Finite Volume Method

Finite volume method (FVM) is another widely used numerical technique. The fundamental conservation property of the FVM makes it the preferred method compared to various existing methods viz. finite difference method (FDM), finite element method (FEM), etc. In this approach, similar to the known numerical methods like FDM or FEM, the volumes are evaluated at discrete places over a meshed geometry. This chapter explains a brief background of the FVM with respect to a simple example problem. It presents the discretization techniques of the FVM. The FVM depends on approximate solution of the integral form with respect to conservation equations. In the FVM, the given domain of differential equation is divided into a set of nonoverlapping finite volumes and then the respective integrals of the conservation equations are evaluated by using nodal (function) values at computational nodes. For easy understanding of readers, the chapter also presents the FVM procedure by solving the convection‐diffusion problem.