A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

Dzanic, Tarik

doi:10.1016/j.jcp.2024.113367

A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

Journal Article · Mon Aug 26 00:00:00 EDT 2024 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2024.113367· OSTI ID:2467589

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Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing

In Dzanic (2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Finally, some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

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

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2467589

Alternate ID(s):: OSTI ID: 2438407

Report Number(s):: LLNL--JRNL-863292; 1096249

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 516; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (12)

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97 MATHEMATICS AND COMPUTING
bounds-preserving
discontinuous Galerkin
high-order
hyperbolic conservation laws
limiting
positivity-preserving

A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

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