An Explicit High Order Accurate Predictor-Corrector Time Integration Method with Consistent Local Time-Stepping for Discontinuous Galerkin Schemes

摘要

In this paper a new explicit discretization for the time integration of the semi discrete discontinuous Galerkin (DG) scheme is presented. The time integration is based on a predictor-corrector approach, where the predictor is the solution of the so-called predictor ODEs, which are simplified versions of the DG ODEs. For the time integration of the predictor ODEs a continuous extension Runge-Kutta scheme is used. The class of schemes shares the property that an analytically, polynomial time solution is available. This analytical time polynomial and the fact that the DG discretization only couples direct neighbor grid cells allows the adoption of a local time stepping algorithm. Despite the local time steps the fully discrete scheme is high order accurate in time, fully conservative and ideally suited for massively parallel computations, allowing an efficient discretization of large scale time dependent problems.