DoD Stabilization for non-linear hyperbolic conservation laws on cut cell meshes in one dimension

Sandra May and Florian Streitbürger

Applied Mathematics and Computation, 2022, vol. 419, issue C

Abstract: In this work, we present the Domain of Dependence (DoD) stabilization for systems of hyperbolic conservation laws in one space dimension. The base scheme uses a method of lines approach consisting of a discontinuous Galerkin scheme in space and an explicit strong stability preserving Runge-Kutta scheme in time. When applied on a cut cell mesh with a time step length that is appropriate for the size of the larger background cells, one encounters stability issues. The DoD stabilization consists of penalty terms that are designed to address these problems by redistributing mass between the inflow and outflow neighbors of small cut cells in a physical way. For piecewise constant polynomials in space and explicit Euler in time, the stabilized scheme is monotone for scalar problems. For higher polynomial degrees p, our numerical experiments show convergence orders of p+1 for smooth flow and robust behavior in the presence of shocks.

Keywords: Embedded boundary method; Cut cell; Small cell problem; Discontinuous Galerkin method; DoD Stabilization; Hyperbolic conservation law (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:419:y:2022:i:c:s0096300321009371

DOI: 10.1016/j.amc.2021.126854

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