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Zbl 1203.76122
Xiu, D.; Sherwin, S.J.; Dong, S.; Karniadakis, G.E.
Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows. (English)
[J] J. Sci. Comput. 25, No. 1-2, 323-346 (2005). ISSN 0885-7474; ISSN 1573-7691/e

Summary: 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.

MSC 2000:: *76M25 Other numerical methods
65M70 Spectral, collocation and related methods (IVP of PDE)

Keywords: semi-Lagrangian method; spectral element method; incompressible flow

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