A Schur Complement Method for Compressible Navier-Stokes Equations

Abstract

Domain decomposition methods were first developed for elliptic problems, taking advantage of the strong regularity of their solutions. In the last two decades, many investigations have been devoted to improve the performance of these methods for elliptic and parabolic problems. The situation is less clear for hyperbolic problems with possible singular solutions. In this paper, we will discuss a nonoverlapping domain decomposition method for nonlinear hyperbolic problems. We use the finite volume method and an implicit version of the Roe approximate Riemann solver, and propose a new interface variable inspired by Dolean and Lanteri [1]. The new variable makes the Schur complement approach simpler and allows the treatment of diffusion terms. Numerical results for the compressible Navier-Stokes equations in various 2D and 3D configurations such as the Sod shock tube problem or the lid driven cavity problem show that our method is robust and efficient. Comparisons of performances on parallel computers with up to 512 processors are also reported. © Springer-Verlag Berlin Heidelberg 2013.