SIMPLE Solver Algorithm

The SIMPLE algorithm is used to control the overall solution. This algorithm may be summarized as follows:

The basic steps in the solution update are as follows:

Set the boundary conditions.

Computed the reconstruction gradients of velocity and pressure.

Compute the velocity and pressure gradients.

Solve the discretized momentum equation to create the intermediate velocity field

Compute the uncorrected mass fluxes at faces

Solve the pressure correction equation to produce cell values of the pressure correction

Update the pressure field:

where

is the under-relaxation factor for pressure.

Update the boundary pressure corrections

Correct the face mass fluxes:

Correct the cell velocities:

where

is the gradient of the pressure corrections,

is the vector of central coefficients for the discretized linear system representing the velocity equation and

is the cell volume.

Update density due to pressure changes.

Free all temporary storage.