摘要:

We study the behavior of two fully-discrete numerical schemes (the step scheme and the cell-edge even-parity scheme) for the transfer equation in diffusive regimes with coarse meshes. The diffusion boundary conditions for these numerical schemes are derived through a boundary layer analysis that matches the interior discrete diffusion approximation to the boundary data for the discrete transfer equation. Requiring that the resulting discrete diffusion boundary condition to be a good approximation to the diffusion boundary conditions obtained for the transfer equation then gives constraints on the discretization. It is shown that the quadrature setBndeveloped in our earlier paper [9] gives accurate extrapolated endpoints, while new discrete one-way flux boundary conditions introduced here that are based on the discreteW-function, give accurate forcing terms. Consequently, as we then demonstrate numerically, these new schemes give more accurate results than traditional schemes for problems containing diffusive regimes that involve boundaries and interfaces.

ISSN:0041-1450    

DOI:10.1080/00411459308203842

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Using particle methods to solve the Boltzmann equation for rarefied gases numerically in realistic streaming problems, huge differences in the total number of particles per cell arise. In order to overcome the resulting numerical difficulties, the application of a weighted particle concept is well-suited. The underlying idea is to use different particle masses in different cells depending on the macroscopic density of the gas. Discrepancy estimates and numerical results are given.

ISSN:0041-1450    

DOI:10.1080/00411459308203843

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

It is proven that the monoenergetic neutron transport operator in the case of a spherically symmetric, isotropically scattering sphere with a cavity in a large body has infinitely many complex time eigenvalues.

ISSN:0041-1450    

DOI:10.1080/00411459308203844

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The linear one-dimensional transport equation with a time dependent acceleration field is examined in the Banach space L1(R; (l + |v|) dv). Conditions are given so that the drift velocity remains bounded as t goes to infinity; the case of a periodic acceleration is examined. A simple problem with constant collision frequency is worked out in detail.

ISSN:0041-1450    

DOI:10.1080/00411459308203845

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Some features of the Boltzmann equation for semiconductor devices are analyzed under the assumption of electron-phonon scattering processes. It is shown how the assembly of the electrons is the union of infinitely many sets of particles; each set has constant mass and its own entropy. Using these properties and assuming weak physical conditions on the initial data, we obtain a simple upper bound of homogeneous continuous solutions. The conclusions of this paper clarify the physical meaning of the results presented by the author in the previous one1.

ISSN:0041-1450    

DOI:10.1080/00411459308203846

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The spectral radius of the integral neutron transport operator in unbounded regions is analyzed A suitable integral operator in a bounded region is found, where previously found monotoneity and continuity results hold and a transitional relation is established.

ISSN:0041-1450    

DOI:10.1080/00411459308203847

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor