Search for Time accuracy: A Variable Time-stepping Algorithm for Computational Fluid Dynamics

Speaker: Wenlong Pei (OSU)
Dates: 2022/12/01
Abstract: Dahlquist, Liniger, and Nevanlinna proposed a two-step time-stepping scheme for systems of ordinary differential equations (ODEs) in 1983. The little-explored variable time-stepping scheme has advantages in numerical simulations for its fine properties such as unconditional G-stability and second-order accuracy. We simplify its implementation through time filters (pre-filter and post-filter) on a certain first-order implicit method. The adaptivity algorithm for this variable time-stepping scheme, highly reducing computation cost as well as keeping time accuracy, has been applied to systems of ODEs and flow models. Moreover we have applied this method to Navier Stokes equations for stability and error analysis.