Subcell limiting strategies for discontinuous Galerkin spectral element methods

Rueda-Ramírez, Andrés M.; Pazner, Will; Gassner, Gregor J.

doi:10.1016/j.compfluid.2022.105627

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Journal Article · Fri Aug 12 00:00:00 EDT 2022 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2022.105627· OSTI ID:2396432

^[1]; Pazner, Will ^[2]; Gassner, Gregor J. ^[1]

Univ. of Cologne (Germany)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous 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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); European Research Council (ERC)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2396432

Alternate ID(s):: OSTI ID: 1961086

Report Number(s):: LLNL--JRNL-831293; 1048229

Journal Information:: Computers and Fluids, Journal Name: Computers and Fluids Vol. 247; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Discontinuous Galerkin spectral element methods subcell limiting
Entropy stability
Invariant domain preservation
Shock capturing

Subcell limiting strategies for discontinuous Galerkin spectral element methods

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References (57)

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