High Resolution Nvd Diierencing Scheme for Arbitrarily Unstructured Meshes

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 TVD and NVD families of diierencing schemes. All of those 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 modiication of the NVD criterion which localises it and thus makes it applicable irrespective of the mesh structure, thus facilitating the implementation of \standard" bounded diierencing schemes on unstructured meshes. Based on this strategy, a new bounded version of Central Diier-encing constructed on the compact computational molecule is proposed and its performance is compared with other popular diierencing schemes on several model problems.