期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 231, 期 19, 页码 6472-6494出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.06.011
关键词
Hyperbolic equations; Riemann problem; ADER method; Cauchy-Kowalewski theorem; Cauchy-Kowalewski procedure; Discontinuous Galerkin methods; Euler equations
We compare four different approximate solvers for the generalized Riemann problem (GRP) for non-linear systems of hyperbolic equations with source terms. The GRP is a special Cauchy problem for a hyperbolic system with source terms whose initial condition is piecewise smooth. We briefly review the four solvers currently available and carry out a systematic assessment of these in terms of accuracy and computational efficiency. These solvers are the building block for constructing high-order numerical schemes of the ADER type for solving the general initial-boundary value problem for inhomogeneous systems in multiple space dimensions, in the frameworks of finite volume and discontinuous Galerkin finite element methods. (C) 2012 Elsevier Inc. All rights reserved.
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