Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 372, Issue -, Pages 640-666Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.06.031
Keywords
Conservation; Entropy stable scheme; Residual distribution scheme; Discontinuous Galerkin scheme; Finite element method
Funding
- SNSF project High fidelity simulation for compressible materials [200021_153604]
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We are interested in the approximation of a steady hyperbolic problem. In some cases, the solution can satisfy an additional conservation relation, at least when it is smooth. This is the case of an entropy. In this paper, we show, starting from the discretization of the original PDE, how to construct a scheme that is consistent with the original PDE and the additional conservation relation. Since one interesting example is given by the systems endowed by an entropy, we provide one explicit solution, and show that the accuracy of the new scheme is at most degraded by one order. In the case of a discontinuous Galerkin scheme and a Residual distribution scheme, we show how not to degrade the accuracy. This improves the recent results obtained in [1-4] in the sense that no particular constraints are set on quadrature formula and that a priori maximum accuracy can still be achieved. We study the behavior of the method on a non linear scalar problem. However, the method is not restricted to scalar problems. (C) 2018 Elsevier Inc. All rights reserved.
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