GPU-Accelerated Flow Simulations on Unstructured Grids Using a Multi-colored Gauss-Seidel Method

Efficient and robust implicit solvers are often required for large-scale applications in Computational Fluid Dynamics (CFD). In this paper, we present the development and implementation of a Multi-Colored Gauss-Seidel (MCGS) method for solving flow equations within an unstructured finite volume framework on the Graphics Processing Unit (GPU). A coloring algorithm is introduced such that no two adjacent elements are painted the same color, and the colors are distributed evenly as much as possible. A reordering of elements is implemented to group elements with the same color. A Jacobian freezing technique is applied to further reduce the computational cost. The capability of the developed framework is demonstrated through transonic flow simulations of the NASA Common Research Model (CRM) Wing-Body configuration on unstructured grids.