A VARIABLE EXPLICIT IMPLICIT NUMERICAL-METHOD FOR CALCULATING ADVECTION ON UNSTRUCTURED MESHES/

A variable explicit/implicit numerical method is presented for calcula ting fluid advection on hybrid unstructured meshes. The method is inte nded for unsteady flows that have a large range of advective time scal es, with subregions where the how may be quasi-steady on time scales o f interest. The method generalizes the method of Collins, Collela, and Glaz by providing an explicit-to-implicit switching criterion that is suitable for use on unstructured meshes. No directional splitting is used; upwinding is in the direction of the material velocity, and thus we define and use a new multidimensional limited gradient that genera lizes Van Leer's MUSCL limiting [7]. After reviewing the one-dimension al method of Collins, Collela, and Glaz, we present the generalization to hybrid unstructured grids and detail the results of four example c alculations that demonstrate the accuracy and flexibility of the new m ethod. (C) 1998 Academic Press.