A parallel unstructured multi-color SOR solver for 3D Navier-Stokes equations on graphics processing units

In this paper, we develop a GPU parallelization technique to accelerate the pressure Poisson solver. We apply it in three-dimensional Navier-Stokes simulations with arbitrary geometries. The numerical method is based on a projection method, and the discretization is obtained by combining a second-order unstructured finite-volume method and a s transformation. The pressure solution is responsible for this formulation's most time-consuming computation tasks. This is because the Poisson equation must be approximated. This work proposes a GPU-based Multi-Color Successive Over-Relaxation (MC-SOR) method to solve the resulting sparse linear system. The proposed parallel finite-volume code is verified and validated by solving the Poisson problem. We employ analytical solutions and well-known benchmark problems with complex flows. These include the Taylor-Green vortex problem and the problem of turbulent flow around a circular cylinder.