New directional vector limiters for discontinuous Galerkin methods

Journal article


Publication Details

Author(s): Hajduk H, Kuzmin D, Aizinger V
Journal: Journal of Computational Physics
Publication year: 2019
Volume: 384
Pages range: 308-325
ISSN: 0021-9991


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 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 Authors / FAU Editors

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


External institutions
Technische Universität Dortmund


How to cite

APA:
Hajduk, H., Kuzmin, D., & Aizinger, V. (2019). New directional vector limiters for discontinuous Galerkin methods. Journal of Computational Physics, 384, 308-325. https://dx.doi.org/10.1016/j.jcp.2019.01.032

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

BibTeX: 

Last updated on 2019-26-03 at 07:38