4. Finite Volume Methods
4.1 Introduction
As in the previous chapter, we consider only the generic conservation equation
for a quantity 4 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:
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.
The usual approach is to define CVs by a suitable grid and assign the
computational node to the CV center. However, one could as well (for structured grids) define the nodal locations first and construct CVs around them,
so that CV faces lie midway between nodes; see Fig. 4.1. Nodes on which
boundary conditions are applied are shown as full symbols in this figure.
Fig. 4.1. Types of FV grids: nodes centered in CVs (left) and CV faces centered
between nodes (right)