Efficient and High-Order Explicit Local Time Stepping on Moving DG Spectral Element Meshes

We outline and extend results for an explicit local time stepping (LTS) strategy designed to operate with the discontinuous Galerkin spectral element method (DGSEM). The LTS procedure is derived from Adams-Bashforth multirate time integration methods. The new results of the LTS method focus on parallelization and reformulation of the LTS integrator to maintain conservation. Discussion is focused on a moving mesh implementation, but the procedures remain applicable to static meshes. In numerical tests, we demonstrate the strong scaling of a parallel, LTS implementation and compare the scaling properties to a parallel, global time stepping (GTS) Runge-Kutta implementation. We also present time-step refinement studies to show that the redesigned, conservative LTS approximations are spectrally accurate in space and have design temporal accuracy.