摘要:

AbstractA new class of synthetic acceleration methods, which can be applied to transport calculations regardless of geometry, discretization scheme, or mesh shape, is presented. Unlike other synthetic acceleration methods that base their acceleration on P1equations, these methods use acceleration equations obtained by projecting the transport solution onto a coarse angular mesh only on cell boundaries. It is demonstrated, via Fourier analysis of a simple model problem as well as numerical calculations of various problems, that the simplest of these methods are unconditionally stable with spectral radius≤c/3 (c being the scattering ratio), for several different discretization schemes in slab geometry.

ISSN:0029-5639    

DOI:10.13182/NSE100-177

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractTwo previously derived approximations to the linear-linear nodal transport method, the linear-nodal (LN) and the linear-linear (LL) methods, are reexamined, together with a new approximation, the bilinear (BL) method, that takes into account the bilinear nodal flux moment. The three methods differ in the degree of analyticity retained in the final discrete variable equations; however, they all possess the very high accuracy characteristic of nodal methods. Unlike previous work, the final equations are manipulated and cast in the form of the classical weighted diamond-difference (WDD) equations (not just a WDD algorithm). This makes them simple to implement in a computer code, especially for those users who have experience with WDD algorithms. Other algorithms, such as the nodal algorithm, also can be used to solve the WDD-form equations.A computer program that solves two-dimensional transport problems using the LN, LL, or the BL method is used to solve three test problems. The results are used to confirm our algebraic manipulations of the nodal equations and also to compare the performance of the three methods from the computational, as well as the theoretical, point of view. The three methods are found to have comparable accuracies for the problems studied, especially on meshes that are sufficiently fine.

ISSN:0029-5639    

DOI:10.13182/NSE88-5

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractAn angular redistribution function for electron scattering based on Goudsmit-Saunderson theory has been implemented in a Monte Carlo electron transport code in the form of a scattering matrix that we term SMART (simulatingmanyaccumulativeRutherfordtrajectories). These matrices were originally developed for use with discrete ordinates electron transport codes. An essential characteristic of this scattering theory is a large effective mean-free-path for electrons, much larger in fact than the true single collision mean-free-path. When this theory is applied to single collision analog Monte Carlo calculations, excellent results are obtained for the principal quantities of interest, transmission and reflection spectra, and energy deposition. A derivation of the SMART scattering matrix is presented, using the method of weighted residuals to obtain the discretized form of the Spencer-Lewis equation for electron transport. Results of Monte Carlo calculations for electron transport in aluminum slabs for both beam source and isotropic source configurations are given. These results are compared with similar benchmark calculations made with the TIGER code series.

ISSN:0029-5639    

DOI:10.13182/NSE88-A29032

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractA hybrid method has been developed to iteratively couple SNand Monte Carlo regions of the same problem. This technique avoids many of the restrictions and limitations of previous attempts to do the coupling and results in a general and relatively efficient method. The method is demonstrated with some simple examples.

ISSN:0029-5639    

DOI:10.13182/NSE88-A29033

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractAmong the classical methods used for solving the neutron diffusion equation, the Lagrange finite element method can be efficiently implemented to provide a fast numerical treatment. Mixed elements are used because they allow simultaneous approximations for the flux and its gradient of the same order. Although the linear systems produced are not positive definite, a solution can be achieved after eliminating some of the unknowns. Numerical results include core calculations of two types of reactors.

ISSN:0029-5639    

DOI:10.13182/NSE88-A29034

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractThe numerical solution of partial differential equations for the simulation of physical phenomena on memory-coupled multiprocessor systems is discussed. The multigrid methods used are well suited for the considered systems, which are based on the distributed reconfigurable multiprocessor kit DIRMU. The implementation of a multilevel nodal diffusion method on special ring configurations built with DIRMU is outlined. The particular iteration scheme employed in the nodal expansion method appears similarly effective in parallel and serial environments. A general approach for mapping multigrid algorithms onto nearest neighbor mesh configurations, called EGPA, is presented and communication mechanisms are explained. Measured speedups for Poisson’s equation and the more complicated steady-state Stokes equation are given. For large problems, the speedup is roughly proportional to the number of processors.

ISSN:0029-5639    

DOI:10.13182/NSE88-A29035

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractUnder a definition suitable to the transport equation, it is shown that the (two-stage explicit) Runge-Kutta (RK) methods having order of at least 2, and requiring“essentially”only one source evaluation per cell, consist of a one-parameter family, plus two additional methods. Two of these, the midpoint corrector and improved Euler methods, are selected for detailed computational comparison with the classical diamond-difference and step characteristic methods. Extensive monodirectional calculations reveal that the RK methods display absolute instability for cell path lengths exceeding 2 mfp, but that they are nearly competitive with the classical methods for small cell widths. It is shown how the two subject RK methods can be augmented by“closure approximations,”so as to permit their use in source iteration for multiple-direction calculations. The results of such calculations show that for small cell widths, the RK methods again are nearly competitive in accuracy, although the absolute stability requirement can impose a stringent upper bound on the acceptable cell widths; the RK methods interact well with source iteration, even though they do not conserve particles; and the particular closure approximations selected retain the second-order accuracy of the basic underlying methods.

ISSN:0029-5639    

DOI:10.13182/NSE88-A29036

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractA Monte Carlo learning and biasing technique that does its learning and biasing in the random number space rather than in the physical phase-space has been implemented in the Monte Carlo computer code MCNP. The technique was successfully applied on a simple penetration problem, and the results are given. The technique was also applied to a streaming problem with only marginal success.

ISSN:0029-5639    

DOI:10.13182/NSE88-A29037

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractThe equations of thermal radiative transfer are time discretized in a semi-implicit manner, yielding a linear transport problem for each time step. The governing equation in this problem has the form of a neutron transport equation with fission but no scattering. Numerical methods are described, whose origins lie in neutron transport, and that have been successfully adapted to this new problem. Acceleration methods that have been developed specifically for the radiative transfer problem, but may have generalizations applicable in neutronics problems, are also discussed.

ISSN:0029-5639    

DOI:10.13182/NSE88-A29038

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor

摘要:

AbstractThe application of the transmission probability method to the calculation of neutron flux distribution in a two-dimensional light water reactor assembly is described. The interior flux within a mesh is assumed to be linearly dependent on X and Y coordinates. At the mesh surfaces the linear space distribution and the P1approximation for the anisotropic angular distribution are considered. Simple expressions for the expansion coefficients are derived. These expressions are determined by outgoing and incoming currents and are renewed after each iteration. Based on the proposed method, the two-dimensional code TPM2D has been encoded and a series of two-dimensional assembly benchmark problems have been tested. The numerical results are in good agreement with those of Sn, surface flux transport, discrete node transport, and collision probability methods.

ISSN:0029-5639    

DOI:10.13182/NSE88-A29039

出版商:Taylor&Francis    

年代:1988

数据来源: Taylor