Transformed Flux-Form Semi-Lagrangian Scheme
NAVAL POSTGRADUATE SCHOOL MONTEREY CA NAVAL OCEAN ANALYSIS AND PREDICTION LAB
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Transformed flux-form semi-Lagrangian TFSL scheme provides stable and accurate algorithm to solve the advection-diffusion equation. Different from the existing flux-form semi- Lagrangian schemes, the flux at boundary of grid cell is treated as the temporal mean between present and next time steps. After the temporal-spatial transformation using the characteristic-line concept, the temporal integration of the flux from present to next time step becomes the spatial integration of the flux at the present time step. This scheme is always stable even for large Courant numbers 20 with the second order accuracy in both time and space. For the Courant number not larger than 0.5, the TFSL scheme reduces to the Lax-Wendroff scheme. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation.
- Physical and Dynamic Oceanography