Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 229, Issue 16, Pages 5653-5691Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.04.002
Keywords
Hyperbolic conservation laws; Time dependent problems; Second order schemes; Explicit schemes; Residual distribution; Runge-Kutta time-stepping
Funding
- EU [AST5-CT-2006-030719]
- ERC [226316]
- European Research Council (ERC) [226316] Funding Source: European Research Council (ERC)
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In this paper, we construct spatially consistent explicit second order discretizations for time dependent hyperbolic problems, starting from a given residual distribution (RD) discrete approximation of the steady operator. We review the existing knowledge on consistent RD mass matrices and highlight the relations between different definitions. We then introduce our explicit approach which is based on three main ingredients: first recast the RD discretization as a stabilized Galerkin scheme, then use a shifted time discretization in the stabilization operator, and lastly apply high order mass lumping on the Galerkin component of the discretization. The discussion is particularly relevant for schemes of the residual distribution type [18,3] which we will use for all our numerical experiments. However, similar ideas can be used in the context of residual-based finite volume discretizations such as the ones proposed in [14,12]. The schemes are tested on a wide variety of classical problems confirming the theoretical expectations. (C) 2010 Elsevier Inc. All rights reserved.
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