The equations solved in this approach arise from the implicit time integration of the incompressible Navier–Stokes equations.
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is computed by first calculating a residual value , resulting from spurious mass flux, then using this mass imbalance to get a new pressure value. The pressure value that is attempted to compute, is such that when plugged into momentum equations a divergence-free velocity field results. The mass imbalance is often also used for control of the outer loop.<br>
The name of this class of methods stems from the fact that the correction of the velocity field is computed through the pressure-field.
The discretization of this is typically done with either the finite element method or the finite volume method. With the latter, one might also encounter the dual mesh, i.e. the computation grid obtained from connecting the centers of the cells that the initial subdivision into finite elements of the computation domain yielded.