A Reduced-Memory Multicolor Gauss-Seidel Relaxation Scheme for Implicit Unstructured-Polyhedral-Grid CFD Solver on GPU

In this paper, we present a reduced-memory multicolor Gauss-Seidel relaxation scheme for an implicit unstructured-polyhedral-grid density-based computational fluid dynamics solver on graphics processing units (GPUs). Towards the goal of efficiently performing large-scale simulations on GPUs with limited memory, we propose to reduce the memory requirement by evaluating a matrix-vector product arising in a linear relaxation scheme with the Fr\'echet derivative. The proposed technique results in a dramatic reduction in the memory requirement because off-diagonal blocks are no longer required and only the diagonal blocks of the residual Jacobian are needed. Numerical results demonstrate that this approach substantially increases the maximum problem size that can be run on a GPU, with a significant speedup over central processing unit (CPU) computations. Moreover, simplified numerical fluxes designed for the Fr\'echet derivative evaluation enable to achieve even a slight speedup in both GPU and CPU computations.