Ansys 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:
(23–1) |
where | |
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Equation 23–1 is applied to each control volume, or cell, in the computational domain. The two-dimensional, triangular cell shown in Figure 23.3: Control Volume Used to Illustrate Discretization of a Scalar Transport Equation is an example of such a control volume. Discretization of Equation 23–1 on a given cell yields
(23–2) |
where | |
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Where is defined in Temporal Discretization. The equations
solved by Ansys Fluent take the same general form as the one given above
and apply readily to multi-dimensional, unstructured meshes composed
of arbitrary polyhedra.
For more information, see the following section: