A quantitative analysis of the dissipation inherent in semi- Lagrangian advection

Abstract

The amplification factors of first, second, third, and fourth-order Lagrangian interpolation schemes are used to calculate the dissipative decay time scale and the resulting effective eddy viscosity as functions of wavelength and residual Courant number. The dissipation inherent in the semi-Lagrangian advection can then be compared to more traditional forms of dissipation, such as Laplacian or biharmonic eddy viscosity. The correspondence between semi-Lagrangian advection and more traditional Eulerian techniques is emphasized. The dependence of the dissipation on the time step and grid spacing is also discussed. -from Author