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Rueda-Ramirez, Andres M., Pazner, Will and Gassner, Gregor J. (2022). Subcell limiting strategies for discontinuous Galerkin spectral element methods. Comput. Fluids, 247. OXFORD: PERGAMON-ELSEVIER SCIENCE LTD. ISSN 1879-0747

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Abstract

We present a general family of subcell limiting strategies to construct robust high-order accurate nodal dis-continuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre-Gauss-Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods.By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach.We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Rueda-Ramirez, Andres M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Pazner, Will UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-670408
DOI:	10.1016/j.compfluid.2022.105627
Journal or Publication Title:	Comput. Fluids
Volume:	247
Date:	2022
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Place of Publication:	OXFORD
ISSN:	1879-0747
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FLUX-CORRECTED TRANSPORT; NONLINEAR CONSERVATION-LAWS; GODUNOV-TYPE METHODS; INVARIANT DOMAINS; SCHEMES; EULER; MHD; FCT; DISCRETIZATION; APPROXIMATION Multiple languages Computer Science, Interdisciplinary Applications; Mechanics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67040