Field by field hybrid upwind splitting methods

Abstract

A new and general approach to upwind splitting is presented. The design principle combines the robustness of flux vector splitting schemes in the capture of nonlinear waves and the accuracy of some flux difference splitting schemes in the resolution of linear waves. The new schemes are derived following a general hybridization technique performed directly at the basic level of the field by field decomposition involved in FDS methods. The scheme does not use a spatial switch to be tuned up according to the local smoothness of the approximate solution.