Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics

JOURNAL OF COMPUTATIONAL PHYSICS

卷:292

Article

Li, Qin¹  Lu, Jianfeng^2,3,4  Sun, Weiran⁵ 

[1] CALTECH, Computing & Math Sci, Pasadena, CA 91125 USA

[2] Duke Univ, Dept Math, Durham, NC 27708 USA

[3] Duke Univ, Dept Phys, Durham, NC 27708 USA

[4] Duke Univ, Dept Chem, Durham, NC 27708 USA

[5] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

关键词: Linear transport equations;    Diffusion approximation;    Domain decomposition;    Kinetic-fluid coupling;   

DOI  :  10.1016/j.jcp.2015.03.014

来源: Elsevier

【 摘 要 】

In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the half-space solver in [20] to resolve the boundary layer equation and obtain the boundary data for the diffusion equation. The algorithms are validated by numerical experiments and also by error analysis for the pure diffusive scaling case. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free