Analysis and design of a local time stepping scheme for LES acceleration in reactive and non-reactive flow simulations

Abstract

Explicit time integration based CFD solvers suffer from restriction on the maximum allowable time step computed from the well known Courant-Friedrichs-Lewy (CFL) stability criterion. This restriction poses severe challenge in carrying out large eddy simulation (LES) of reactive and non-reactive flows, where the grid resolution is fine. The challenge of restricted time step is further augmented when dealing with large computational domains that pose a wide disparity in the system time scales. In this study, a numerical methodology is presented based on local time stepping in an overset grid framework. The attainable speedup is found to be a function of the ratio of time steps used in the sub-domains and the ratio of the number of computational degrees of freedom. The method is analyzed using global spectral analysis (GSA) and shows excellent agreement in solution accuracy with the conventional explicit time integration based solver. The impact of local time stepping on the order of accuracy and global conservation properties are also presented. This method is then applied to simulate three flow test cases to demonstrate the ability of the method to reproduce the first and second-order turbulent statistics at reduced computational time.