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.

翻译：我们研究了可压缩计算流体动力学（CFD）中显式龙格-库塔方法的时间步长控制，包括纳维-斯托克斯方程和双曲型守恒律系统（如欧拉方程）。我们证明了基于误差的方法在广泛应用中具有便利性，并将其与基于库朗-弗里德里希斯-刘维（CFL）数的经典步长控制方法进行了比较。数值算例表明，基于误差的步长控制易于使用、鲁棒且高效，适用于（初始）瞬态阶段、复杂几何构型、非线性激波捕捉方法以及采用非线性熵投影的格式。我们通过从学术界广泛认可的测试问题到工业级大规模计算（基于两个独立代码库：开源Julia包Trixi.jl结合OrdinaryDiffEq.jl，以及基于PETSc的C/Fortran代码SSDC）验证了这些特性。