摘要:

AbstractA class of“projected discrete ordinates”(PDO) methods is described for obtaining iterative solutions of discrete ordinates problems with convergence rates comparable to those observed using diffusion synthetic acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the choice of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented that illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18163

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractA new three-point nonlinear difference scheme for diffusion synthetic acceleration (DSA) of the radiation transport equation is described. The new scheme is compared with the standard one-point method on two test problems. In addition, the two DSA methods are used to accelerate a variety of discrete ordinates difference schemes. The methods are very effective in accelerating the convergence of the transport iteration. Each of the DSA methods is accelerated by grey, or one-group, diffusion acceleration equation, which is also successful in increasing efficiency. The new method is at least 50% faster than one-point DSA method and this advantage increases with the difficulty of the problem and with tighter convergence criteria. The new acceleration method reduces computer time by at least one order of magnitude compared to unaccelerated calculations.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18164

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractThe equations of the high-order linear-nodal numerical scheme are cast in an augmented weighted-difference form for three-dimensional Cartesian nodes. The coupling exhibited by these equations indicates that this new algorithm is simpler and, hence, faster than previous nodal schemes of this degree of accuracy. A well-logging problem and a fast reactor problem are examined. The new scheme developed is compared with the classical linear-linear nodal scheme and the diamond-difference scheme. For the well-logging problem, it is found that the new scheme is both faster and simpler than the classical linear-linear nodal scheme while sacrificing little in accuracy. Even though the new scheme is more accurate than the diamond-difference scheme for the reactor problem, the results indicate that state-of-the-art acceleration methods are needed for nodal schemes.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18165

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractIt is often desirable to solve the two-dimensional multigroup transport equation for (r-z) geometries directly given by hydrodynamic calculations. Usually, only Monte Carlo codes can computeαor k eigenvalues on such geometries. Most deterministic codes use an orthogonal mesh or restrict the mesh to a regular triangular grid. Other methods were developed at Commissariatàl'Energie Atomique and Los Alamos National Laboratory but do not solve the problem of sliding between two Lagrangian blocks. Thus, a production code has been developed that solves these problems and is able to obtainαor k eigenvalues with a good degree of accuracy for such geometries.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18166

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractSeveral finite element formulations of nodal schemes for neutron diffusion problems are presented: They include nonconforming primal formulations as well as mixed and mixed-hybrid ones, with exact or approximate evaluation of the matrix coefficients. These different formulations are compared to one another and also related to well-known point- and mesh-centered finite difference schemes. Some numerical results are given in one and two dimensions with different schemes. Applications to two-dimensional neutron transport problems are also proposed through the general approach of transverse integration.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18167

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractA hybrid method for two-dimensional neutron transport calculations in (r-z) geometry has been developed. In this method the equation in void regions is solved by the discrete cones (DCN) method, whereas the equation in nonvoid regions is solved by the standard discrete ordinates (SN) method. The two methods are incorporated in one computer program so that a user does not see the difference from a program applying only the SNmethod. This DCN-SNhybrid method significantly mitigates the ray effects in a void compared with a solution by the same order SN. The method, however, requires a little more computing effort and it is difficult for the method to yield a sufficiently accurate solution for narrow duct streaming problems.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18168

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractA type of“phase-space discontinuous diamond”difference scheme, or“phase-space linear discontinuous finite element”approximation, is implemented to solve the two-dimensional [(x-y) or (r-z)] neutron transport equation. The results obtained on some well-known transport benchmark problems are much more accurate than discrete ordinates solutions attained with spatial diamond differencing or discontinuous finite element approximations. Error studies show convergence to the phase-space fine-mesh limit solution with an approximateandconvergence rate, at least in the case of rectangular cells on phase-space domain D×V. In addition, phase-space fine-mesh limit results have been estimated with the help of extrapolation procedures for some neutron transport benchmark problems. This phase-space linear discontinuous finite element approach can be easily enlarged to more general spaces.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18169

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractA review is made of multidimensional radiation transport techniques that are being used to model nuclear oil well logging measurements. Both Monte Carlo and deterministic methods are employed for this work, and it is found that the realism that can be incorporated into these models has led to greater understanding of all kinds of logging measurements. As a result, models are now used as part of the new logging tool design process in much the same way that they are used to support nuclear reactor and shielding designs.Despite the success so far, there is still room to improve both Monte Carlo and especially deterministic methods for logging applications. Monte Carlo codes, impressive as they are, are still expensive computations for many logging problems. Although improvements in basic Monte Carlo can still be made, it seems that the next significant improvement in the efficiency of Monte Carlo will come from computer architecture in the form of multiprocessor machines. On the other hand, the principal limitation of deterministic calculations centers mainly on the lack of accurate, practical, three-dimensional transport capabilities. With this in mind, some recent work to extend a nodal, discrete ordinates method to three dimensions for logging applications is reviewed.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18170

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractThe interface current method is generally used in supercell codes to accelerate computation of the collision probabilities needed for resolution of the integral neutron transport equation. This method was used to compute all the collision probabilities for a cluster geometry. The resulting complete collision probabilities were then compared with those computed using a direct method. The interface current method was much faster than the direct method for computing collision probabilities, with a loss in precision within the limits of error acceptable for reactor design calculations.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18171

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractA flat-flux expansion on axially symmetric zones has been used, together with a uniform double PIexpansion for the boundary angular fluxes, to construct an interface-current method for the calculation of two-dimensional hexagonal cells. Collision and escape probabilities are computed in a volume-preserving, cylindrical cell model, while one of three separate PSS models is used for the calculation of the transmission probabilities. When only one zone has been cylinderized, then use of the heterogeneous PSS model is equivalent to an exact calculation in the actual two-dimensional cell geometry (without cylinderization). Comparison between the different approximations and a Monte Carlo calculation are presented for a typical undermoderated assembly.

ISSN:0029-5639    

DOI:10.13182/NSE86-A18172

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor