摘要:

Two new slab geometry spatial quadrature schemes for use in discrete ordinates neutral particle transport computer codes are presented. The step adaptive and linear adaptive quadratures are derived as characteristic quadratures. They differ from previous schemes in using strictly non-negative finite elements representations of the scattering source within a spatial cell. These representations adapt to match the zeroth and first spatial moments of the source in the cell (which are known from the outer iteration). The resulting quadratures are nonlinear and strictly non-negative, while satisfying zeroth-spatial-moment and first-spatial-moment balances globally. They strongly ameliorate the numerical diffusion usually encountered with optically thick cells. Both schemes perform much better than conventional spatial quadratures (diamond difference, linear discontinuous, linear characteristic, linear nodal, etc.) for a deep penetration test problem, presented here. With optically thin cells, the linear adaptive scheme is equivalent to the linear nodal scheme. Hence, it retains the accuracy and high order of asymptotic convergence of that method, while also performing well in streaming-dominated problems with optically thick cells.

ISSN:0041-1450    

DOI:10.1080/00411459008260818

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

A constructive method for solving stationary slab and half-space problems for a class of linear kinetic equations is derived. Fundamental solutions of such 'problems are approximated by an iterative scheme. We prove convergence for the resulting numerical procedure and present some examples. Finally we apply the method to an instationary inverse problem, i.e. we show how to calculate the scattering kernel of a transport problem, knowing the albedo-part of its solution.

ISSN:0041-1450    

DOI:10.1080/00411459008260819

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

We consider an initial-boundary value problem for the Boltzmann equation with a source term. The spatial domain is assumed to be a rectangular box with specularly reflecting boundaries. It is proved that this problem possesses a unique solution globally in time, provided initial data are sufficiently close to a spatially homogeneous function, and the source term is small in a space of functions polynomially decaying for large velocities. This result extends earlier results of Arkeryd, Esposito and Pulvirenti, who considered a similar problem without a source term, and of Busoni and Palczewski, who obtained a solution for an exponentially decaying source and with initial data close to a global equilibrium.

ISSN:0041-1450    

DOI:10.1080/00411459008260820

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

We obtain a variational estimate of the flux at infinity for a subcritical homogeneous halfspace driven by both an incident flux and an internal source. The angular dependences of the scattering phase function, the incident flux, and the internal source are allowed to be arbitrary. The basic variational functional is derived incorporating the transport equation and boundary conditions in the defining problem as constraints, using a Lagrange multiplier technique. Explicit results are obtained using asymptotic (Case discrete mode) trial functions. Improvements in the basic result are obtained by treating the uncollided and once collided fluxes exactly, and by iterating a lower order variational result. A by-product of this analysis is two approximations to Chandrasekhar's H-function, and we compare these simple analytic approximations with exact results in the special case of isotropic scattering.

ISSN:0041-1450    

DOI:10.1080/00411459008260821

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

A numerical method for the one-dimensional Vlasov-Poisson system is developed and a proof of convergence is given. The proof extends the result of [10]. The numerical method can be used on a computer and the proof of convergence shows that in the absence of computer roundoff error, the computed solution converges to the exact solution of the Vlasov-Poisson system as discretization parameters approach zero.

ISSN:0041-1450    

DOI:10.1080/00411459008260822

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

The paper studies the flow of a viscous conducting and thermally radiating gas in a vertical channel with linear axial temperature variation when the radiative flux satisfies the exact integral expression. It is assumed that the flow is fully developed in terms of velocity but not in terms of temperature. Retaining only terms which are linear in the axial temperature gradient, the problem is reduced to a set of nonlinear integro-ordinary differential equations. The solution methodology involves perturbing the temperature about the nonlinear general differential approximation for radiation and the resultant linear equation is of the mixed Fredholm - Volterra type which is tackled by method of successive approximation. The temperature and velocity distributions are discussed quantitatively.

ISSN:0041-1450    

DOI:10.1080/00411459008260823

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

Consider a system ofNhard spheres of radiidi> 0 and massesmi< 0,i= 1,…,N. The spheres may interact through elastic pair collisions but move freely otherwise in all of R3. It is shown that (with the exception of a set of initial states of measure zero) there are at most finitely many collisions for any given initial state of the system.

ISSN:0041-1450    

DOI:10.1080/00411459008260824

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411459008260825

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411459008260826

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor