A Class of Semi-Lagrangian Integrated-Mass (SLM) Numerical Transport Algorithms

Abstract

A class of conservative numerical transport algorithms is developed based on the concept of Lagrangian mass transport between fixed cells in which density distribution is estimated on the basis of local and adjacent gridpoint values. Upstream and downstream variants of the proposed class of semi-Lagrangian integrated-mass (SLIM) schemes are presented; the upstream form corresponds in essence to the scheme developed by Rancic. Both variants of SLIM are compared with the traditional semi-Lagrangian scheme in two spatial dimensions in Cartesian geometry: on canonical tests, as well as in a bubble convection experiment.