FLUENT uses a control-volume-based technique to convert a general scalar transport equation to an algebraic equation that can be solved numerically. This control volume technique consists of integrating the transport equation about each control volume, yielding a discrete equation that expresses the conservation law on a control-volume basis.
Discretization of the governing equations can be illustrated most easily by considering the unsteady conservation equation for transport of a scalar quantity . This is demonstrated by the following equation written in integral form for an arbitrary control volume as follows:
|=||velocity vector (= in 2D)|
|=||surface area vector|
|=||diffusion coefficient for|
|=||gradient of (= in 2D)|
|=||source of per unit volume|
Equation 25.2-1 is applied to each control volume, or cell, in the computational domain. The two-dimensional, triangular cell shown in Figure 25.2.1 is an example of such a control volume. Discretization of Equation 25.2-1 on a given cell yields
|=||number of faces enclosing cell|
|=||value of convected through face|
|=||mass flux through the face|
|=||area of face , (= in 2D)|
|=||gradient of at face|
Where is defined in Section 25.3.2. The equations solved by FLUENT take the same general form as the one given above and apply readily to multi-dimensional, unstructured meshes composed of arbitrary polyhedra.