Finite Volume Methods

Abstract

As in the previous chapter, we consider only the generic conservation equation for a quantity ϕ and assume that the velocity field and all fluid properties are known. The finite volume method uses the integral form of the conservation equation as the starting point:

$$ \int_s {\rho \varphi v \cdot ndS = } \int_s {\Gamma grad\varphi \cdot ndS + \int_\Omega q } _\varphi d\Omega $$

(4.1)

The solution domain is subdivided into a finite number of small control volumes (CVs) by a grid which, in contrast to the finite difference (FD) method, defines the control volume boundaries, not the computational nodes. For the sake of simplicity we shall demonstrate the method using Cartesian grids; complex geometries are treated in Chap. 8.M