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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:
where | |||
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= | density | |
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= | velocity vector (=
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= | surface area vector | |
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= | diffusion coefficient for
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= | gradient of
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= | source of
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Equation 18.2-1 is applied to each control volume, or cell, in the computational domain. The two-dimensional, triangular cell shown in Figure 18.2.1 is an example of such a control volume. Discretization of Equation 18.2-1 on a given cell yields
where | |||
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= | number of faces enclosing cell | |
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= | value of
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= | mass flux through the face | |
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= | area of face
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= | gradient of
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= | cell volume |
Where
is defined in Section
18.3.2. 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.