Eliminating the interpolation associated with the semi-Lagrangian scheme.

Abstract

There are several reasons why it is desirable to eliminate the interpolation associated with the conventional semi-Lagrangian scheme. Interpolation leads to smoothing and is also the most costly operation associated with the technique. Furthermore, its elimination produces a scheme that is more readily adaptable to a spectral model. In the conventional semi-Lagrangian method, in order to predict a field value at grid point (Ai, Yj) it is necessary to calculate the trajectory over one time step for the fluid element that arrives at (Xi, Yj). One then moves along this trajectory in order to extract the field value at an upstream location that generally lies between the grid points, and hence requires the use of interpolation formula. This trajectory can be represented as a vector. In the new scheme, the trajectory vector is considered to be the sum of two other vectors - a first vector joining (Xi, Yj) to the grid point (Xu, Yu) nearest the upstream location, and a second vector joining (Xu, Yu) to the upstream location. -from Author