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

  • Authors:

  • Shanqin Chen;Weinan E;Yunxian Liu;Chi-Wang Shu

  • Affiliations:

  • Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA;Department of Mathematics, Princeton University, Princeton, NJ 08544-1000, USA;School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

Quantified Score

Hi-index 31.46

Visualization

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.