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

Shanqin Chen, Weinan E, Yunxian Liu, Chi Wang Shu

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

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 sub-domains 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 sub-domains 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.

Original languageEnglish (US)
Pages (from-to)1314-1330
Number of pages17
JournalJournal of Computational Physics
Volume225
Issue number2
DOIs
StatePublished - Aug 10 2007

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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