On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics

TL;DR

This paper evaluates error-based step size control methods for explicit Runge-Kutta schemes in compressible CFD, showing they are robust, efficient, and easier to implement than traditional CFL-based methods across various complex scenarios.

Contribution

It demonstrates the effectiveness and robustness of error-based step size control in compressible fluid dynamics simulations, including complex geometries and shock capturing, across multiple software implementations.

Findings

Error-based control is robust and efficient.

Suitable for complex geometries and shock capturing.

Works well across different CFD code bases.

Abstract

We study temporal step size control of explicit Runge-Kutta 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 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.