A Semi-Lagrangian Transport Scheme with Spectral Interpolation

Abstract

Advective transport using the flexible and stable semi-Lagrangian scheme coupled with the highly accurate spectral interpolation in a limited domain is demonstrated. The spectral method for solving nonperiodic boundary problems is based on a technique of decomposing a solution into a polynomial and a periodic Fourier residual. The fast Fourier transform is applied only to a periodic residual. A fifth-order polynomial is used and a method to obtain it is described. The numerical tests of the advective transport of a mass in a nonuniform deformational and a uniform rotational flow, as well as the plume transport from a continuous source, are also presented. As will be shown in the paper, the technique proved to be efficient and accurate, providing excellent results.