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

Authors:
Andrew R. Winters;David A. Kopriva
Affiliations:
Department of Mathematics, The Florida State University, Tallahassee, USA 32306;Department of Mathematics, The Florida State University, Tallahassee, USA 32306
Venue:
Journal of Scientific Computing
Year:
2014

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Abstract

We derive and evaluate an explicit local time stepping (LTS) integration for the discontinuous Galerkin spectral element method on moving meshes. The LTS procedure is derived from Adams---Bashforth multirate time integration methods. We also present speedup and memory estimates, which show that the explicit LTS integration scales well with problem size. Time-step refinement studies with static and moving meshes show that the approximations are spectrally accurate in space and have design temporal accuracy. The numerical tests validate theoretical estimates that the LTS procedure can reduce computational cost by as much as an order of magnitude for time accurate problems.