The discretization scheme described in Discretization for a scalar transport equation
is also used to discretize the momentum equations. For example, the 
-momentum equation can be
obtained by setting 
:
 | (23–41) |
If the pressure field and face mass fluxes are known, Equation 23–41 can be solved in the manner outlined in Discretization, and a velocity field obtained. However, the pressure field and face mass fluxes are not known a priori and must be obtained as a part of the solution. There are important issues with respect to the storage of pressure and the discretization of the pressure gradient term; these are addressed next.
Ansys Fluent uses a co-located scheme, whereby pressure and
velocity are both stored at cell centers. However, Equation 23–41 requires the value of the pressure at the
face between cells 
and 
, shown in Figure 23.3: Control Volume Used to Illustrate Discretization of a Scalar
Transport Equation. Therefore, an interpolation
scheme is required to compute the face values of pressure from the
cell values.
Ansys Fluent offers the following options for interpolating the pressure values at the faces. By default the Second Order scheme is used except in the case of mixture or VOF multiphase simulations in which case PRESTO! is the default.
The Linear scheme computes the face pressure as the average of the pressure values in the adjacent cells.
The Standard scheme interpolates the pressure values at the faces using momentum equation coefficients [554]:
(23–42)
This procedure works well as long as the pressure variation between cell centers is smooth. When there are jumps or large gradients in the momentum source terms between control volumes, the pressure profile has a high gradient at the cell face, and cannot be interpolated using this scheme. If this scheme is used, the discrepancy shows up in overshoots/undershoots of cell velocity.
Flows for which the standard pressure interpolation scheme will have trouble include flows with large body forces, such as in strongly swirling flows, in high-Rayleigh-number natural convection and the like. In such cases, it is necessary to pack the mesh in regions of high gradient to resolve the pressure variation adequately.
Another source of error is that Ansys Fluent assumes that the normal pressure gradient at the wall is zero. This is valid for boundary layers, but not in the presence of body forces or curvature. Again, the failure to correctly account for the wall pressure gradient is manifested in velocity vectors pointing in/out of walls.
The Second Order scheme reconstructs the face pressure using a central differencing scheme. The pressure values at the faces are given by:
(23–43)
This scheme may provide improved accuracy over the Standard and Linear schemes.
For flows simulated using the Eulerian multiphase model, the Second Order scheme is not applicable in this form due to large changes in flow properties that may occur across a face. However, by incorporating the effect of the pressure gradient on face pressure into Equation 23–43 and combining it with the Standard scheme (Equation 23–42), the Second Order scheme for Eulerian multiphase flows can be obtained as:
(23–44)
This scheme is more robust than PRESTO! for Eulerian multiphase cases where the mesh topology deviates largely from orthogonality.
The Body Force Weighted scheme computes the face pressure by assuming that the normal gradient of the difference between pressure and body forces is constant. This works well if the body forces are known a priori in the momentum equations (for example, buoyancy and axisymmetric swirl calculations). For Eulerian Multi-Fluid VOF cases where body forces dominate and the mesh deviates largely from orthogonality, the Body Force Weighted scheme is more robust than PRESTO!.
Important: When a case contains porous media, the body-force-weighted scheme is applied only for non-porous faces, where the scheme takes into account the discontinuity of explicit body forces (for example, gravity, swirl, Coriolis) and the discontinuity of pressure gradients for flows with rapidly changing densities (for example, natural convection, VOF). All interior and exterior porous faces are treated with a special scheme that preserves the continuity of the normal velocity across cell faces in spite of the discontinuity of the resistance.
The Modified Body Force Weighted scheme is an extended variant of the Body Force Weighted scheme, which overcomes the shortcomings of the Body Force Weighted scheme for highly viscous and rotating flows and provides better solution stability and robustness in general. This scheme is available with the VOF and Mixture multiphase models only.
The PRESTO! (PREssure STaggering Option) scheme uses the discrete continuity balance for a "staggered" control volume about the face to compute the "staggered" (that is, face) pressure. This procedure is similar in spirit to the staggered-grid schemes used with structured meshes [507]. Note that for triangular, tetrahedral, hybrid, and polyhedral meshes, comparable accuracy is obtained using a similar algorithm. The PRESTO! scheme is available for all meshes.
For recommendations on when to use these alternate schemes, see Choosing the Pressure Interpolation Scheme in the User’s Guide.