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

Hendrik Ranocha; Lisandro Dalcin; Matteo Parsani; David I. Ketcheson

doi:10.1007/s42967-021-00159-w

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 journal › Article › peer-review

17 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 language	English (US)
Pages (from-to)	1191-1228
Number of pages	38
Journal	Communications on Applied Mathematics and Computation
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/s42967-021-00159-w
State	Published - 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

Access to Document

10.1007/s42967-021-00159-w

Cite this

@article{9115d2f8f726446f836ceb904cb69e29,

title = "Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics",

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.",

keywords = "Compressible Euler equations, Compressible Navier-Stokes equations, Explicit Runge-Kutta methods, hp-adaptive spatial discretizations, Step size control",

author = "Hendrik Ranocha and Lisandro Dalcin and Matteo Parsani and Ketcheson, {David I.}",

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{\textquoteright}s Excellence Strategy EXC 2044-390685587, Mathematics M{\"u}nster: 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{\textquoteright}s Excellence Strategy EXC 2044-390685587, Mathematics M{\"u}nster: 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: {\textcopyright} 2021, The Author(s).",

year = "2022",

month = dec,

doi = "10.1007/s42967-021-00159-w",

language = "English (US)",

volume = "4",

pages = "1191--1228",

journal = "Communications on Applied Mathematics and Computation",

issn = "2096-6385",

publisher = "Springer",

number = "4",

}

TY - JOUR

T1 - Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

AU - Ranocha, Hendrik

AU - Dalcin, Lisandro

AU - Parsani, Matteo

AU - Ketcheson, David I.

N1 - 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).

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

KW - Compressible Euler equations

KW - Compressible Navier-Stokes equations

KW - Explicit Runge-Kutta methods

KW - hp-adaptive spatial discretizations

KW - Step size control

UR - http://www.scopus.com/inward/record.url?scp=85121707103&partnerID=8YFLogxK

U2 - 10.1007/s42967-021-00159-w

DO - 10.1007/s42967-021-00159-w

M3 - Article

AN - SCOPUS:85121707103

SN - 2096-6385

VL - 4

SP - 1191

EP - 1228

JO - Communications on Applied Mathematics and Computation

JF - Communications on Applied Mathematics and Computation

IS - 4

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this