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New directional vector limiters for discontinuous Galerkin methods

Title data

Hajduk, Hennes ; Kuzmin, Dmitri ; Aizinger, Vadym:
New directional vector limiters for discontinuous Galerkin methods.
In: Journal of Computational Physics. Vol. 384 (2019) . - pp. 308-325.
ISSN 1090-2716
DOI: https://doi.org/10.1016/j.jcp.2019.01.032

Abstract in another language

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 vertex-based 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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Hyperbolic conservation laws; Discontinuous Galerkin methods; Vector limiters; Objectivity; Shallow water equations; Euler equations
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Lehrstuhl Wissenschaftliches Rechnen
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Lehrstuhl Wissenschaftliches Rechnen > CLehrstuhl Wissenschaftliches Rechnen - Univ.-Prof. Dr. Mario Bebendorf
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics >
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > >
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions > Research Centres > Forschungszentrum für Wissenschaftliches Rechnen an der Universität Bayreuth - HPC-Forschungszentrum
Result of work at the UBT: No
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 24 Sep 2019 07:28
Last Modified: 24 Sep 2019 07:28
URI: https://eref.uni-bayreuth.de/id/eprint/52379