Authors: Hajduk, Hennes
Kuzmin, Dmitri
Aizinger, Vadym
Title: Frame-invariant directional vector limiters for discontinuous Galerkin methods
Language (ISO): en
Abstract: Second and higher order numerical approximations of conservation laws for vector fields call for the use of limiting techniques based on generalized monotonicity criteria. In this paper, we introduce a family of directional vertexbased slope limiters for tensor-valued gradients of formally second-order accurate piecewise-linear discontinuous Galerkin (DG) discretizations. The proposed methodology enforces local maximum principles for scalar products corresponding to projections of a vector field onto the unit vectors of a frame-invariant orthogonal basis. In particular, we consider anisotropic limiters based on singular value decompositions and the Gram-Schmidt orthogonalization procedure. The proposed extension to hyperbolic systems features a sequential limiting strategy and a global invariant domain fix. The pros and cons of different approaches to vector limiting are illustrated by the results of numerical studies for the two-dimensional shallow water equations and for the Euler equations of gas dynamics.
Subject Headings: hyperbolic conservation laws
discontinuous Galerkin methods
vector limiters
shallow water equations
Euler equations
Issue Date: 2018-06
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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