Overset Surface Integral

This report is particularly useful for overset mesh simulations. It computes the surface integral of a scalar quantity by taking into account the area of the overlapping cells of overlapping regions only once.

The surface integral of a scalar quantity is computed as:

Figure 1. EQUATION_DISPLAY
Scalar Surface Integralϕda=fϕfAf
(394)

where ϕ f is the face value of the selected scalar and A f is the corrected face area magnitude. The corrected cell face area is obtained by evaluating the Overset Grid Area field function. See Overset Mesh Field Function Reference.

For axisymmetric cases, the mesh is assumed to be swept through an angle of 1 radian. For applications that use a mass flow inlet, the mass flow is therefore given in kg/rad s. Any volumetric or area quantities reported for the Axisymmetric model are assumed to be for a sector of 1 radian.

For two-dimensional models, the surface is assumed to have a unit depth (in SI units). Therefore any volumetric or area quantities that are reported for a two-dimensional model are assumed to be “per meter”.

The surface integral of a vector quantity is computed as:

Figure 2. EQUATION_DISPLAY
Vector Surface Integral=S(Fn^)da
(395)

where n ^ is a unit normal vector and F is the vector field. Similarly to the scalar surface integral calculation, the quantity in the integrand is computed for each face and the result is the sum over all faces. This calculation is supported for surfaces in both 2D and 3D models. Vector surface integrals are not supported for surface intersections with shell regions (e.g., thin films). Vector surface integrals cannot be computed for degenerate geometries (geometries for which the surface normal is not well-defined), such as plane-boundary intersections or plane-plane intersections within a region.