New directional vector limiters for discontinuous Galerkin methods

Beitrag in einer Fachzeitschrift

Details zur Publikation

Autor(en): Hajduk H, Kuzmin D, Aizinger V
Zeitschrift: Journal of Computational Physics
Jahr der Veröffentlichung: 2019
Band: 384
Seitenbereich: 308-325
ISSN: 0021-9991


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 tensorvalued 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. (C) 2019 Elsevier Inc. All rights reserved.

FAU-Autoren / FAU-Herausgeber

Aizinger, Vadym, Ph.D.
Lehrstuhl für Angewandte Mathematik

Autor(en) der externen Einrichtung(en)
Technische Universität Dortmund


Hajduk, H., Kuzmin, D., & Aizinger, V. (2019). New directional vector limiters for discontinuous Galerkin methods. Journal of Computational Physics, 384, 308-325.

Hajduk, Hennes, Dmitri Kuzmin, and Vadym Aizinger. "New directional vector limiters for discontinuous Galerkin methods." Journal of Computational Physics 384 (2019): 308-325.


Zuletzt aktualisiert 2019-26-03 um 07:38