Wang, LaiYu, Meilin2019-05-062019-05-062019-04-09Lai 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/1904.04825http://hdl.handle.net/11603/13653We 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.29 pagesen-USThis 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.linearly implicit Rosenbrock-WannerESDIRKBackward Differentiation FormulaJacobian- Freereconstruction/correction procedure via reconstructionhigh-order spatiotemporal methodsunsteady flowsUMBC High Performance Computing Facility (HPCF)Text