The Pressure Problem of The Incompressible Flow Equations

Numerical solutions for the incompressible flow equations encounter a numerical problem because of the lack of an equation for the pressure. To resolve this problem, the continuity equation is modified or replaced to derive pressure equations. These equations are derived from: (1) analogy with the compressible flow equations by introducing a time dependent pressure term into the continuity equation, and (2) divergence of the momentum equation and the enforcement of the continuity equation. These techniques are known as the artificial compressibility (AC) method, and the pressure Poisson (PP) method respectively. The pressure equation in the AC method is first order partial differential equation, and in the PP method is second order partial differential equation of the Poisson type