High resolution NVD differencing scheme for arbitrarily unstructured meshes

Abstract

The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the well-known total variation diminishing (TVD) and normalised variable diagram (NVD) families of differencing schemes. All of these use some sort of an ‘unboundedness indicator’ in order to determine the parts of the domain where intervention in the discretisation practice is needed. These, however, all use the ‘far upwind’ value for each face under consideration, which is not appropriate for unstructured meshes. This paper proposes a modification of the NVD criterion that localises it and thus makes it applicable irrespective of the mesh structure, facilitating the implementation of ‘standard’ bounded differencing schemes on unstructured meshes. Based on this strategy, a new bounded version of central differencing constructed on the compact computational molecule is proposed and its performance is compared with other popular differencing schemes on several model problems. Copyright © 1999 John Wiley & Sons, Ltd.