Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows

Authors:
D. Xiu;S. J. Sherwin;S. Dong;G. E. Karniadakis
Affiliations:
Division of Applied Mathematics, Brown University, Providence, UK;Department of Aeronautics, Imperial College, London, UK;Division of Applied Mathematics, Brown University, Providence, UK;Division of Applied Mathematics, Brown University, Providence, UK
Venue:
Journal of Scientific Computing
Year:
2005

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Abstract

We present a review of the semi-Lagrangian method for advection---diffusion and incompressible Navier---Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable.