Artificial pressure for pressure-linked equation

The discretized pressure-linked equation can be proven to possess a singular coefficient matrix. This implies that the pressure solution corresponding to a given velocity would not exist unless this velocity precisely satisfies the continuity equation. In the present investigation, an artificial source term is added to the pressure-linked equation. This additional term will generate an extra pressure called the ‘artificial pressure’ for each updated velocity to compensate for their nonzero dilation. The use of the artificial pressure is equivalent to creating an extra mass for the need of the updated velocity in satisfying the continuity equation. This treatment guarantees the existence and uniqueness of the pressure solution such that the pressure can be directly solved without recourse to the conventional pressure correction equation. Based on the concept of artificial pressure, the APPLE (Artificial Pressure for Pressure-Linked Equation) and the NAPPLE (Nonstaggered APPLE) algorithms are developed for incompressible flows. Through two well-known examples, the APPLE algorithm is found to produce essentially the same results with only about 40% CPU time as compared with the SIMPLER algorithm. Due to its simplicity, the NAPPLE algorithm has a potential use for problems with arbitrarily shaped domain as long as the grid size is not large.