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

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.