Chapter 7 - Unstructured Finite Volume Method

Abstract

The finite volume method is extended in this chapter to unstructured mesh topology. The Gauss divergence theorem, which serves as the foundation of the finite volume method, is first ascribed a physical interpretation. Next, it is used to discretize the generalized advection–diffusion equation using the finite volume method on an arbitrary unstructured mesh. The diffusion flux at a cell face is split into normal and tangential components and derivation of both components is presented in detail. Processing the mesh to generate connectivity information is also considered, followed by a discussion of the procedures for calculating critical geometric quantities, such as surface area, volume, surface normal, and surface tangents. The steps required to develop an unstructured finite volume code from ground up are listed. The chapter concludes with an example that demonstrates all of these concepts.