Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

Hendrik Ranocha*, Lisandro Dalcin, Matteo Parsani, David I. Ketcheson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications.

Original languageEnglish (US)
Pages (from-to)1191-1228
Number of pages38
JournalCommunications on Applied Mathematics and Computation
Volume4
Issue number4
DOIs
StatePublished - Dec 2022

Bibliographical note

Funding Information:
Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at KAUST. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure. Special thanks are extended to the McLaren F1 racing Team for providing data, CAD geometries, and setup of the Imperial Front Wing test case.

Funding Information:
Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at KAUST. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure. Special thanks are extended to the McLaren F1 racing Team for providing data, CAD geometries, and setup of the Imperial Front Wing test case.

Publisher Copyright:
© 2021, The Author(s).

Keywords

  • Compressible Euler equations
  • Compressible Navier-Stokes equations
  • Explicit Runge-Kutta methods
  • hp-adaptive spatial discretizations
  • Step size control

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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