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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics
University of Hamburg, Germany.ORCID iD: 0000-0002-3456-2277
Linköping University, Faculty of Science & Engineering. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-5902-1522
King Abdullah University of Science and Technology (KAUST), Saudi Arabia.ORCID iD: 0000-0003-1715-1238
King Abdullah University of Science and Technology (KAUST), Saudi Arabia.ORCID iD: 0000-0001-8086-0155
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2023 (English)In: Communications on Applied Mathematics and Computation, ISSN 2096-6385Article in journal (Refereed) Epub ahead of print
Abstract [en]

We study a temporal step size control of explicit Runge-Kutta (RK) methods for compressible computational fluid dynamics (CFD), including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler equations. We demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy (CFL) number. Our numerical examples show that the error-based step size control is easy to use, robust, and efficient, e.g., for (initial) transient periods, complex geometries, nonlinear shock capturing approaches, and schemes that use nonlinear entropy projections. We demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases, the open source Julia packages Trixi.jl with OrdinaryDiffEq.jl and the C/Fortran code SSDC based on PETSc.

Place, publisher, year, edition, pages
SPRINGERNATURE , 2023.
Keywords [en]
Explicit Runge-Kutta (RK) methods; Step size control; Compressible fluid dynamics; Adaptivity in space and time; Shock capturing
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-194018DOI: 10.1007/s42967-023-00264-yISI: 000992387000001OAI: oai:DiVA.org:liu-194018DiVA, id: diva2:1758258
Funder
Swedish Research Council, 2020-03642Swedish Research Council, 2018-05973German Research Foundation (DFG), DFG-FOR5409
Note

Funding: Projekt DEAL; Vetenskapsradet, Sweden [2020-03642 VR]; Swedish Research Council [2018-05973]; King Abdullah University of Science and Technology [P2021-0004]; Klaus-Tschira Stiftung via the project "HiFiLab"; Deutsche Forschungsgemeinschaft through the research unit "SNuBIC" [DFG-FOR5409]

Available from: 2023-05-22 Created: 2023-05-22 Last updated: 2023-10-10Bibliographically approved

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Winters, Andrew Ross

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