larissa V

2016-01-01

Vaginal mesh complications necessitating excision are increasingly prevalent. We aim to study whether subclinical chronically infected mesh contributes to the development of delayed-onset mesh complications or recurrent urinary tract infections (UTIs). Women undergoing mesh removal from August 2013 through May 2014 were identified by surgical code for vaginal mesh removal. Only women undergoing removal of anti-incontinence mesh were included. Exclusion criteria included any women undergoing simultaneous prolapse mesh removal. We abstracted preoperative and postoperative information from the medical record and compared mesh culture results from patients with and without mesh extrusion, de novo recurrent UTIs, and delayed-onset pain. One hundred seven women with only anti-incontinence mesh removed were included in the analysis. Onset of complications after mesh placement was within the first 6 months in 70 (65%) of 107 and delayed (≥6 months) in 37 (35%) of 107. A positive culture from the explanted mesh was obtained from 82 (77%) of 107 patients, and 40 (37%) of 107 were positive with potential pathogens. There were no significant differences in culture results when comparing patients with delayed-onset versus immediate pain, extrusion with no extrusion, and de novo recurrent UTIs with no infections. In this large cohort of patients with mesh removed for a diverse array of complications, cultures of the explanted vaginal mesh demonstrate frequent low-density bacterial colonization. We found no differences in culture results from women with delayed-onset pain versus acute pain, vaginal mesh extrusions versus no extrusions, or recurrent UTIs using standard culture methods. Chronic prosthetic infections in other areas of medicine are associated with bacterial biofilms, which are resistant to typical culture techniques. Further studies using culture-independent methods are needed to investigate the potential role of chronic bacterial infections in delayed vaginal mesh

A TN adaptive ray effect mitigation for Styx 3D

International Nuclear Information System (INIS)

Aussourd, Ch.

2003-01-01

Ray effect (RE) is a non-physical flaw of discrete ordinate methods characterized by spurious rays becoming sharper when small bright neutron sources radiate through low scattering media. While this effect has low impact on integral parameters (α and K eff ), it can ruin simulations of diagnostic problem in terms of neutron dose received by a detector. 3 cumulative factors may affect the RE intensity: the source size, the scattering cross-sections, and the mesh size. We introduce an adaptive Ray Effect Mitigation (REM) aimed at locally improving the angular accuracy of the 3 dimension AMR (adaptive mesh refinement) deterministic neutron transport code Styx. Promising preliminary results have been obtained using a recursively refined octahedron based sphere tessellation in place of the standard S N quadrature. This angular mesh, referred to as T N , has valuable features for local refinement

A T{sub N} adaptive ray effect mitigation for Styx 3D

Energy Technology Data Exchange (ETDEWEB)

Aussourd, Ch. [CEA Bruyeres-le-Chatel, 91 (France)

2003-07-01

Ray effect (RE) is a non-physical flaw of discrete ordinate methods characterized by spurious rays becoming sharper when small bright neutron sources radiate through low scattering media. While this effect has low impact on integral parameters ({alpha} and K{sub eff}), it can ruin simulations of diagnostic problem in terms of neutron dose received by a detector. 3 cumulative factors may affect the RE intensity: the source size, the scattering cross-sections, and the mesh size. We introduce an adaptive Ray Effect Mitigation (REM) aimed at locally improving the angular accuracy of the 3 dimension AMR (adaptive mesh refinement) deterministic neutron transport code Styx. Promising preliminary results have been obtained using a recursively refined octahedron based sphere tessellation in place of the standard S{sub N} quadrature. This angular mesh, referred to as T{sub N}, has valuable features for local refinement.

Cable Television Report and Suggested Ordinance.

Science.gov (United States)

League of California Cities, Sacramento.

Guidelines and suggested ordinances for cable television regulation by local governments are comprehensively discussed in this report. The emphasis is placed on franchising the cable operator. Seventeen legal aspects of franchising are reviewed, and an exemplary ordinance is presented. In addition, current statistics about cable franchising in…

Estimating Ordinal Reliability for Likert-Type and Ordinal Item Response Data: A Conceptual, Empirical, and Practical Guide

Science.gov (United States)

Gadermann, Anne M.; Guhn, Martin; Zumbo, Bruno D.

2012-01-01

This paper provides a conceptual, empirical, and practical guide for estimating ordinal reliability coefficients for ordinal item response data (also referred to as Likert, Likert-type, ordered categorical, or rating scale item responses). Conventionally, reliability coefficients, such as Cronbach's alpha, are calculated using a Pearson…

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.)

Semi-supervised learning for ordinal Kernel Discriminant Analysis.

Science.gov (United States)

Pérez-Ortiz, M; Gutiérrez, P A; Carbonero-Ruz, M; Hervás-Martínez, C

2016-12-01

Ordinal classification considers those classification problems where the labels of the variable to predict follow a given order. Naturally, labelled data is scarce or difficult to obtain in this type of problems because, in many cases, ordinal labels are given by a user or expert (e.g. in recommendation systems). Firstly, this paper develops a new strategy for ordinal classification where both labelled and unlabelled data are used in the model construction step (a scheme which is referred to as semi-supervised learning). More specifically, the ordinal version of kernel discriminant learning is extended for this setting considering the neighbourhood information of unlabelled data, which is proposed to be computed in the feature space induced by the kernel function. Secondly, a new method for semi-supervised kernel learning is devised in the context of ordinal classification, which is combined with our developed classification strategy to optimise the kernel parameters. The experiments conducted compare 6 different approaches for semi-supervised learning in the context of ordinal classification in a battery of 30 datasets, showing (1) the good synergy of the ordinal version of discriminant analysis and the use of unlabelled data and (2) the advantage of computing distances in the feature space induced by the kernel function. Copyright © 2016 Elsevier Ltd. All rights reserved.

Ordinance on nuclear third party liability (ORCN)

International Nuclear Information System (INIS)

1983-12-01

The Ordinance exempts from the application of the 1983 Act on Nuclear Third Party Liability some substances with low radiation effects. It determines the amount of private insurance cover and defines the risks that insurers may exclude from cover. It establishes a special fund for nuclear damage made up of contributions from the nuclear operators. Specifications are given on the amount of the contributions and their conditions, as well as on administration of the fund. The Ordinance repeals the Ordinance of 13 June 1960 on funds for delayed atomic damage, the Order of 19 December 1960 on contributions to the fund for delayed atomic damage and the Ordinance of 30 November 1981 on cover for third party liability resulting from nuclear power plant operation [fr

Urogynecologic Surgical Mesh Implants

Science.gov (United States)

... procedures performed to treat pelvic floor disorders with surgical mesh: Transvaginal mesh to treat POP Transabdominal mesh to treat ... address safety risks Final Order for Reclassification of Surgical Mesh for Transvaginal Pelvic Organ Prolapse Repair Final Order for Effective ...

Coarse mesh and one-cell block inversion based diffusion synthetic acceleration

Science.gov (United States)

Kim, Kang-Seog

DSA (Diffusion Synthetic Acceleration) has been developed to accelerate the SN transport iteration. We have developed solution techniques for the diffusion equations of FLBLD (Fully Lumped Bilinear Discontinuous), SCB (Simple Comer Balance) and UCB (Upstream Corner Balance) modified 4-step DSA in x-y geometry. Our first multi-level method includes a block Gauss-Seidel iteration for the discontinuous diffusion equation, uses the continuous diffusion equation derived from the asymptotic analysis, and avoids void cell calculation. We implemented this multi-level procedure and performed model problem calculations. The results showed that the FLBLD, SCB and UCB modified 4-step DSA schemes with this multi-level technique are unconditionally stable and rapidly convergent. We suggested a simplified multi-level technique for FLBLD, SCB and UCB modified 4-step DSA. This new procedure does not include iterations on the diffusion calculation or the residual calculation. Fourier analysis results showed that this new procedure was as rapidly convergent as conventional modified 4-step DSA. We developed new DSA procedures coupled with 1-CI (Cell Block Inversion) transport which can be easily parallelized. We showed that 1-CI based DSA schemes preceded by SI (Source Iteration) are efficient and rapidly convergent for LD (Linear Discontinuous) and LLD (Lumped Linear Discontinuous) in slab geometry and for BLD (Bilinear Discontinuous) and FLBLD in x-y geometry. For 1-CI based DSA without SI in slab geometry, the results showed that this procedure is very efficient and effective for all cases. We also showed that 1-CI based DSA in x-y geometry was not effective for thin mesh spacings, but is effective and rapidly convergent for intermediate and thick mesh spacings. We demonstrated that the diffusion equation discretized on a coarse mesh could be employed to accelerate the transport equation. Our results showed that coarse mesh DSA is unconditionally stable and is as rapidly convergent

Intravesical midurethral sling mesh erosion secondary to transvaginal mesh reconstructive surgery

Directory of Open Access Journals (Sweden)

Sukanda Bin Jaili

2015-05-01

Conclusion: Repeated vaginal reconstructive surgery may jeopardize a primary mesh or sling, and pose a high risk of mesh erosion, which may be delayed for several years. Removal of the mesh erosion and bladder repair are feasible pervaginally with good outcome.

Mesh versus non-mesh repair of ventral abdominal hernias

International Nuclear Information System (INIS)

Jawaid, M.A.; Talpur, A.H.

2008-01-01

To investigate the relative effectiveness of mesh and suture repair of ventral abdominal hernias in terms of clinical outcome, quality of life and rate of recurrence in both the techniques. This is a retrospective descriptive analysis of 236 patients with mesh and non-mesh repair of primary ventral hernias performed between January 2000 to December 2004 at Surgery Department, Liaquat University of Medical and Health Sciences, Jamshoro. The record sheets of the patients were analyzed and data retrieved to compare the results of both techniques for short-term and long-term results. The data retrieved is statistically analyzed on SPSS version 11. There were 43 (18.22%) males and 193 (81.77%) females with a mean age of 51.79 years and a range of 59 (81-22). Para-umbilical hernia was the commonest of ventral hernia and accounted for 49.8% (n=118) of the total study population followed by incisional hernia comprising 24% (n=57) of the total number. There was a significant difference in the recurrent rate at 3 years interval with 23/101 (22.77%) recurrences in suture-repaired subjects compared to 10/135 (7.40%) in mesh repair group. Chronic pain lasting up to 1-2 years was noted in 14 patients with suture repair. Wound infection is comparatively more common (8.14%) in mesh group. The other variables such as operative and postoperative complications, total hospital stay and quality of life is also discussed. Mesh repair of ventral hernia is much superior to non-mesh suture repair in terms of recurrence and overall outcome. (author)

An energy recondensation method using the discrete generalized multigroup energy expansion theory

International Nuclear Information System (INIS)

Zhu Lei; Forget, Benoit

2011-01-01

Highlights: → Discrete-generalized multigroup method was implemented as a recondensation scheme. → Coarse group cross-sections were recondensed from core-level solution. → Neighboring effect of reflector and MOX bundle was improved. → Methodology was shown to be fully consistent when a flat angular flux approximation is used. - Abstract: In this paper, the discrete generalized multigroup (DGM) method was used to recondense the coarse group cross-sections using the core level solution, thus providing a correction for neighboring effect found at the core level. This approach was tested using a discrete ordinates implementation in both 1-D and 2-D. Results indicate that 2 or 3 iterations can substantially improve the flux and fission density errors associated with strong interfacial spectral changes as found in the presence of strong absorbers, reflector of mixed-oxide fuel. The methodology is also proven to be fully consistent with the multigroup methodology as long as a flat-flux approximation is used spatially.

Production of neutronic discrete equations for a cylindrical geometry in one group energy and benchmark the results with MCNP-4B code with one group energy library

International Nuclear Information System (INIS)

Salehi, A. A.; Vosoughi, N.; Shahriari, M.

2002-01-01

In reactor core neutronic calculations, we usually choose a control volume and investigate about the input, output, production and absorption inside it. Finally, we derive neutron transport equation. This equation is not easy to solve for simple and symmetrical geometry. The objective of this paper is to introduce a new direct method for neutronic calculations. This method is based on physics of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equation series without production of neutron transport differential equation and mandatory passing form differential equation bridge. This method, which is named Direct Discrete Method, was applied in static state, for a cylindrical geometry in one group energy. The validity of the results from this new method are tested with MCNP-4B code with a one group energy library. One energy group direct discrete equation produces excellent results, which can be compared with the results of MCNP-4B

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

A general coarse and fine mesh solution scheme for fluid flow modeling in VHTRS

International Nuclear Information System (INIS)

Clifford, I; Ivanov, K; Avramova, M.

2011-01-01

Coarse mesh Computational Fluid Dynamics (CFD) methods offer several advantages over traditional coarse mesh methods for the safety analysis of helium-cooled graphite-moderated Very High Temperature Reactors (VHTRs). This relatively new approach opens up the possibility for system-wide calculations to be carried out using a consistent set of field equations throughout the calculation, and subsequently the possibility for hybrid coarse/fine mesh or hierarchical multi scale CFD simulations. To date, a consistent methodology for hierarchical multi-scale CFD has not been developed. This paper describes work carried out in the initial development of a multi scale CFD solver intended to be used for the safety analysis of VHTRs. The VHTR is considered on any scale to consist of a homogenized two-phase mixture of fluid and stationary solid material of varying void fraction. A consistent set of conservation equations was selected such that they reduce to the single-phase conservation equations for the case where void fraction is unity. The discretization of the conservation equations uses a new pressure interpolation scheme capable of capturing the discontinuity in pressure across relatively large changes in void fraction. Based on this, a test solver was developed which supports fully unstructured meshes for three-dimensional time-dependent compressible flow problems, including buoyancy effects. For typical VHTR flow phenomena the new solver shows promise as an effective candidate for predicting the flow behavior on multiple scales, as it is capable of modeling both fine mesh single phase flows as well as coarse mesh flows in homogenized regions containing both fluid and solid materials. (author)

Mesh removal following transvaginal mesh placement: a case series of 104 operations.

Science.gov (United States)

Marcus-Braun, Naama; von Theobald, Peter

2010-04-01

The objective of the study was to reveal the way we treat vaginal mesh complications in a trained referral center. This is a retrospective review of all patients who underwent surgical removal of transvaginal mesh for mesh-related complications during a 5-year period. Eighty-three patients underwent 104 operations including 61 complete mesh removal, 14 partial excision, 15 section of sub-urethral sling, and five laparoscopies. Main indications were erosion, infection, granuloma, incomplete voiding, and pain. Fifty-eight removals occurred more than 2 years after the primary mesh placement. Mean operation time was 21 min, and there were two intraoperative and ten minor postoperative complications. Stress urinary incontinence (SUI) recurred in 38% and cystocele in 19% of patients. In a trained center, mesh removal was found to be a quick and safe procedure. Mesh-related complications may frequently occur more than 2 years after the primary operation. Recurrence was mostly associated with SUI and less with genital prolapse.

Overstatement in happiness reporting with ordinal, bounded scale.

Science.gov (United States)

Tanaka, Saori C; Yamada, Katsunori; Kitada, Ryo; Tanaka, Satoshi; Sugawara, Sho K; Ohtake, Fumio; Sadato, Norihiro

2016-02-18

There are various methods by which people can express subjective evaluations quantitatively. For example, happiness can be measured on a scale from 1 to 10, and has been suggested as a measure of economic policy. However, there is resistance to these types of measurement from economists, who often regard welfare to be a cardinal, unbounded quantity. It is unclear whether there are differences between subjective evaluation reported on ordinal, bounded scales and on cardinal, unbounded scales. To answer this question, we developed functional magnetic resonance imaging experimental tasks for reporting happiness from monetary gain and the perception of visual stimulus. Subjects tended to report higher values when they used ordinal scales instead of cardinal scales. There were differences in neural activation between ordinal and cardinal reporting scales. The posterior parietal area showed greater activation when subjects used an ordinal scale instead of a cardinal scale. Importantly, the striatum exhibited greater activation when asked to report happiness on an ordinal scale than when asked to report on a cardinal scale. The finding that ordinal (bounded) scales are associated with higher reported happiness and greater activation in the reward system shows that overstatement bias in happiness data must be considered.

Analysis of an a posteriori error estimator for the transport equation with SN and discontinuous Galerkin discretizations

International Nuclear Information System (INIS)

Fournier, D.; Le Tellier, R.; Suteau, C.

2011-01-01

We present an error estimator for the S N neutron transport equation discretized with an arbitrary high-order discontinuous Galerkin method. As a starting point, the estimator is obtained for conforming Cartesian meshes with a uniform polynomial order for the trial space then adapted to deal with non-conforming meshes and a variable polynomial order. Some numerical tests illustrate the properties of the estimator and its limitations. Finally, a simple shielding benchmark is analyzed in order to show the relevance of the estimator in an adaptive process.

Numerical homogenization of concrete microstructures without explicit meshes

International Nuclear Information System (INIS)

Sanahuja, Julien; Toulemonde, Charles

2011-01-01

Life management of electric hydro or nuclear power plants requires to estimate long-term concrete properties on facilities, for obvious safety and serviceability reasons. Decades-old structures are foreseen to be operational for several more decades. As a large number of different concrete formulations are found in EDF facilities, empirical models based on many experiments cannot be an option for a large fleet of power plant buildings. To build predictive models, homogenization techniques offer an appealing alternative. To properly upscale creep, especially at long term, a rather precise description of the microstructure is required. However, the complexity of the morphology of concrete poses several challenges. In particular, concrete is formulated to maximize the packing density of the granular skeleton, leading to aggregates spanning several length scales with small inter particle spacings. Thus, explicit meshing of realistic concrete microstructures is either out of reach of current meshing algorithms or would produce a number of degrees of freedom far higher than the current generic FEM codes capabilities. This paper proposes a method to deal with complex matrix-inclusions microstructures such as the ones encountered at the mortar or concrete scales, without explicitly meshing them. The microstructure is superimposed to an independent mesh, which is a regular Cartesian grid. This inevitably yields so called 'gray elements', spanning across multiple phases. As the reliability of the estimate of the effective properties highly depends on the behavior affected to these gray elements, special attention is paid to them. As far as the question of the solvers is concerned, generic FEM codes are found to lack efficiency: they cannot reach high enough levels of discretization with classical free meshes, and they do not take advantage of the regular structure of the mesh. Thus, a specific finite differences/finite volumes solver has been developed. At first, generic off

Analysis of a HP-refinement method for solving the neutron transport equation using two error estimators

International Nuclear Information System (INIS)

Fournier, D.; Le Tellier, R.; Suteau, C.; Herbin, R.

2011-01-01

The solution of the time-independent neutron transport equation in a deterministic way invariably consists in the successive discretization of the three variables: energy, angle and space. In the SNATCH solver used in this study, the energy and the angle are respectively discretized with a multigroup approach and the discrete ordinate method. A set of spatial coupled transport equations is obtained and solved using the Discontinuous Galerkin Finite Element Method (DGFEM). Within this method, the spatial domain is decomposed into elements and the solution is approximated by a hierarchical polynomial basis in each one. This approach is time and memory consuming when the mesh becomes fine or the basis order high. To improve the computational time and the memory footprint, adaptive algorithms are proposed. These algorithms are based on an error estimation in each cell. If the error is important in a given region, the mesh has to be refined (h−refinement) or the polynomial basis order increased (p−refinement). This paper is related to the choice between the two types of refinement. Two ways to estimate the error are compared on different benchmarks. Analyzing the differences, a hp−refinement method is proposed and tested. (author)

Polygonal Prism Mesh in the Viscous Layers for the Polyhedral Mesh Generator, PolyGen

International Nuclear Information System (INIS)

Lee, Sang Yong; Park, Chan Eok; Kim, Shin Whan

2015-01-01

Polyhedral mesh has been known to have some benefits over the tetrahedral mesh. Efforts have been made to set up a polyhedral mesh generation system with open source programs SALOME and TetGen. The evaluation has shown that the polyhedral mesh generation system is promising. But it is necessary to extend the capability of the system to handle the viscous layers to be a generalized mesh generator. A brief review to the previous works on the mesh generation for the viscous layers will be made in section 2. Several challenging issues for the polygonal prism mesh generation will be discussed as well. The procedure to generate a polygonal prism mesh will be discussed in detail in section 3. Conclusion will be followed in section 4. A procedure to generate meshes in the viscous layers with PolyGen has been successfully designed. But more efforts have to be exercised to find the best way for the generating meshes for viscous layers. Using the extrusion direction of the STL data will the first of the trials in the near future

Amendment of Atomic Ordinance

International Nuclear Information System (INIS)

1987-10-01

This amendment to the 1984 Ordinance on definitions and licences in the atomic energy field aims essentially to ensure that the commitments under the Treaty on the Non-Proliferation of Nuclear Weapons are complied with in Switzerland. The goods and articles involving uranium enrichment by the gas centrifuge process and nuclear fuel reprocessing as specified by the competent international bodies, are henceforth included in the goods subject to notification or licensing listed in the Annex to the Ordinance. Also, it is provided that a construction and an operating licence for a nuclear installation may be granted simultaneously in cases where safe operating conditions can be fully assessed. (NEA) [fr

The Monte Carlo photoionization and moving-mesh radiation hydrodynamics code CMACIONIZE

Science.gov (United States)

Vandenbroucke, B.; Wood, K.

2018-04-01

We present the public Monte Carlo photoionization and moving-mesh radiation hydrodynamics code CMACIONIZE, which can be used to simulate the self-consistent evolution of HII regions surrounding young O and B stars, or other sources of ionizing radiation. The code combines a Monte Carlo photoionization algorithm that uses a complex mix of hydrogen, helium and several coolants in order to self-consistently solve for the ionization and temperature balance at any given type, with a standard first order hydrodynamics scheme. The code can be run as a post-processing tool to get the line emission from an existing simulation snapshot, but can also be used to run full radiation hydrodynamical simulations. Both the radiation transfer and the hydrodynamics are implemented in a general way that is independent of the grid structure that is used to discretize the system, allowing it to be run both as a standard fixed grid code, but also as a moving-mesh code.

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

Science.gov (United States)

Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

2017-05-01

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

Nyx: Adaptive mesh, massively-parallel, cosmological simulation code

Science.gov (United States)

Almgren, Ann; Beckner, Vince; Friesen, Brian; Lukic, Zarija; Zhang, Weiqun

2017-12-01

Nyx code solves equations of compressible hydrodynamics on an adaptive grid hierarchy coupled with an N-body treatment of dark matter. The gas dynamics in Nyx use a finite volume methodology on an adaptive set of 3-D Eulerian grids; dark matter is represented as discrete particles moving under the influence of gravity. Particles are evolved via a particle-mesh method, using Cloud-in-Cell deposition/interpolation scheme. Both baryonic and dark matter contribute to the gravitational field. In addition, Nyx includes physics for accurately modeling the intergalactic medium; in optically thin limits and assuming ionization equilibrium, the code calculates heating and cooling processes of the primordial-composition gas in an ionizing ultraviolet background radiation field.

A hierarchical model for ordinal matrix factorization

DEFF Research Database (Denmark)

Paquet, Ulrich; Thomson, Blaise; Winther, Ole

2012-01-01

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based...

Toward An Unstructured Mesh Database

Science.gov (United States)

Rezaei Mahdiraji, Alireza; Baumann, Peter Peter

2014-05-01

Unstructured meshes are used in several application domains such as earth sciences (e.g., seismology), medicine, oceanography, cli- mate modeling, GIS as approximate representations of physical objects. Meshes subdivide a domain into smaller geometric elements (called cells) which are glued together by incidence relationships. The subdivision of a domain allows computational manipulation of complicated physical structures. For instance, seismologists model earthquakes using elastic wave propagation solvers on hexahedral meshes. The hexahedral con- tains several hundred millions of grid points and millions of hexahedral cells. Each vertex node in the hexahedrals stores a multitude of data fields. To run simulation on such meshes, one needs to iterate over all the cells, iterate over incident cells to a given cell, retrieve coordinates of cells, assign data values to cells, etc. Although meshes are used in many application domains, to the best of our knowledge there is no database vendor that support unstructured mesh features. Currently, the main tool for querying and manipulating unstructured meshes are mesh libraries, e.g., CGAL and GRAL. Mesh li- braries are dedicated libraries which includes mesh algorithms and can be run on mesh representations. The libraries do not scale with dataset size, do not have declarative query language, and need deep C++ knowledge for query implementations. Furthermore, due to high coupling between the implementations and input file structure, the implementations are less reusable and costly to maintain. A dedicated mesh database offers the following advantages: 1) declarative querying, 2) ease of maintenance, 3) hiding mesh storage structure from applications, and 4) transparent query optimization. To design a mesh database, the first challenge is to define a suitable generic data model for unstructured meshes. We proposed ImG-Complexes data model as a generic topological mesh data model which extends incidence graph model to multi

Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers

Science.gov (United States)

Sozer, Emre; Brehm, Christoph; Kiris, Cetin C.

2014-01-01

A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties

Mesh optimization for microbial fuel cell cathodes constructed around stainless steel mesh current collectors

KAUST Repository

Zhang, Fang

2011-02-01

Mesh current collectors made of stainless steel (SS) can be integrated into microbial fuel cell (MFC) cathodes constructed of a reactive carbon black and Pt catalyst mixture and a poly(dimethylsiloxane) (PDMS) diffusion layer. It is shown here that the mesh properties of these cathodes can significantly affect performance. Cathodes made from the coarsest mesh (30-mesh) achieved the highest maximum power of 1616 ± 25 mW m-2 (normalized to cathode projected surface area; 47.1 ± 0.7 W m-3 based on liquid volume), while the finest mesh (120-mesh) had the lowest power density (599 ± 57 mW m-2). Electrochemical impedance spectroscopy showed that charge transfer and diffusion resistances decreased with increasing mesh opening size. In MFC tests, the cathode performance was primarily limited by reaction kinetics, and not mass transfer. Oxygen permeability increased with mesh opening size, accounting for the decreased diffusion resistance. At higher current densities, diffusion became a limiting factor, especially for fine mesh with low oxygen transfer coefficients. These results demonstrate the critical nature of the mesh size used for constructing MFC cathodes. © 2010 Elsevier B.V. All rights reserved.

Block-structured Adaptive Mesh Refinement - Theory, Implementation and Application

Directory of Open Access Journals (Sweden)

Deiterding Ralf

2011-12-01

Full Text Available Structured adaptive mesh refinement (SAMR techniques can enable cutting-edge simulations of problems governed by conservation laws. Focusing on the strictly hyperbolic case, these notes explain all algorithmic and mathematical details of a technically relevant implementation tailored for distributed memory computers. An overview of the background of commonly used finite volume discretizations for gas dynamics is included and typical benchmarks to quantify accuracy and performance of the dynamically adaptive code are discussed. Large-scale simulations of shock-induced realistic combustion in non-Cartesian geometry and shock-driven fluid-structure interaction with fully coupled dynamic boundary motion demonstrate the applicability of the discussed techniques for complex scenarios.

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

Science.gov (United States)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Why Overlearned Sequences are Special: Distinct Neural Networks for Ordinal Sequences

Directory of Open Access Journals (Sweden)

Vani ePariyadath

2012-12-01

Full Text Available Several observations suggest that overlearned ordinal categories (e.g., letters, numbers, weekdays, months are processed differently than non-ordinal categories in the brain. In synesthesia, for example, anomalous perceptual experiences are most often triggered by members of ordinal categories (Rich et al., 2005; Eagleman, 2009. In semantic dementia, the processing of ordinal stimuli appears to be preserved relative to non-ordinal ones (Cappelletti et al., 2001. Moreover, ordinal stimuli often map onto unconscious spatial representations, as observed in the SNARC effect (Dehaene et al, 1993; Fias, 1996. At present, little is known about the neural representation of ordinal categories. Using functional neuroimaging, we show that words in ordinal categories are processed in a fronto-temporo-parietal network biased toward the right hemisphere. This differs from words in non-ordinal categories (such as names of furniture, animals, cars and fruit, which show an expected bias toward the left hemisphere. Further, we find that increased predictability of stimulus order correlates with smaller regions of BOLD activation, a phenomenon we term prediction suppression. Our results provide new insights into the processing of ordinal stimuli, and suggest a new anatomical framework for understanding the patterns seen in synesthesia, unconscious spatial representation, and semantic dementia.

Ordinance of 8 February 1984 on the radioactivity of timepieces

International Nuclear Information System (INIS)

1984-01-01

This Ordinance regulates the approval of radioluminescent timepieces (wristwatches, fob-watches, alarm-clocks, clocks, etc.) imported or made in Switzerland. Such timepieces must comply with conditions in particular regarding their maximum radioactivity as laid down by the Ordinance and are subject to controls by the Federal Office of Public Health. The Ordinance, which came into force on 1 March 1984, replaces a similar Ordinance of 18 April 1968. (NEA) [fr

MeSH Now: automatic MeSH indexing at PubMed scale via learning to rank.

Science.gov (United States)

Mao, Yuqing; Lu, Zhiyong

2017-04-17

MeSH indexing is the task of assigning relevant MeSH terms based on a manual reading of scholarly publications by human indexers. The task is highly important for improving literature retrieval and many other scientific investigations in biomedical research. Unfortunately, given its manual nature, the process of MeSH indexing is both time-consuming (new articles are not immediately indexed until 2 or 3 months later) and costly (approximately ten dollars per article). In response, automatic indexing by computers has been previously proposed and attempted but remains challenging. In order to advance the state of the art in automatic MeSH indexing, a community-wide shared task called BioASQ was recently organized. We propose MeSH Now, an integrated approach that first uses multiple strategies to generate a combined list of candidate MeSH terms for a target article. Through a novel learning-to-rank framework, MeSH Now then ranks the list of candidate terms based on their relevance to the target article. Finally, MeSH Now selects the highest-ranked MeSH terms via a post-processing module. We assessed MeSH Now on two separate benchmarking datasets using traditional precision, recall and F 1 -score metrics. In both evaluations, MeSH Now consistently achieved over 0.60 in F-score, ranging from 0.610 to 0.612. Furthermore, additional experiments show that MeSH Now can be optimized by parallel computing in order to process MEDLINE documents on a large scale. We conclude that MeSH Now is a robust approach with state-of-the-art performance for automatic MeSH indexing and that MeSH Now is capable of processing PubMed scale documents within a reasonable time frame. http://www.ncbi.nlm.nih.gov/CBBresearch/Lu/Demo/MeSHNow/ .

A numerical method for the quasi-incompressible Cahn–Hilliard–Navier–Stokes equations for variable density flows with a discrete energy law

International Nuclear Information System (INIS)

Guo, Z.; Lin, P.; Lowengrub, J.S.

2014-01-01

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C 0 finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy law (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C 0 finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme

Comparison of two ordinal prediction models

DEFF Research Database (Denmark)

Kattan, Michael W; Gerds, Thomas A

2015-01-01

system (i.e. old or new), such as the level of evidence for one or more factors included in the system or the general opinions of expert clinicians. However, given the major objective of estimating prognosis on an ordinal scale, we argue that the rival staging system candidates should be compared...... on their ability to predict outcome. We sought to outline an algorithm that would compare two rival ordinal systems on their predictive ability. RESULTS: We devised an algorithm based largely on the concordance index, which is appropriate for comparing two models in their ability to rank observations. We...... demonstrate our algorithm with a prostate cancer staging system example. CONCLUSION: We have provided an algorithm for selecting the preferred staging system based on prognostic accuracy. It appears to be useful for the purpose of selecting between two ordinal prediction models....

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

Time-Discrete Higher-Order ALE Formulations: Stability

KAUST Repository

Bonito, Andrea

2013-01-01

Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Laparoscopic appendicectomy for suspected mesh-induced appendicitis after laparoscopic transabdominal preperitoneal polypropylene mesh inguinal herniorraphy

Directory of Open Access Journals (Sweden)

Jennings Jason

2010-01-01

Full Text Available Laparoscopic inguinal herniorraphy via a transabdominal preperitoneal (TAPP approach using Polypropylene Mesh (Mesh and staples is an accepted technique. Mesh induces a localised inflammatory response that may extend to, and involve, adjacent abdominal and pelvic viscera such as the appendix. We present an interesting case of suspected Mesh-induced appendicitis treated successfully with laparoscopic appendicectomy, without Mesh removal, in an elderly gentleman who presented with symptoms and signs of acute appendicitis 18 months after laparoscopic inguinal hernia repair. Possible mechanisms for Mesh-induced appendicitis are briefly discussed.

Radiation Protection Ordinance 1989. Supplement with Radiation Protection Register Ordinance, general administration regulation pursuant to Sect. 45 Radiation Protection Ordinance, general administration regulation pursuant to Sect. 62 sub-sect. radiation passport

International Nuclear Information System (INIS)

Veith, H.M.

1990-01-01

The addendum contains regulations issued supplementary to the Radiation Protection Ordinance: The Radiation Protection Register as of April 3, 1990 including the law on the setting up of a Federal Office on Radiation Protection; the general administration regulation pursuant to Sect. 45 Radiation Protection Ordinance as of February 21, 1990; the general administration regulation pursuant to Sect. 62 sub-sect. 2 Radiation Protection Ordinance as of May 3, 1990 (AVV Radiation passport). The volume contains, apart from the legal texts, the appropriate decision by the Bundesrat, the official explanation from the Bundestag Publications as well as a comprehensive introduction into the new legal matter. (orig.) [de

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

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

Boundary treatment for fourth-order staggered mesh discretizations of the incompressible Navier-Stokes equations

NARCIS (Netherlands)

Sanderse, B.; Verstappen, R.W.C.P.; Koren, B.

2014-01-01

A discretization method for the incompressible Navier–Stokes equations conserving the secondary quantities kinetic energy and vorticity was introduced, besides the primary quantities mass and momentum. This method was extended to fourth order accuracy. In this paper we propose a new consistent

Optimal mesh hierarchies in Multilevel Monte Carlo methods

KAUST Repository

Von Schwerin, Erik

2016-01-01

I will discuss how to choose optimal mesh hierarchies in Multilevel Monte Carlo (MLMC) simulations when computing the expected value of a quantity of interest depending on the solution of, for example, an Ito stochastic differential equation or a partial differential equation with stochastic data. I will consider numerical schemes based on uniform discretization methods with general approximation orders and computational costs. I will compare optimized geometric and non-geometric hierarchies and discuss how enforcing some domain constraints on parameters of MLMC hierarchies affects the optimality of these hierarchies. I will also discuss the optimal tolerance splitting between the bias and the statistical error contributions and its asymptotic behavior. This talk presents joint work with N.Collier, A.-L.Haji-Ali, F. Nobile, and R. Tempone.

Optimal mesh hierarchies in Multilevel Monte Carlo methods

KAUST Repository

Von Schwerin, Erik

2016-01-08

I will discuss how to choose optimal mesh hierarchies in Multilevel Monte Carlo (MLMC) simulations when computing the expected value of a quantity of interest depending on the solution of, for example, an Ito stochastic differential equation or a partial differential equation with stochastic data. I will consider numerical schemes based on uniform discretization methods with general approximation orders and computational costs. I will compare optimized geometric and non-geometric hierarchies and discuss how enforcing some domain constraints on parameters of MLMC hierarchies affects the optimality of these hierarchies. I will also discuss the optimal tolerance splitting between the bias and the statistical error contributions and its asymptotic behavior. This talk presents joint work with N.Collier, A.-L.Haji-Ali, F. Nobile, and R. Tempone.

Persistent pelvic pain following transvaginal mesh surgery: a cause for mesh removal.

Science.gov (United States)

Marcus-Braun, Naama; Bourret, Antoine; von Theobald, Peter

2012-06-01

Persistent pelvic pain after vaginal mesh surgery is an uncommon but serious complication that greatly affects women's quality of life. Our aim was to evaluate various procedures for mesh removal performed at a tertiary referral center in cases of persistent pelvic pain, and to evaluate the ensuing complications and outcomes. A retrospective study was conducted at the University Hospital of Caen, France, including all patients treated for removal or section of vaginal mesh due to pelvic pain as a primary cause, between January 2004 and September 2009. Ten patients met the inclusion criteria. Patients were diagnosed between 10 months and 3 years after their primary operation. Eight cases followed suburethral sling procedures and two followed mesh surgery for pelvic organ prolapse. Patients presented with obturator neuralgia (6), pudendal neuralgia (2), dyspareunia (1), and non-specific pain (1). The surgical treatment to release the mesh included: three cases of extra-peritoneal laparoscopy, four cases of complete vaginal mesh removal, one case of partial mesh removal and two cases of section of the suburethral sling. In all patients with obturator neuralgia, symptoms were resolved or improved, whereas in both cases of pudendal neuralgia the symptoms continued. There were no intra-operative complications. Post-operative Retzius hematoma was observed in one patient after laparoscopy. Mesh removal in a tertiary center is a safe procedure, necessary in some cases of persistent pelvic pain. Obturator neuralgia seems to be easier to treat than pudendal neuralgia. Early diagnosis is the key to success in prevention of chronic disease. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Modeling of radiant heat transfers in non-grey gases using the discrete ordinate method in association with a narrow bands statistical model; Modelisation des transferts radiatifs dans des gaz non gris par la methode des ordonnees discretes associee a un modele statistique a bandes etroites

Energy Technology Data Exchange (ETDEWEB)

Miranda, A.B. de; Delmas, A; Sacadura, J F [Institut National des Sciences Appliquees (INSA), 69 - Villeurbanne (France)

1997-12-31

A formulation based on the use of the discrete ordinate method applied to the integral form of the radiant heat transfer equation is proposed for non-grey gases. The correlations between transmittances are neglected and no explicit wall reflexion is considered. The configuration analyzed consists in a flat layer of non-isothermal steam-nitrogen mixture. Cavity walls are grey with diffuse reflexion and emission. A narrow band statistical model is used to represent the radiative properties of the gas. The distribution of the radiative source term inside the cavity is calculated along two temperature profiles in a uniform steam concentration. Results obtained using this simplified approach are in good agreement with those found in the literature for the same temperature and concentration distributions. This preliminary study seems to indicate that the algorithm based on the integration of radiant heat transfer along the luminance path is less sensitive to de-correlation effects than formulations based on the differential form the the radiant heat transfer. Thus, a more systematic study of the influence of the neglecting of correlations on the integral approach is analyzed in this work. (J.S.) 16 refs.

Modeling of radiant heat transfers in non-grey gases using the discrete ordinate method in association with a narrow bands statistical model; Modelisation des transferts radiatifs dans des gaz non gris par la methode des ordonnees discretes associee a un modele statistique a bandes etroites

Energy Technology Data Exchange (ETDEWEB)

Miranda, A.B. de; Delmas, A.; Sacadura, J.F. [Institut National des Sciences Appliquees (INSA), 69 - Villeurbanne (France)

1996-12-31

A formulation based on the use of the discrete ordinate method applied to the integral form of the radiant heat transfer equation is proposed for non-grey gases. The correlations between transmittances are neglected and no explicit wall reflexion is considered. The configuration analyzed consists in a flat layer of non-isothermal steam-nitrogen mixture. Cavity walls are grey with diffuse reflexion and emission. A narrow band statistical model is used to represent the radiative properties of the gas. The distribution of the radiative source term inside the cavity is calculated along two temperature profiles in a uniform steam concentration. Results obtained using this simplified approach are in good agreement with those found in the literature for the same temperature and concentration distributions. This preliminary study seems to indicate that the algorithm based on the integration of radiant heat transfer along the luminance path is less sensitive to de-correlation effects than formulations based on the differential form the the radiant heat transfer. Thus, a more systematic study of the influence of the neglecting of correlations on the integral approach is analyzed in this work. (J.S.) 16 refs.

Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

Science.gov (United States)

Boscheri, Walter; Dumbser, Michael

2017-10-01

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total

Knowledge of the ordinal position of list items in pigeons.

Science.gov (United States)

Scarf, Damian; Colombo, Michael

2011-10-01

Ordinal knowledge is a fundamental aspect of advanced cognition. It is self-evident that humans represent ordinal knowledge, and over the past 20 years it has become clear that nonhuman primates share this ability. In contrast, evidence that nonprimate species represent ordinal knowledge is missing from the comparative literature. To address this issue, in the present experiment we trained pigeons on three 4-item lists and then tested them with derived lists in which, relative to the training lists, the ordinal position of the items was either maintained or changed. Similar to the findings with human and nonhuman primates, our pigeons performed markedly better on the maintained lists compared to the changed lists, and displayed errors consistent with the view that they used their knowledge of ordinal position to guide responding on the derived lists. These findings demonstrate that the ability to acquire ordinal knowledge is not unique to the primate lineage. (PsycINFO Database Record (c) 2011 APA, all rights reserved).

Open Method of Co-Ordination for Demoi-Cracy?

DEFF Research Database (Denmark)

Borrás, Susana; Radaelli, Claudio

2014-01-01

Under which conditions does the open method of co-ordination match the standards for demoi-cracy? To answer this question, we need some explicit standards about demoi-cracy. In fact, open co-ordination serves three different but interrelated purposes in European Union policy: to facilitate...... convergence; to support learning processes; and to encourage exploration of policy innovation. By intersecting standards and purposes, we find open co-ordination is neither inherently ‘good’ nor ‘bad’ for demoi-cracy, as it depends on how it has been put into practice. Therefore, we qualify the answer...

Numerical electromagnetic frequency domain analysis with discrete exterior calculus

Science.gov (United States)

Chen, Shu C.; Chew, Weng Cho

2017-12-01

In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations in terms of DEC for 3-D and 2-D inhomogeneous structures, and also show that the charge continuity relation is naturally satisfied. Then we introduce a general construction for signed dual volume to incorporate material information and take into account the case when circumcenters fall outside triangles or tetrahedrons, which may lead to negative dual volume without Delaunay triangulation. Then we examine the boundary terms induced by the dual mesh and provide a systematical treatment of various boundary conditions, including perfect magnetic conductor (PMC), perfect electric conductor (PEC), Dirichlet, periodic, and absorbing boundary conditions (ABC) within this method. An excellent agreement is achieved through the numerical calculation of several problems, including homogeneous waveguides, microstructured fibers, photonic crystals, scattering by a 2-D PEC, and resonant cavities.

3-D extension C5G7 MOX benchmark results using PARTISN

Energy Technology Data Exchange (ETDEWEB)

Dahl, J.A. [Los Alamos National Laboratory, CCS-4 Transport Methods Group, Los Alamos, NM (United States)

2005-07-01

We have participated in the Expert Group of 3-D Radiation Transport Benchmarks' proposed 3-dimensional Extension C5G7 MOX problems using the discrete ordinate transport code PARTISN. The computational mesh was created using the FRAC-IN-THE-BOX code, which produces a volume fraction Cartesian mesh from combinatorial geometry descriptions. k{sub eff} eigenvalues, maximum pin powers, and average fuel assembly powers are reported and compared to a benchmark quality Monte Carlo solution. We also present a two dimensional mesh convergence study examining the affects of using volume fractions to approximate the water-pin cell interface. It appears that the control rod pin cell must be meshed twice as fine as a fuel pin cell in order to achieve the same spatial error when using the volume fraction method to define water channel-pin cell interfaces. It is noted that the previous PARTISN results provided to the OECD/NEA Expert Group on 3-dimensional Radiation Benchmarks contained a cross section error, and therefore should be disregarded.

3-D extension C5G7 MOX benchmark results using PARTISN

International Nuclear Information System (INIS)

Dahl, J.A.

2005-01-01

We have participated in the Expert Group of 3-D Radiation Transport Benchmarks' proposed 3-dimensional Extension C5G7 MOX problems using the discrete ordinate transport code PARTISN. The computational mesh was created using the FRAC-IN-THE-BOX code, which produces a volume fraction Cartesian mesh from combinatorial geometry descriptions. k eff eigenvalues, maximum pin powers, and average fuel assembly powers are reported and compared to a benchmark quality Monte Carlo solution. We also present a two dimensional mesh convergence study examining the affects of using volume fractions to approximate the water-pin cell interface. It appears that the control rod pin cell must be meshed twice as fine as a fuel pin cell in order to achieve the same spatial error when using the volume fraction method to define water channel-pin cell interfaces. It is noted that the previous PARTISN results provided to the OECD/NEA Expert Group on 3-dimensional Radiation Benchmarks contained a cross section error, and therefore should be disregarded

Early experience with mesh excision for adverse outcomes after transvaginal mesh placement using prolapse kits.

Science.gov (United States)

Ridgeway, Beri; Walters, Mark D; Paraiso, Marie Fidela R; Barber, Matthew D; McAchran, Sarah E; Goldman, Howard B; Jelovsek, J Eric

2008-12-01

The purpose of this study was to determine the complications, treatments, and outcomes in patients choosing to undergo removal of mesh previously placed with a mesh procedural kit. This was a retrospective review of all patients who underwent surgical removal of transvaginal mesh for mesh-related complications during a 3-year period at Cleveland Clinic. At last follow-up, patients reported degree of pain, level of improvement, sexual activity, and continued symptoms. Nineteen patients underwent removal of mesh during the study period. Indications for removal included chronic pain (6/19), dyspareunia (6/19), recurrent pelvic organ prolapse (8/19), mesh erosion (12/19), and vesicovaginal fistula (3/19), with most patients (16/19) citing more than 1 reason. There were few complications related to the mesh removal. Most patients reported significant relief of symptoms. Mesh removal can be technically difficult but appears to be safe with few complications and high relief of symptoms, although some symptoms can persist.

Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm

Science.gov (United States)

Küchlin, Stephan; Jenny, Patrick

2018-06-01

Recently, a parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors. Fokker-Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker-Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code.

Mesh erosion after abdominal sacrocolpopexy.

Science.gov (United States)

Kohli, N; Walsh, P M; Roat, T W; Karram, M M

1998-12-01

To report our experience with erosion of permanent suture or mesh material after abdominal sacrocolpopexy. A retrospective chart review was performed to identify patients who underwent sacrocolpopexy by the same surgeon over 8 years. Demographic data, operative notes, hospital records, and office charts were reviewed after sacrocolpopexy. Patients with erosion of either suture or mesh were treated initially with conservative therapy followed by surgical intervention as required. Fifty-seven patients underwent sacrocolpopexy using synthetic mesh during the study period. The mean (range) postoperative follow-up was 19.9 (1.3-50) months. Seven patients (12%) had erosions after abdominal sacrocolpopexy with two suture erosions and five mesh erosions. Patients with suture erosion were asymptomatic compared with patients with mesh erosion, who presented with vaginal bleeding or discharge. The mean (+/-standard deviation) time to erosion was 14.0+/-7.7 (range 4-24) months. Both patients with suture erosion were treated conservatively with estrogen cream. All five patients with mesh erosion required transvaginal removal of the mesh. Mesh erosion can follow abdominal sacrocolpopexy over a long time, and usually presents as vaginal bleeding or discharge. Although patients with suture erosion can be managed successfully with conservative treatment, patients with mesh erosion require surgical intervention. Transvaginal removal of the mesh with vaginal advancement appears to be an effective treatment in patients failing conservative management.

Ordinance on measures for preparation of a radioactive waste repository (Ordinance on preparatory measures) of 24 October 1979

International Nuclear Information System (INIS)

1981-01-01

This Ordinance contains details concerning the special procedure provided for under Section 10(2) of the Federal Order of 6th October 1978 concerning the Atomic Energy Act whereby the Federal Council must grant permission before preparations for the construction of radioactive waste repositories may be undertaken. The Ordinance defines the preparatory measures, which include maps and plans of the area, a geological report, etc. (NEA) [fr

Surgical management of lower urinary mesh perforation after mid-urethral polypropylene mesh sling: mesh excision, urinary tract reconstruction and concomitant pubovaginal sling with autologous rectus fascia.

Science.gov (United States)

Shah, Ketul; Nikolavsky, Dmitriy; Gilsdorf, Daniel; Flynn, Brian J

2013-12-01

We present our management of lower urinary tract (LUT) mesh perforation after mid-urethral polypropylene mesh sling using a novel combination of surgical techniques including total or near total mesh excision, urinary tract reconstruction, and concomitant pubovaginal sling with autologous rectus fascia in a single operation. We retrospectively reviewed the medical records of 189 patients undergoing transvaginal removal of polypropylene mesh from the lower urinary tract or vagina. The focus of this study is 21 patients with LUT mesh perforation after mid-urethral polypropylene mesh sling. We excluded patients with LUT mesh perforation from prolapse kits (n = 4) or sutures (n = 11), or mesh that was removed because of isolated vaginal wall exposure without concomitant LUT perforation (n = 164). Twenty-one patients underwent surgical removal of mesh through a transvaginal approach or combined transvaginal/abdominal approaches. The location of the perforation was the urethra in 14 and the bladder in 7. The mean follow-up was 22 months. There were no major intraoperative complications. All patients had complete resolution of the mesh complication and the primary symptom. Of the patients with urethral perforation, continence was achieved in 10 out of 14 (71.5 %). Of the patients with bladder perforation, continence was achieved in all 7. Total or near total removal of lower urinary tract (LUT) mesh perforation after mid-urethral polypropylene mesh sling can completely resolve LUT mesh perforation in a single operation. A concomitant pubovaginal sling can be safely performed in efforts to treat existing SUI or avoid future surgery for SUI.

Lanthanide co-ordination frameworks: Opportunities and diversity

International Nuclear Information System (INIS)

Hill, Robert J.; Long, De-Liang; Hubberstey, Peter; Schroeder, Martin; Champness, Neil R.

2005-01-01

Significant successes have been made over recent years in preparing co-ordination framework polymers that show macroscopic material properties, but in the vast majority of cases this has been achieved with d-block metal-based systems. Lanthanide co-ordination frameworks also offer attractive properties in terms of their potential applications as luminescent, non-linear optical and porous materials. However, lanthanide-based systems have been far less studied to date than their d-block counterparts. One possible reason for this is that the co-ordination spheres of lanthanide cations are more difficult to control and, in the absence of design strategies for lanthanide co-ordination frameworks, it is significantly more difficult to target materials with specific properties. However, this article highlights some of the exciting possibilities that have emerged from the earliest investigations in this field with new topological families of compounds being discovered from relatively simple framework components, including unusual eight, seven and five-connected framework systems. Our own research, as well as others, is leading to a much greater appreciation of the factors that control framework formation and the resultant observed topologies of these polymers. As this understanding develops targeting particular framework types will become more straightforward and the development of designed polyfunctional materials more accessible. Thus, it can be seen that lanthanide co-ordination frameworks have the potential to open up previously unexplored directions for materials chemistry. This article focuses on the underlying concepts for the construction of these enticing and potentially highly important materials

The new X-ray ordinance: what's new?

International Nuclear Information System (INIS)

Reichow, H.

2000-01-01

The augmented requirements for the minimisation of the radiation dose in medical exposure and the experiences gained from the implementation of the ordinance in force call for more extensive measures for reducing radiation, for quality assurance and expertise in radiological protection. In future physicians, dentists, veterinarians and other people using X-rays will have to bring their necessary expert knowledge regarding radiological protection up to date at regular intervals, and prove that they have done so. To protect the public against radiation exposure from targeted use, the limit value of the effective dose is reduced to 1 mSv in the calendar year. The dose level for the protection of people professionally exposed to radiation is reduced to 20 mSv. The further development of information technology and digital imaging demands that appropriate framework conditions be laid down in response to the changing requirements for radiation protection such as those in telemedicine and in digital recording and documentation possibilities in radiology. The draft further clarifies the distinction between the Radiological Protection Ordinance and the X-Ray Ordinance in relation to accelerators, in which electrons are accelerated with the aim of producing ionizing radiation, and reduces the limit energy from 3 MeV to 1 MeV. It is discussed to remove the X-ray therapy from the X-ray Ordinance and to insert it into the Radiological Protection Ordinance, in order to conform to the higher protection requirements in X-ray therapy. (orig.) [de

Numerical instability of time-discretized one-point kinetic equations

International Nuclear Information System (INIS)

Hashimoto, Kengo; Ikeda, Hideaki; Takeda, Toshikazu

2000-01-01

The one-point kinetic equations with numerical errors induced by the explicit, implicit and Crank-Nicolson integration methods are derived. The zero-power transfer functions based on the present equations are demonstrated to investigate the numerical stability of the discretized systems. These demonstrations indicate unconditional stability for the implicit and Crank-Nicolson methods but present the possibility of numerical instability for the explicit method. An upper limit of time mesh spacing for the stability is formulated and several numerical calculations are made to confirm the validity of this formula

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

Energy Technology Data Exchange (ETDEWEB)

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan); Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610 (Belgium); Chen, W. [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan)

2016-08-07

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.

Preparing the generalized Harvey–Shack rough surface scattering method for use with the discrete ordinates method

DEFF Research Database (Denmark)

Johansen, Villads Egede

2015-01-01

The paper shows how to implement the generalized Harvey–Shack (GHS) method for isotropic rough surfaces discretized in a polar coordinate system and approximated using Fourier series. This is particularly relevant for the use of the GHS method as a boundary condition for radiative transfer proble...

Revision without ordinals

NARCIS (Netherlands)

Rivello, Edoardo

2013-01-01

We show that Herzberger’s and Gupta’s revision theories of truth can be recast in purely inductive terms, without any appeal neither to the transfinite ordinal numbers nor to the axiom of Choice. The result is presented in an abstract and general setting, emphasising both its validity for a wide

The Pakistan atomic energy commission ordinance, 1965 ordinance no. XVII of 1965

International Nuclear Information System (INIS)

1983-01-01

This act, entitled Pakistan Atomic Energy Commission ordinance 1965, allows amendments incorporated under PAEC (amendment) act 1974 upto August 1983. The amendments relates to regulations concerned with the composition and functions of the commission and some miscellaneous rules. (A.B.)

Collection of laws and ordinances concerning regulation of atomic energy, 1991 edition

International Nuclear Information System (INIS)

1990-01-01

This is the collection of the laws and ordinances on the regulation of atomic energy, 1991 edition, published under the supervision of Nuclear Safety Bureau, Science and Technology Agency. First, the abbreviated indication of the laws and ordinances is shown. The contents are those as of September 30, 1990. 12 basic laws and ordinances, 45 laws and ordinances on the regulation of nuclear raw materials, nuclear fuel materials and nuclear reactors, 26 laws and ordinances on the prevention of the radiation injuries due to radioisotopes and others, and 29 related laws and ordinances are collected in this book. (K.I.)

Surface meshing with curvature convergence

KAUST Repository

Li, Huibin; Zeng, Wei; Morvan, Jean-Marie; Chen, Liming; Gu, Xianfengdavid

2014-01-01

Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.

Surface meshing with curvature convergence

KAUST Repository

Li, Huibin

2014-06-01

Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.

Ordinal Log-Linear Models for Contingency Tables

Directory of Open Access Journals (Sweden)

Brzezińska Justyna

2016-12-01

Full Text Available A log-linear analysis is a method providing a comprehensive scheme to describe the association for categorical variables in a contingency table. The log-linear model specifies how the expected counts depend on the levels of the categorical variables for these cells and provide detailed information on the associations. The aim of this paper is to present theoretical, as well as empirical, aspects of ordinal log-linear models used for contingency tables with ordinal variables. We introduce log-linear models for ordinal variables: linear-by-linear association, row effect model, column effect model and RC Goodman’s model. Algorithm, advantages and disadvantages will be discussed in the paper. An empirical analysis will be conducted with the use of R.

Urban Runoff: Model Ordinances for Erosion and Sediment Control

Science.gov (United States)

The model ordinance in this section borrows language from the erosion and sediment control ordinance features that might help prevent erosion and sedimentation and protect natural resources more fully.

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

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

Mesh size in Lichtenstein repair: a systematic review and meta-analysis to determine the importance of mesh size.

Science.gov (United States)

Seker, D; Oztuna, D; Kulacoglu, H; Genc, Y; Akcil, M

2013-04-01

Small mesh size has been recognized as one of the factors responsible for recurrence after Lichtenstein hernia repair due to insufficient coverage or mesh shrinkage. The Lichtenstein Hernia Institute recommends a 7 × 15 cm mesh that can be trimmed up to 2 cm from the lateral side. We performed a systematic review to determine surgeons' mesh size preference for the Lichtenstein hernia repair and made a meta-analysis to determine the effect of mesh size, mesh type, and length of follow-up time on recurrence. Two medical databases, PubMed and ISI Web of Science, were systematically searched using the key word "Lichtenstein repair." All full text papers were selected. Publications mentioning mesh size were brought for further analysis. A mesh surface area of 90 cm(2) was accepted as the threshold for defining the mesh as small or large. Also, a subgroup analysis for recurrence pooled proportion according to the mesh size, mesh type, and follow-up period was done. In total, 514 papers were obtained. There were no prospective or retrospective clinical studies comparing mesh size and clinical outcome. A total of 141 papers were duplicated in both databases. As a result, 373 papers were obtained. The full text was available in over 95 % of papers. Only 41 (11.2 %) papers discussed mesh size. In 29 studies, a mesh larger than 90 cm(2) was used. The most frequently preferred commercial mesh size was 7.5 × 15 cm. No papers mentioned the size of the mesh after trimming. There was no information about the relationship between mesh size and patient BMI. The pooled proportion in recurrence for small meshes was 0.0019 (95 % confidence interval: 0.007-0.0036), favoring large meshes to decrease the chance of recurrence. Recurrence becomes more marked when follow-up period is longer than 1 year (p < 0.001). Heavy meshes also decreased recurrence (p = 0.015). This systematic review demonstrates that the size of the mesh used in Lichtenstein hernia repair is rarely

A local level set method based on a finite element method for unstructured meshes

International Nuclear Information System (INIS)

Ngo, Long Cu; Choi, Hyoung Gwon

2016-01-01

A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time

A local level set method based on a finite element method for unstructured meshes

Energy Technology Data Exchange (ETDEWEB)

Ngo, Long Cu; Choi, Hyoung Gwon [School of Mechanical Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of)

2016-12-15

A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time.

Atomic ordinance - amendment of 28 october 1987

International Nuclear Information System (INIS)

1987-10-01

This Ordinance amends certain provisions of the 1984 Ordinance on licences for the construction and operation of nuclear installations, import, export and transit of nuclear fuel, as well as the export of nuclear reactors, equipment and technical data. The Order also amends the provisions on the delivery procedure for these licences and makes minor amendments to the 1983 Order on nuclear third party liability [fr

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

Voltammetry at micro-mesh electrodes

Directory of Open Access Journals (Sweden)

Wadhawan Jay D.

2003-01-01

Full Text Available The voltammetry at three micro-mesh electrodes is explored. It is found that at sufficiently short experimental durations, the micro-mesh working electrode first behaves as an ensemble of microband electrodes, then follows the behaviour anticipated for an array of diffusion-independent micro-ring electrodes of the same perimeter as individual grid-squares within the mesh. During prolonged electrolysis, the micro-mesh electrode follows that behaviour anticipated theoretically for a cubically-packed partially-blocked electrode. Application of the micro-mesh electrode for the electrochemical determination of carbon dioxide in DMSO electrolyte solutions is further illustrated.

Streaming simplification of tetrahedral meshes.

Science.gov (United States)

Vo, Huy T; Callahan, Steven P; Lindstrom, Peter; Pascucci, Valerio; Silva, Cláudio T

2007-01-01

Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish real-time visualization necessary for scientific analysis. We propose a two-step approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/O-efficient format that allows coherent access to the tetrahedral cells. A quadric-based simplification is sequentially performed on small portions of the mesh in-core. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates out-of-core to process meshes too large for main memory.

Adaptive multilevel mesh refinement method for the solution of low Mach number reactive flows; Methode adaptative de raffinement local multi-niveaux pour le calcul d'ecoulements reactifs a faible nombre de Mach

Energy Technology Data Exchange (ETDEWEB)

Core, X.

2002-02-01

The isobar approximation for the system of the balance equations of mass, momentum, energy and chemical species is a suitable approximation to represent low Mach number reactive flows. In this approximation, which neglects acoustics phenomena, the mixture is hydrodynamically incompressible and the thermodynamic effects lead to an uniform compression of the system. We present a novel numerical scheme for this approximation. An incremental projection method, which uses the original form of mass balance equation, discretizes in time the Navier-Stokes equations. Spatial discretization is achieved through a finite volume approach on MAC-type staggered mesh. A higher order de-centered scheme is used to compute the convective fluxes. We associate to this discretization a local mesh refinement method, based on Flux Interface Correction technique. A first application concerns a forced flow with variable density which mimics a combustion problem. The second application is natural convection with first small temperature variations and then beyond the limit of validity of the Boussinesq approximation. Finally, we treat a third application which is a laminar diffusion flame. For each of these test problems, we demonstrate the robustness of the proposed numerical scheme, notably for the density spatial variations. We analyze the gain in accuracy obtained with the local mesh refinement method. (author)

An approach to solve group-decision-making problems with ordinal interval numbers.

Science.gov (United States)

Fan, Zhi-Ping; Liu, Yang

2010-10-01

The ordinal interval number is a form of uncertain preference information in group decision making (GDM), while it is seldom discussed in the existing research. This paper investigates how the ranking order of alternatives is determined based on preference information of ordinal interval numbers in GDM problems. When ranking a large quantity of ordinal interval numbers, the efficiency and accuracy of the ranking process are critical. A new approach is proposed to rank alternatives using ordinal interval numbers when every ranking ordinal in an ordinal interval number is thought to be uniformly and independently distributed in its interval. First, we give the definition of possibility degree on comparing two ordinal interval numbers and the related theory analysis. Then, to rank alternatives, by comparing multiple ordinal interval numbers, a collective expectation possibility degree matrix on pairwise comparisons of alternatives is built, and an optimization model based on this matrix is constructed. Furthermore, an algorithm is also presented to rank alternatives by solving the model. Finally, two examples are used to illustrate the use of the proposed approach.

Co-ordinated action between youth-care and sports: facilitators and barriers.

Science.gov (United States)

Hermens, Niels; de Langen, Lisanne; Verkooijen, Kirsten T; Koelen, Maria A

2017-07-01

In the Netherlands, youth-care organisations and community sports clubs are collaborating to increase socially vulnerable youths' participation in sport. This is rooted in the idea that sports clubs are settings for youth development. As not much is known about co-ordinated action involving professional care organisations and community sports clubs, this study aims to generate insight into facilitators of and barriers to successful co-ordinated action between these two organisations. A cross-sectional study was conducted using in-depth semi-structured qualitative interview data. In total, 23 interviews were held at five locations where co-ordinated action between youth-care and sports takes place. Interviewees were youth-care workers, representatives from community sports clubs, and Care Sport Connectors who were assigned to encourage and manage the co-ordinated action. Using inductive coding procedures, this study shows that existing and good relationships, a boundary spanner, care workers' attitudes, knowledge and competences of the participants, organisational policies and ambitions, and some elements external to the co-ordinated action were reported to be facilitators or barriers. In addition, the participants reported that the different facilitators and barriers influenced the success of the co-ordinated action at different stages of the co-ordinated action. Future research is recommended to further explore the role of boundary spanners in co-ordinated action involving social care organisations and community sports clubs, and to identify what external elements (e.g. events, processes, national policies) are turning points in the formation, implementation and continuation of such co-ordinated action. © 2017 John Wiley & Sons Ltd.

Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

International Nuclear Information System (INIS)

Botchorishvili, Ramaz; Pironneau, Olivier

2003-01-01

We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000 2 grid points

Laparoscopic mesh explantation and drainage of sacral abscess remote from transvaginal excision of exposed sacral colpopexy mesh.

Science.gov (United States)

Roth, Ted M; Reight, Ian

2012-07-01

Sacral colpopexy may be complicated by mesh exposure, and the surgical treatment of mesh exposure typically results in minor postoperative morbidity and few delayed complications. A 75-year-old woman presented 7 years after a laparoscopic sacral colpopexy, with Mersilene mesh, with an apical mesh exposure. She underwent an uncomplicated transvaginal excision and was asymptomatic until 8 months later when she presented with vaginal drainage and a sacral abscess. This was successfully treated with laparoscopic enterolysis, drainage of the abscess, and explantation of the remaining mesh. Incomplete excision of exposed colpopexy mesh can lead to ascending infection and sacral abscess. Laparoscopic drainage and mesh removal may be considered in these patients.

Mesh optimization for microbial fuel cell cathodes constructed around stainless steel mesh current collectors

KAUST Repository

Zhang, Fang; Merrill, Matthew D.; Tokash, Justin C.; Saito, Tomonori; Cheng, Shaoan; Hickner, Michael A.; Logan, Bruce E.

2011-01-01

that the mesh properties of these cathodes can significantly affect performance. Cathodes made from the coarsest mesh (30-mesh) achieved the highest maximum power of 1616 ± 25 mW m-2 (normalized to cathode projected surface area; 47.1 ± 0.7 W m-3 based on liquid

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

SUPERIMPOSED MESH PLOTTING IN MCNP

Energy Technology Data Exchange (ETDEWEB)

J. HENDRICKS

2001-02-01

The capability to plot superimposed meshes has been added to MCNP{trademark}. MCNP4C featured a superimposed mesh weight window generator which enabled users to set up geometries without having to subdivide geometric cells for variance reduction. The variance reduction was performed with weight windows on a rectangular or cylindrical mesh superimposed over the physical geometry. Experience with the new capability was favorable but also indicated that a number of enhancements would be very beneficial, particularly a means of visualizing the mesh and its values. The mathematics for plotting the mesh and its values is described here along with a description of other upgrades.

Amendment of the Ordinance on the export and transit of goods

International Nuclear Information System (INIS)

1989-12-01

This Ordinance amends the Annex of the Ordinance of 7 March 1983 on the export and transit of dangerous goods which lists the nuclear items, ie nuclear reactors, equipment and materials subject to export restrictions. The Ordinance came into force on 1 January 1990 (NEA) [fr

Cache-Oblivious Mesh Layouts

International Nuclear Information System (INIS)

Yoon, S; Lindstrom, P; Pascucci, V; Manocha, D

2005-01-01

We present a novel method for computing cache-oblivious layouts of large meshes that improve the performance of interactive visualization and geometric processing algorithms. Given that the mesh is accessed in a reasonably coherent manner, we assume no particular data access patterns or cache parameters of the memory hierarchy involved in the computation. Furthermore, our formulation extends directly to computing layouts of multi-resolution and bounding volume hierarchies of large meshes. We develop a simple and practical cache-oblivious metric for estimating cache misses. Computing a coherent mesh layout is reduced to a combinatorial optimization problem. We designed and implemented an out-of-core multilevel minimization algorithm and tested its performance on unstructured meshes composed of tens to hundreds of millions of triangles. Our layouts can significantly reduce the number of cache misses. We have observed 2-20 times speedups in view-dependent rendering, collision detection, and isocontour extraction without any modification of the algorithms or runtime applications

Variational boundary conditions based on the Nitsche method for fitted and unfitted isogeometric discretizations of the mechanically coupled Cahn-Hilliard equation

Science.gov (United States)

Zhao, Ying; Schillinger, Dominik; Xu, Bai-Xiang

2017-07-01

The primal variational formulation of the fourth-order Cahn-Hilliard equation requires C1-continuous finite element discretizations, e.g., in the context of isogeometric analysis. In this paper, we explore the variational imposition of essential boundary conditions that arise from the thermodynamic derivation of the Cahn-Hilliard equation in primal variables. Our formulation is based on the symmetric variant of Nitsche's method, does not introduce additional degrees of freedom and is shown to be variationally consistent. In contrast to strong enforcement, the new boundary condition formulation can be naturally applied to any mapped isogeometric parametrization of any polynomial degree. In addition, it preserves full accuracy, including higher-order rates of convergence, which we illustrate for boundary-fitted discretizations of several benchmark tests in one, two and three dimensions. Unfitted Cartesian B-spline meshes constitute an effective alternative to boundary-fitted isogeometric parametrizations for constructing C1-continuous discretizations, in particular for complex geometries. We combine our variational boundary condition formulation with unfitted Cartesian B-spline meshes and the finite cell method to simulate chemical phase segregation in a composite electrode. This example, involving coupling of chemical fields with mechanical stresses on complex domains and coupling of different materials across complex interfaces, demonstrates the flexibility of variational boundary conditions in the context of higher-order unfitted isogeometric discretizations.

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Science.gov (United States)

Batina, John T.

1990-01-01

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

User Manual for the PROTEUS Mesh Tools

Energy Technology Data Exchange (ETDEWEB)

Smith, Micheal A. [Argonne National Lab. (ANL), Argonne, IL (United States); Shemon, Emily R. [Argonne National Lab. (ANL), Argonne, IL (United States)

2015-06-01

This report describes the various mesh tools that are provided with the PROTEUS code giving both descriptions of the input and output. In many cases the examples are provided with a regression test of the mesh tools. The most important mesh tools for any user to consider using are the MT_MeshToMesh.x and the MT_RadialLattice.x codes. The former allows the conversion between most mesh types handled by PROTEUS while the second allows the merging of multiple (assembly) meshes into a radial structured grid. Note that the mesh generation process is recursive in nature and that each input specific for a given mesh tool (such as .axial or .merge) can be used as “mesh” input for any of the mesh tools discussed in this manual.

Anisotropic evaluation of synthetic surgical meshes.

Science.gov (United States)

Saberski, E R; Orenstein, S B; Novitsky, Y W

2011-02-01

The material properties of meshes used in hernia repair contribute to the overall mechanical behavior of the repair. The anisotropic potential of synthetic meshes, representing a difference in material properties (e.g., elasticity) in different material axes, is not well defined to date. Haphazard orientation of anisotropic mesh material can contribute to inconsistent surgical outcomes. We aimed to characterize and compare anisotropic properties of commonly used synthetic meshes. Six different polypropylene (Trelex(®), ProLite™, Ultrapro™), polyester (Parietex™), and PTFE-based (Dualmesh(®), Infinit) synthetic meshes were selected. Longitudinal and transverse axes were defined for each mesh, and samples were cut in each axis orientation. Samples underwent uniaxial tensile testing, from which the elastic modulus (E) in each axis was determined. The degree of anisotropy (λ) was calculated as a logarithmic expression of the ratio between the elastic modulus in each axis. Five of six meshes displayed significant anisotropic behavior. Ultrapro™ and Infinit exhibited approximately 12- and 20-fold differences between perpendicular axes, respectively. Trelex(®), ProLite™, and Parietex™ were 2.3-2.4 times. Dualmesh(®) was the least anisotropic mesh, without marked difference between the axes. Anisotropy of synthetic meshes has been underappreciated. In this study, we found striking differences between elastic properties of perpendicular axes for most commonly used synthetic meshes. Indiscriminate orientation of anisotropic mesh may adversely affect hernia repairs. Proper labeling of all implants by manufacturers should be mandatory. Understanding the specific anisotropic behavior of synthetic meshes should allow surgeons to employ rational implant orientation to maximize outcomes of hernia repair.