New directional vector limiters for discontinuous Galerkin methods
Hajduk H, Kuzmin D, Aizinger V (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 384
Pages Range: 308-325
DOI: 10.1016/j.jcp.2019.01.032
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.
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Germany (DE)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.
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