TY - JOUR
T1 - Efficient two-step Runge-Kutta methods for fluid dynamics simulations
AU - Figueroa, Alejandro
AU - Jackiewicz, Zdzisław
AU - Löhner, Rainald
N1 - Publisher Copyright:
© 2020 IMACS
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2021/1
Y1 - 2021/1
N2 - Explicit two-step Runge-Kutta (TSRK) methods offer an efficient alternative to traditional explicit Low-Storage Runge-Kutta (LSRK) schemes for solving the Navier-Stokes equations. A special class of TSRK methods that reduce requirement compared to previous TSRK schemes are derived. Schemes of fourth, fifth and sixth order are implemented and tested. The new schemes are evaluated with two common test cases, a 2D cylinder and a 3D Taylor-Green vortex. The results are compared with classical time discretization strategies. Timings obtained in three different hardware configurations show that the new TSRK methods of order four are 25% faster than LSRK schemes of the same order. Fifth and sixth order TSRK methods are tested with the same 3D test case and the results are compared to LSRK algorithms. Results show TSRK schemes of fifth and sixth order are competitive compared to LSRK methods of the same orders, as LSRK methods are of second order for non linear differential systems.
AB - Explicit two-step Runge-Kutta (TSRK) methods offer an efficient alternative to traditional explicit Low-Storage Runge-Kutta (LSRK) schemes for solving the Navier-Stokes equations. A special class of TSRK methods that reduce requirement compared to previous TSRK schemes are derived. Schemes of fourth, fifth and sixth order are implemented and tested. The new schemes are evaluated with two common test cases, a 2D cylinder and a 3D Taylor-Green vortex. The results are compared with classical time discretization strategies. Timings obtained in three different hardware configurations show that the new TSRK methods of order four are 25% faster than LSRK schemes of the same order. Fifth and sixth order TSRK methods are tested with the same 3D test case and the results are compared to LSRK algorithms. Results show TSRK schemes of fifth and sixth order are competitive compared to LSRK methods of the same orders, as LSRK methods are of second order for non linear differential systems.
KW - Computational fluid dynamics solvers
KW - Large-eddy simulations
KW - Stability analysis
KW - Stage order and order conditions
KW - Two-step Runge-Kutta methods
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U2 - 10.1016/j.apnum.2020.08.013
DO - 10.1016/j.apnum.2020.08.013
M3 - Article
AN - SCOPUS:85089848399
VL - 159
SP - 1
EP - 20
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
ER -