In order to be able to calculate a physically meaningful pressure even in the zones where geometrical overlapping occurs (that is, to avoid pressure modes associated with the locking of the element), the mass conservation equation is modified to become

(22–4)

where is a relative compression factor, and is the local viscosity.

The relative compression factor is a key aspect of the mesh superposition technique. If there are pressure peaks in regions where a large number of geometrical constraints exist, then the fluid cannot be considered incompressible. To prevent these pressure peaks, the mass conservation equation has been modified so that the fluid is slightly compressible.

The loss or gain of fluid volume per unit time is linked to the Laplacian of the pressure through the relative compression factor. It is absolutely essential to select the value of this factor carefully. If this factor is too small, pressure peaks will appear in tiny contact regions, especially when the mesh is so coarse that one element exists between the boundary and contact regions.

When the factor is too large, the fluid is unphysically compressible and all pressure gradients will be smoothed out, leading to an unphysically low pressure prediction. In Ansys Polydata, the default value of 0.01 has been shown to be the best choice for this factor when stick conditions are considered along the moving parts. When slipping is considered along the moving parts, a lower value may be needed: it can be acceptable to select a value as low as 10^‑5 or 10^‑6 in order to satisfy the mass conservation.

Since a constant pressure per element is assumed, Equation 22–4 is discretized for each element of the flow domain.