The parallelization effort will allow larger problems to be considered as well as further development of the method to correctly handle velocity boundary conditions. The vorticity-based equations also lend themselves to a multitude of problems where vorticity is a strong component. Serial code is memory-intensive, which limits the size of problems that can be solved on typical workstations.
Parallelism allows larger problems to be solved while reducing the computation time.
Currently, the flow in a square cavity is considered, but the method lends itself to consider external vorticity-based flows. The parallelization effort can be divided into three distinct sections. The GHD consists of time-independent terms which can be calculated once, outside the time loop, and are then multiplied by the current vorticity inside the time loop. The decision to calculate the integral terms once and save them is a design decision to reduce the time spent inside of the time loop, but it exacts a price in the size of the problem that can be solved on a specific system, as the calculations become very memory intensive. By distributing the memory required to save these terms among processors on a parallel computing platform, larger problems can be considered.