Journal of Scientific Computing

, Volume 25, Issue 1, pp 323–346 | Cite as

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

  • D. Xiu
  • S. J. Sherwin
  • S. Dong
  • G. E. Karniadakis


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.


Semi-Lagrangian method spectral element method incompressible flow 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • D. Xiu
    • 1
  • S. J. Sherwin
    • 2
  • S. Dong
    • 1
  • G. E. Karniadakis
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUK
  2. 2.Department of AeronauticsImperial CollegeLondonUK

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