Frame-invariant directional vector limiters for discontinuous Galerkin methods
| dc.contributor.author | Hajduk, Hennes | |
| dc.contributor.author | Kuzmin, Dmitri | |
| dc.contributor.author | Aizinger, Vadym | |
| dc.date.accessioned | 2018-06-12T09:01:32Z | |
| dc.date.available | 2018-06-12T09:01:32Z | |
| dc.date.issued | 2018-06 | |
| dc.description.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. | en |
| dc.identifier.issn | 2190-1767 | |
| dc.identifier.uri | http://hdl.handle.net/2003/36906 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-18905 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Ergebnisberichte des Instituts für Angewandte Mathematik;588 | de |
| dc.subject | hyperbolic conservation laws | en |
| dc.subject | discontinuous Galerkin methods | en |
| dc.subject | vector limiters | en |
| dc.subject | objectivity | en |
| dc.subject | shallow water equations | en |
| dc.subject | Euler equations | en |
| dc.subject.ddc | 610 | |
| dc.title | Frame-invariant directional vector limiters for discontinuous Galerkin methods | en |
| dc.type | Text | |
| dc.type.publicationtype | preprint | |
| dcterms.accessRights | open access | |
| eldorado.secondarypublication | false |