Abstract

AbstractThe aim of this paper is to investigate and evaluate a multi-stage and multi-step method that is an evolution of the more common Backward Differentiation Formulae (BDF). This new class of formulae, called Two Implicit Advanced Step-point (TIAS), has been applied to a high-order Discontinuous Galerkin (DG) discretization of the Navier-Stokes equations, coupling the high temporal accuracy gained by the TIAS scheme with the high space accuracy of the DG method. The performance of the DG-TIAS scheme has been evaluated by means of two test cases: an inviscid isentropic convecting vortex and a laminar vortex shedding behind a circular cylinder. The advantages of the high-order time discretization are illustrated comparing the sixth-order accurate TIAS scheme with the second-order accurate BDF scheme using the same spatial discretization.KeywordsCircular CylinderSpatial DiscretizationDiscontinuous GalerkinTemporal SchemeBackward Differentiation FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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