A comparative study of implicit Jacobian-free Rosenbrock-Wanner, ESDIRK and BDF methods for unsteady flow simulation with high-order flux reconstruction formulations

Thumbnail Image

Files

1904.04825.pdf (1.32 MB)

Links to Files

https://arxiv.org/abs/1904.04825

Permanent Link

http://hdl.handle.net/11603/13653

Collections

UMBC Mechanical Engineering Department
UMBC Faculty Collection
UMBC Student Collection

Author/Creator

Author/Creator ORCID

Date

2019-04-09

Type of Work

journal articles preprints
Text

Department

Program

Citation of Original Publication

Lai Wang, Meilin Yu, A comparative study of implicit Jacobian-free Rosenbrock-Wanner, ESDIRK and BDF methods for unsteady flow simulation with high-order flux reconstruction formulations, 2019, https://arxiv.org/abs/1904.04825

Rights

This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.

Subjects

linearly implicit Rosenbrock-Wanner
ESDIRK
Backward Differentiation Formula
Jacobian- Free
reconstruction/correction procedure via reconstruction
high-order spatiotemporal methods
unsteady flows
UMBC High Performance Computing Facility (HPCF)

Abstract

We conduct a comparative study of the Jacobian-free linearly implicit Rosenbrock-Wanner (ROW) methods, the explicit rst stage, singly diagonally implicit Runge-Kutta (ESDIRK) methods, and the second-order backward differentiation formula (BDF2) for unsteady flow simulation using spatially high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) formulations. The pseudo-transient continuation is employed to solve the nonlinear systems resulting from the temporal discretizations with ESDIRK and BDF2. A Jacobian-free implementation of the restarted generalized minimal residual method (GMRES) solver is employed with a low storage element-Jacobi preconditioner to solve linear systems, including those in linearly implicit ROW methods and those from linearization of the nonlinear systems in ESDIRK and BDF2 methods. We observe that all ROW and ESDIRK schemes (from second order to fourth order) are more computationally efficient than BDF2, and ROW methods can potentially be more efficient than ESDIRK methods. However, the convergence tolerance of the GMRES solver for ROW methods needs to be sufficiently tight to preserve the nominal order of accuracy. In general, ESDIRK methods allow a larger physical time step size for unsteady flow simulation than ROW methods do.