The area of a surface is computed by summing the areas of the facets that define the surface. Facets on a surface are either triangular or quadrilateral in shape.
 | (25–11) |
An integral on a surface is computed by summing the product of the facet area and the selected field variable facet value, such as density or pressure. For details on the computation of the facet values, see Surface Integration.
The area-weighted average of a quantity is computed by dividing the summation of the product of the selected field variable and facet area by the total area of the surface:
 | (25–12) |
The custom vector-based flux of a quantity is computed by summing the value of the selected field variable multiplied by the dot product of the custom velocity vector and the area vector.
 | (25–13) |
The custom vector flux is computed by summing the dot product of the custom velocity vector and the area vector.
 | (25–14) |
The custom vector-weighted average of a quantity is computed by dividing the summation of the value of the selected field variable multiplied by the absolute value of the dot product of the custom velocity vectors and the area vectors by the summation of the absolute value of the dot product of the custom velocity vectors and the area vectors.
 | (25–15) |
The flow rate of a quantity through a surface is computed by summing the value of the selected field variable multiplied by the density and the dot product of the facet area vector and the facet velocity vector.
 | (25–16) |
The mass flow rate through a surface is computed by summing the value of the selected field variable multiplied by the density and the dot product of the facet area vector and the facet velocity vector.
 | (25–17) |
The mass-weighted average of a quantity is computed by dividing the summation of the value of the selected field variable multiplied by the absolute value of the dot product of the facet area and momentum vectors by the summation of the absolute value of the dot product of the facet area and momentum vectors (surface mass flux):
 | (25–18) |
Note: Ansys Fluent uses bulk-based fluxes for computing mass-weighted averages. With
bulk-density represented as 
and bulk-velocity represented as 
, the discrete mass-weighted average of a quantity
is given by:
 | (25–19) |
where the index, 
, goes over the face points. Since 
is always positive, it can be re-written as:
 | (25–20) |
The computation of 
depends on the model. For single-phase cases, it
is:
 | (25–21) |
where 
is the porosity of the medium. For multiphase cases, it
is:
 | (25–22) |
where the summation of 
goes over the phases, and 
is the 
phase-fraction computed from the appropriate model.
Important: For multiphase flows, the mass-weighted average computation is only recommended for mixture-level variables, not phase-level ones.
The sum of a specified field variable on a surface is computed by summing the value of the selected variable at each facet:
 | (25–23) |
The facet average of a specified field variable on a surface is computed by dividing the summation of the facet values of the selected variable by the total number of facets. See Node, Cell, and Facet Values in the User's Guide for definitions of facet values.
 | (25–24) |
The facet minimum of a specified field variable on a surface is the minimum facet value of the selected variable on the surface. See Node, Cell, and Facet Values in the User's Guide for definitions of facet values.
The facet maximum of a specified field variable on a surface is the maximum facet value of the selected variable on the surface. See Node, Cell, and Facet Values in the User's Guide for definitions of facet values.
The vertex average of a specified field variable on a surface is computed by dividing the summation of the vertex values of the selected variable by the total number of vertices. See Node, Cell, and Facet Values in the User's Guide for definitions of vertex values.
 | (25–25) |
The vertex minimum of a specified field variable on a surface is the minimum vertex value of the selected variable on the surface. See Node, Cell, and Facet Values in the User's Guide for definitions of vertex values.
The vertex maximum of a specified field variable on a surface is the maximum vertex value of the selected variable on the surface. See Node, Cell, and Facet Values in the User's Guide for definitions of vertex values.
The standard deviation of a specified field variable on a surface is computed using the mathematical expression below:
 | (25–26) |
where 
is the cell value of the selected variables at each facet,
is the mean of 
and 
is the total number of facets. See Node, Cell, and Facet Values in the User's Guide for definitions
of facet values.
The uniformity index represents how a specified field variable varies over a surface, where a value of 1 indicates the highest uniformity. The uniformity index can be weighted by area or mass: the area-weighted uniformity index captures the variation of the quantity (for example, the species concentration), whereas the mass-weighted uniformity index captures the variation of the flux (for example, the species flux).
The area-weighted uniformity index (
) of a specified field
variable 
is calculated using the following equation:
 | (25–27) |
where 
is the facet index of a surface with 
facets, and 
is the average value of the field variable over
the surface:
 | (25–28) |
The equation for the mass-weighted uniformity index (
) is different
than Equation 25–27 in that it incorporates flux terms:
 | (25–29) |
where 
is
the average flux of the field variable through the surface:
 | (25–30) |
