TY - JOUR
T1 - On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics
AU - Ranocha, Hendrik
AU - Winters, Andrew R.
AU - Castro, Hugo Guillermo
AU - Dalcin, Lisandro
AU - Schlottke-Lakemper, Michael
AU - Gassner, Gregor J.
AU - Parsani, Matteo
N1 - Funding Information:
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, partially funded by the Swedish Research Council under Grant Agreement No. 2018-05973. Hugo Guillermo Castro was funded through the award P2021-0004 of King Abdullah University of Science and Technology. Some of the simulations were enabled by the Supercomputing Laboratory and the Extreme Computing Research Center at King Abdullah University of Science and Technology. Gregor Gassner acknowledges 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).
Publisher Copyright:
© 2023, The Author(s).
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Adaptivity in space and time
KW - Compressible fluid dynamics
KW - Explicit Runge-Kutta (RK) methods
KW - Shock capturing
KW - Step size control
UR - http://www.scopus.com/inward/record.url?scp=85160091035&partnerID=8YFLogxK
U2 - 10.1007/s42967-023-00264-y
DO - 10.1007/s42967-023-00264-y
M3 - Article
AN - SCOPUS:85160091035
SN - 2096-6385
JO - Communications on Applied Mathematics and Computation
JF - Communications on Applied Mathematics and Computation
ER -