A Class of Single-Cell Transportation Schemes

摘要

A class of semi-Lagrangian methods for advection transportation equation are presented. Teh schemes are based on the CIP concept and treat the gradients of the interploation function as additional physical variables. The resulting schemes are highly compact and cover only a single gid-cell. he fundamental scheme is constructed from a rational function. It has third-order accuracy in smooth region anc possesses oscillation suppressing property near discontinuity of steep gradient. There is no need of caluclating slope limiter as othe rhigh resolution schemes do to eliminate numerical oscillation. Some variants of the scheme in 2D are presented and discussed with numerical experiments. Finally, implementation of the schemes on a distributed memory computer is also discussed.