Markert, Johannes 
ORCID: 0000-0001-6297-9494, Gassner, Gregor and Walch, Stefanie
.
A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods.
Commun. Appl. Math. Comput..
LONDON:
SPRINGERNATURE.
ISSN 2661-8893
Abstract
In this paper, a new strategy for a sub-element-based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low-to-high-order discretizations on this set of data, including a first-order finite volume scheme up to the full-order DG scheme. The different DG discretizations are then blended according to sub-element troubled cell indicators, resulting in a final discretization that adaptively blends from low to high order within a single DG element. The goal is to retain as much high-order accuracy as possible, even in simulations with very strong shocks, as, e.g., presented in the Sedov test. The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing. The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.
| Item Type: | Journal Article | ||||||||||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-566474 | ||||||||||||||||
| DOI: | 10.1007/s42967-021-00120-x | ||||||||||||||||
| Journal or Publication Title: | Commun. Appl. Math. Comput. | ||||||||||||||||
| Publisher: | SPRINGERNATURE | ||||||||||||||||
| Place of Publication: | LONDON | ||||||||||||||||
| ISSN: | 2661-8893 | ||||||||||||||||
| Language: | English | ||||||||||||||||
| Faculty: | Unspecified | ||||||||||||||||
| Divisions: | Unspecified | ||||||||||||||||
| Subjects: | no entry | ||||||||||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/56647 |
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