On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics

Abstract

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.

Keywords

Explicit Runge-Kutta (RK) methods / Step size control / Compressible fluid dynamics / Adaptivity in space and time / Shock capturing / 65L06 / 65M20 / 65M70 / 76M10 / 76M22 / 76N99 / 35L50

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Funding

Vetenskapsrådet(2020-03642 VR)

King Abdullah University of Science and Technology(P2021-0004)

Klaus Tschira Stiftung

Deutsche Forschungsgemeinschaft(DFG-FOR5409)

Universität Hamburg (1037)

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