Parallelization of an unstructured Navier-Stokes solver using a multi-color ordering method for OpenMP

A multi-color ordering method has been developed for the Gauss-Seidel (GS) method in the framework of the unstructured-grid based Navier-Stokes equations solver using OpenMP. The multi-color ordering method is required to avoid the data race condition in do-loop parallelization and to achieve the uniqueness of a solution of GS. A coloring algorithm of painting neighbor cells with different colors is proposed for the multi-color ordering method. The method is tested for four sample simulation cases: one case of two-dimensional simulation and three cases of three-dimensional simulation. Through the sample simulations, the uniqueness of the solution of the Multi-Color ordering Gauss Seidel (MCGS) method is verified, and the convergence ratio of MCGS is found to be in the similar level to that of GS and better than the Jacobi method. The parallel efficiency is examined for workstations with two hexa-core CPUs or two octa-core CPUs. Although the parallel efficiency is dependent on computer systems and simulation cases, the speed up ratio of MCGS reaches 14 using two octa-core CPUs in the maximum case using 14 million cells.