We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fuid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the...We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fuid 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 efcient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing 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 pack-ages Trixi.jl with OrdinaryDiffEq.jl and the C/Fortran code SSDC based on PETSc.展开更多
基金Open Access funding enabled and organized by Projekt DEAL.Andrew Winters was funded through Vetenskapsrådet,Sweden Grant Agreement 2020-03642 VR.Some computations were enabled by resources provided by the Swedish National Infrastructure for Computing(SNIC)at Tetralith,par-tially funded by the Swedish Research Council under Grant Agreement No.2018-05973Hugo Guillermo Castro was funded through the award P2021-0004 of King Abdullah University of Science and Technol-ogy.Some of the simulations were enabled by the Supercomputing Laboratory and the Extreme Comput-ing Research Center at King Abdullah University of Science and Technology.Gregor Gassner acknowl-edges funding through the Klaus-Tschira Stiftung via the project“HiFiLab”.Gregor Gassner and Michael Schlottke-Lakemper acknowledge funding from the Deutsche Forschungsgemeinschaft through the research unit“SNuBIC”(DFG-FOR5409).
文摘We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fuid 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 efcient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing 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 pack-ages Trixi.jl with OrdinaryDiffEq.jl and the C/Fortran code SSDC based on PETSc.
