Application of the Piecewise Parabolic Method (PPM) to meteorological modeling

The Piecewise Parabolic Method (PPM), a numerical technique developed in astrophysics for modelling fluid flows with strong shocks and discontinuities, is adapted for treating sharp gradients in small-scale meteorological flows. PPM is a finite volume scheme, and thus represents physical variables as averages over a grid zone rather than single values at discrete points. A unique, monotonic parabola is fit to the zone average of each dependent variable using information from neighboring zone averages. Each zone boundary is treated as a discontinuity. Comparisons made against gridpoint cloud models reveal that PPM provides superior solutions at equivalent spatial resolution. The PPM model has excellent mass and energy conservation properties, and exhibits virtually no numerical dissipation of resolvable modes. -from Authors