摘要:

The paper deals with nonlinear numerical methods for solving the transport equation. The Quasi-Diffusion method and nonlinear flux methods are considered. Two approaches to discretization of the considered method equations are compared. Consistent and independent difference schemes are considered. The described nonlinear methods are analyzed to formulate conditions on difference schemes that guarantee satisfying the small scattering limit, the diffusion limit, and the balance equation by a numerical solution. It is shown that in some curvilinear geometry transport problems a small parameter at the highest derivative arises in the moment equations of the nonlinear flux methods. Convergence rates of iteration processes of considered methods are compared. An idea for deriving a nonlinear monotone difference scheme for the multidimensional transport equation is proposed.

ISSN:0041-1450    

DOI:10.1080/00411459308203810

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The Quasi-Diffusion (QD) method [1]–[3] is a nonlinear algorithm for solving linear transport problems. Because the QD method utilizes both a transport sweep and a diffusion calculation within each iteration, it is operationally more complex than the Source Iteration (SI) method, which utilizes only a transport sweep within each iteration. However, the QD method often converges rapidly and with high accuracy, especially for optically thick regions with scattering ratios c close to unity; these are the regions for which acceleration is most needed. A difficulty with the QD method is that because it is nonlinear, every scalar flux iterate must be positive at each point in the system. Also, the formulation of diffusion boundary conditions to optimize accuracy and speed of convergence is not obvious. In this paper, we consider both of these issues. Specifically, we propose a new formulation of the QD method in spherical geometry to guarantee positivity of the analytic solution, and we propose new diffusion boundary conditions in planar and spherical geometry that lead to more accurate and efficient solution algorithms. Also, we discuss ways to accurately and positively discretize the transport and diffusion equations, and we give extensive numerical results.

ISSN:0041-1450    

DOI:10.1080/00411459308203811

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We discuss certain flux-limited diffusion theories which approximately describe radiative transfer in the presence of steep spatial gradients. A new formulation is presented which generalizes a flux-limited description currently in widespread use for large radiation hydrodynamic calculations. This new formulation allows more than one Case discrete mode to be described by a flux-limited diffusion equation. Such behavior is not extant in existing formulations. Numerical results predicted by these flux-limited diffusion models are presented for radiation penetration into an initially cold halfspace.

ISSN:0041-1450    

DOI:10.1080/00411459308203812

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A new second order method (CDSN-method) for solving the transport equation is developed. This method takes into consideration a local property of the transport equation solution in each mesh cell. Every cell is divided into three subdomains by two characteristic lines intersecting the vertices. In each subdomain the solution is a smooth function, if incident fluxes are smooth. This allows us to construct a new algorithm. Taking into account the linear character of the transport equation, its solution in every cell may be considered to be a sum of two solutions. One of them is a solution depending on boundary radiation and a zero spatial source (E–component). The other is a solution depending on a spatial source and zero boundary radiation (S–component). Different combined methods were obtained by using various algorithms for construction of E–and S–components.

ISSN:0041-1450    

DOI:10.1080/00411459308203813

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

There continues to be considerable interest in the application of the even-parity transport equation to problems of radiation transfer and neutron transport'−8. The motivation for this interest arises from several potential advantages of this equation when compared with the more traditional first-order form of the equation. First, assuming that the scalar flux is of primary interest, the angular domain under consideration is one-half of that required for the first-order equation. Thus, for the same degree of accuracy, one would hopefully require substantiably fewer unknown values of the dependent variable to be determined. Secondly, the elliptic-like nature of the set of even-parity equations should allow certain parallel computer architectures to be used more readily3.

ISSN:0041-1450    

DOI:10.1080/00411459308203814

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

In this paper we apply the recently developed theory ofinformation-based complexityto two-dimensional transport. For a model problem we obtain the radius of the cell-average information, which is the optimal (worst-case) error. The corresponding central algorithm that possesses this optimal error is developed. Further, we theoretically and numerically compare four algorithms, the step-characteristic, diamond-difference, (C, C) nodal-transport, and corner-balance algorithms, for a single cell. A number of figures and table are presented for those comparisons. Such results allow the best choice of algorithm to solve the model problem, depending on the angular variables (μ,η) and cell widthh.

ISSN:0041-1450    

DOI:10.1080/00411459308203815

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The spectrum of the monoenergetic boundary value transport equation problem with general boundary conditions is studied. For the problems with special scattering cross-sections, the variational minima–maxima principles for the characteristic values (c.v.) are obtained. The dependence of the c.v. on the problem parameters (total and scattering cross–sections, boundary conditions, size and shape of the region) is studied. In some cases the result is the monotonicity, in some cases the result is the continuity, and in some cases the analyticity of the c.v. dependence on these parameters.

ISSN:0041-1450    

DOI:10.1080/00411459308203816

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

This paper is devoted to sensitivity and uncertainty analysis via the investigation of functionals of neutron and gamma fluxes within the core and reactor shielding. The new code ZAKAT-2.2 developed in the USSR for sensitivity theory application is used to perform these calculations. The transport calculations are carried out with one and two-dimensional discrete ordinates codes. A code system is written to calculate sensitivity coefficients of linear and fractionlinear functionals and to estimate uncertainties in calculation result due to uncertanties in the input parameters (cross-sections). It allows simultaneous calculation of sensitivity coefficients in the core and reactor shielding and implements channel theory for the energy and spatial variables. The statistical nature of cross-section data is pointed out. In this case the result of a calculation is function not only of the average magnitude of cross-sections but also of its probability distribution. Therefore, usage of the average magnitude of cross-sections causes an underestimation of the calculation results. A method for estimating this effect on the basis of sensitivity coefficients and error estimations is introduced. The probability distribution of the calculation results is investigated.

ISSN:0041-1450    

DOI:10.1080/00411459308203817

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

An approach to the reconstruction of a positive function from its truncated Legendre expansion based on the maxent method is proposed.

ISSN:0041-1450    

DOI:10.1080/00411459308203818

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Highly accurate solutions for neutron transport problems are achievable using high order nodal methods, such as the General Order Nodal Transport (GONT) class of methods. The final equations for these methods constitute a set of Weighted Diamond-Difference (WDD) equations that are solved using standard mesh sweeps. A parallel algorithm for solving these equations, based on decomposition of the angular domain is particularly suited for message-passing computers as it embodies a statically-scheduled, coarsegrained parallelization. The parallel code, P-GONT implemented on Intel's iPSC/2 hypercube produces large speedup factors at very high parallel efficiencies. A mathematical model for execution time as a function of the problem parameters: spatial approximation order, number of mesh cells, and angular quadrature order, as well as the number of utilized processors, agrees very well with measured results. The model shows that the parallel efficiency is insensitive to the number of mesh cells, but improves with the spatial approximation and angular quadrature orders. It also shows that the speedup factor increases monotonically with the number of utilized processors, if the latter divides exactly the number of independent processes.

ISSN:0041-1450    

DOI:10.1080/00411459308203819

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor