An Accurate Semi-Lagrangian Scheme for Raindrop Sedimentation

Abstract

An accurate method for explicitly computing the transport of rainwater is devised and tested. The scheme is conservative and positive definite. A cubic polynomial is employed to approximate the spatial distribution of the rainwater; thus, the resulting scheme is of high accuracy. With a slope modification, numerical oscillations can be easily eliminated in the vicinity of large gradients. Being essentially of Lagrangian type, the scheme is stable even with a Courant?Friedrichs?Lewy number larger than 1. The scheme was tested with the numerical example of Kato and was found to have a computational stability similar to the box-Lagrangian scheme, but it is more accurate.