Space-Time Transformation in Flux-form Semi-Lagrangian Schemes

  • Author(s): Peter C. Chu and Chenwu Fan
  • DOI: 10.3319/TAO.2009.05.25.01(IWNOP)
  • Keywords: TFSL scheme, Flux-form semi-Lagrangian scheme, Characteristic line, Advection-diffusion equation, Finite volume, ConserConservative finite difference, Equatorial Rossby soliton
  • Citation: Chu, P. C. and C. Fan, 2010: Space-time transformation in flux-form semi-Lagrangian schemes. Terr. Atmos. Ocean. Sci., 21, 17-26, doi: 10.3319/TAO.2009.05.25.01(IWNOP)

With a finite volume approach, a flux-form semi-Lagrangian (TFSL) scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space) for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation), but also has higher accuracy (of a second order in both time and space). The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.

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