The performance of classical versus modern finite-volume advection schemes for atmospheric modeling in a one-dimensional test-bed

Abstract

The methods discussed encompass leapfrog time stepping, with both discrete and spectral spatial resolution, various filters, and four Eulerian finite-volume advection schemes: the Prather scheme, the Bott scheme, the piecewise parabolic method (PPM), and four versions of the multidimensional positive-definite advection transport algorithm (MPDATA). The modern advection schemes, perform considerably better where computationally relatively inexpensive schemes (Bott, MPDATA) are recommended if a certain amount of numerical diffusion can be tolerated. The latter problem can almost completely be avoided if more sophisticated methods (Prather, PPM) are employed. This, however, increases the computational effort considerably. -from Author