Efficient Preconditioners for a Shock Capturing Space-Time Discontinuous Galerkin Method for Systems of Conservation Laws
Year: 2015
Communications in Computational Physics, Vol. 17 (2015), Iss. 5 : pp. 1320–1359
Abstract
An entropy stable fully discrete shock capturing space-time Discontinuous Galerkin (DG) method was proposed in a recent paper [20] to approximate hyperbolic systems of conservation laws. This numerical scheme involves the solution of a very large nonlinear system of algebraic equations, by a Newton-Krylov method, at every time step. In this paper, we design efficient preconditioners for the large, nonsymmetric linear system, that needs to be solved at every Newton step. Two sets of preconditioners, one of the block Jacobi and another of the block Gauss-Seidel type are designed. Fourier analysis of the preconditioners reveals their robustness and a large number of numerical experiments are presented to illustrate the gain in efficiency that results from preconditioning. The resulting method is employed to compute approximate solutions of the compressible Euler equations, even for very high CFL numbers.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.140214.271114a
Communications in Computational Physics, Vol. 17 (2015), Iss. 5 : pp. 1320–1359
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
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