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Shock capturing for discontinuous Galerkin methods using finite volume subcells. (English) Zbl 1426.76429
Fuhrmann, Jürgen (ed.) et al., Finite volumes for complex applications VII – elliptic, parabolic and hyperbolic problems. Proceedings of the FVCA 7, Berlin, Germany, June 15–20, 2014. Vol. II. Cham: Springer. Springer Proc. Math. Stat. 78, 945-953 (2014).
Summary: We present a shock capturing procedure for high order discontinuous Galerkin methods, by which shock regions are refined and treated by the finite volume techniques. Hence, our approach combines the good properties of the discontinuous Galerkin method in smooth parts of the flow with the perfect properties of a total variation diminishing finite volume method for resolving shocks without spurious oscillations. Due to the subcell approach the interior resolution on the discontinuous Galerkin grid cell is preserved and the number of degrees of freedom remains the same. In this paper we focus on an implementation of this coupled method and show our first results.
For the entire collection see [Zbl 1291.65005].

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
76N15 Gas dynamics (general theory)
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