摘要:

AbstractThe problem of linear transport in a stationary stochastic medium is examined in the context of stochastic geometry. Boolean models of stochastic media allow calculation of density correlations without use of Markovian assumptions. Most correlation functions are well represented by linear combinations of a few exponentials. Systems of integrodifferential equations are obtained either (a) by a perturbative treatment or (b) by truncation of the hierarchy of moments. The presence of an integral term (i.e., a nonlocal flux) can be avoided by the use of an approximate equivalence between the product of the transport Green function by an exponential with the transport Green function of a modified problem. Introduction of auxiliary unknowns gives rise to a system of coupled Boltzmann equations describing the ensemble average of the flux.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24220

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractUsing the operator form of a synthetic acceleration, the P1acceleration [diffusion synthetic acceleration (DSA)] and P2acceleration schemes for one-dimensional slab and the P1and simplified P2acceleration schemes for two-dimensional x-y geometry are derived. The convergence rate of each scheme for a simple model problem is compared, and the result is generalized by performing a Fourier analysis. In the one-dimensional case, the new second-moment P2acceleration outperforms an earlier third-moment P2acceleration developed by Miller and Larsen. However, it is still less efficient than P1acceleration. Similar results show that the P1acceleration converges faster than the simplified P2acceleration in two-dimensional x-y geometry. These results confirm that one cannot simply assume that replacement of the DSA method with a higher order operator will lead to a smaller spectral radius.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24221

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractRecent pressure vessel fast fluence calculations have revealed numerical difficulties (spatial oscillations) in the SNsolutions, which have persisted in spite of mesh refinement. It is demonstrated that other shielding/deep-penetration applications may be affected; in fact, any SNsolution in which the uncollided flux component is significant is likely to exhibit such difficulties. Test problems have been designed to characterize and understand numerical difficulties. Main analyses are performed using the diamond-difference (DD) scheme, which is linear and forms the basis for other (more complex) low-order differencing schemes. The genesis of oscillations is shown to be related to several effects specific for multidimensional geometries as follows: ambiguity in the interpretation of boundary conditions, discontinuities, and different directions of particle streaming and differencing. It has further been explained why the mesh refinement does not produce the intuitively expected results. Other low-order differencing schemes (e.g., the DD with negative flux fixup and theθ-weighted) may partly remedy the situation by reducing the oscillations or by eliminating the oscillations at a cost of“oversmoothing”the results everywhere (e.g., the zero-weighted scheme). These schemes provide more robust solutions, but the inherent difficulties (although reduced) still remain. Types of discontinuities that trigger the oscillations are also examined; it is difficult to envisage an actual practical application free of such discontinuities. The magnitude of numerical difficulties (oscillations) and their practical relevance will depend on all SNmodel features, the differencing scheme being used, and the application requirements, but this study has shown that they are inherent to multidimensional finite-difference SNalgorithms.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24222

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractThe analytical representation of eigenfunctions for finite moments method approximations of radiative transport equations is constructed in slab geometry problems. The truncated balance algorithm is used. An angle dependence of discrete eigenfunctions is determined by discrete characteristic equation solutions. It is established that space-dependent factors of discrete eigenfunctions are Pade approximations of the exponential functions and correspond to the original transport problem eigenfunctions. This technique proves to be useful for analyzing solvability and accuracy of finite moment approximations and also for developing computational algorithms. Slowly changing eigenfunctions are included in the regular component of the optically thick slab problem solution. Coarse-mesh algorithms or diffusion approximations at specific boundary conditions can be used to determine these components. Other eigenfunctions determine the singular component of the mesh solution. This component represents the transition regime on coarse meshes with typical oscillations or with a slow decrease in boundary layers. It is strongly different from the singular component of the exact solution.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24223

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractRecently, the nonlinear characteristic (NC) scheme for spatially discretizing the discrete ordinates equations was introduced. This scheme is accurate for both optically thin and optically thick spatial meshes and produces strictly positive angular fluxes. The NC discrete ordinates equations can be solved using the source iteration method; however, it is well known that this method converges prohibitively slowly for optically thick problems with scattering ratios at or near unity. A general nonlinear diffusion synthetic acceleration method for solving the NC equations in slab geometry is described. Numerical results to show the effectiveness and efficiency of the new solution method are provided.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24224

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractTwo methods based on the variational nodal transport method have been developed to account for localized heterogeneities and local transport effects in full core calculations. A local mesh refinement technique relies on using the projected partial ingoing surface currents produced during coarse-mesh iterations as boundary conditions for fine-mesh calculations embedded within the coarse-mesh calculations. The outgoing fine-mesh partial currents are averaged to serve in the coarse-mesh iterations. Then, a mixed transport-diffusion method using two levels of angular approximations for the surface partial currents depending on the node considered has been implemented to account for local transport effects in full core diffusion calculations. These methods have been tested for a model of the Superphenix complementary shutdown rods.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24225

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractParticle transport in rod and plane geometry random media is considered. The cross section is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. In rod geometry, an exact closure is constructed for semi-infinite media that yields exact equations for the ensemble-averaged scalar fluxΦand current J. The same closure scheme yields a Fokker-Planck equation for the joint probability distribution function ofΦand J, from which ensemble-averaged equations for higher order quantities are derived and solved exactly for an arbitrary correlation function. Finally, the penetration of a beam of charged particles in a highly forward scattering random medium is considered, and circumstances that yield a closed ensemble-averaged transport equation are determined.

ISSN:0029-5639    

DOI:10.13182/NSE124-89

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractSeveral polynomial finite elements of nodal type are introduced that should lead to convergence of O(h1) in the L2norm. Two of these methods are new and are expected to achieve the same orders of convergence with fewer parameters than the third method. They are applied to the one-group diffusion equation under different formulations, namely, several versions (with or without reduced and transverse integrations) of the primal and the mixed-hybrid formulations. Convergence rates are checked for a model problem with an analytical solution. Two of these methods exhibit superconvergence phenomena [O(h4) instead of O(h3)], a fact that can be explained heuristically. The most promising method, with only five parameters per cell, turns out to yield only O(h2) in its most algebraically efficient versions, while it has the potential of O(h3) convergence rates. Again, an explanation is given for this behavior and a fully O(h3) version is developed. Finally, these methods are applied to more realistic multigroup situations. In all cases, they are compared with results obtained from polynomial nodal methods in response matrix formalism. In the multigroup case, a well-known reference solution is also used.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24227

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractNew reactor physics and computation methods have been developed in our three-dimensional pressurized water reactor (PWR) core dynamics SIMTRAN code for on-line surveillance and prediction. The accuracy of the coupled neutronic thermal-hydraulic solution is improved, and its scope is extended to provide, mainly, the calculation of the fission reaction rates at the in-core minidetectors, the responses at the ex-core detectors, and the in-vessel coolant flow and temperature distributions.The functional capabilities implemented in the on-line SIMTRAN code include on-line surveillance, in-core-ex-core calibration, evaluation of peak power factors and thermal margins, nominal cycle follow, prediction of maneuvers, and diagnosis offast transients and oscillations. The new code has been operating on-line at the Vandellós-II PWR unit in Spain since the startup of its cycle 7 in mid-June 1994, including the machine-man interfaces for on-line acquisition of measured data and interactive graphical utilization. The agreement of the simulations with the measurements, along the full cycle 7 and the first months of cycle 8 operation, is well within the accuracy requirements. The performance and usefulness for operational support shown during the demo and routine use phases have proved that the on-line SIMTRAN code has the qualities for the accurate, reliable, comprehensive, and user-friendly on-line core surveillance and prediction.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24228

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor

摘要:

AbstractA standard model for describing time-dependent two-phase flows is the so-called six-equation or two-fluid model, where mass, energy, and momentum equations are considered for each phase. It is well known that the single-pressure form of this model can contain complex characteristics and is therefore ill posed. This ill-posedness has been blamed for numerical instabilities that have at times been observed when finite difference solutions of these equations have been attempted. One method to render the characteristics real is to include viscous terms. The numerical implications of adding viscous terms to the six-equation model are considered, and the potential impact of these implications on the stability of the finite difference solution is evaluated.

ISSN:0029-5639    

DOI:10.13182/NSE96-A24229

出版商:Taylor&Francis    

年代:1996

数据来源: Taylor