A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations

作者：Chen Shanqin; Weinan E; Liu Yunxian; Shu Chi Wang^*

来源：Journal of Computational Physics, 2007, 225(2): 1314-1330.

DOI：10.1016/j.jcp.2007.01.025

• domain decomposition method
• discontinuous galerkin method
• gas dynamics
• semi-conductor device simulation
• hydrodynamics model
• high-field model

In this paper we develop a domain decomposition method (DDM), based on the discontinuous Galerkin (DG) and the local discontinuous Galerkin (LDG) methods, for solving multiscale problems involving macro sub-domains, where a macro model is valid, and micro sub-domains, where the macro model is not valid and a more costly micro model must be used. We take two examples, one from compressible gas dynamics where the micro sub-domains are around shocks, contacts and corners of rarefaction fans, and another one from semiconductor device simulations where the micro subdomains are around the jumps in the doping profile. The macro model is taken as the Euler equations for the gas dynamics problem and as a hydrodynamic model and a high field model for the semiconductor device problem. The micro model for both problems is taken as a kinetic equation. We pay special attention to the effective coupling between the macro subdomains and the micro sub-domains, in which we utilize the advantage of the discontinuous Galerkin method in its compactness of the computational stencil. Numerical results demonstrate the effectiveness of our DDM-DG method in solving such multi-scale problems.

• 出版日期2007-8-10
• 单位山东大学