Parallelization DILU and Gauss-Seidel Algorithms Based on Domestic GPGPU in the Matrix Solvers of Open FOAM

This study presents a parallel acceleration framework for computational fluid dynamics (CFD) simulations in OpenFOAM through the integration of domestic general-purpose GPU (GPGPU) accelerator cards with two novel matrix coloring algorithms based on the LDU matrix format. Focusing on preconditioning techniques optimization, we specifically address the parallel implementation challenges of Diagonal Incomplete LU (DILU) decomposition and Gauss-Seidel smoother algorithms. To resolve critical data race issues inherent in parallel computations, we develop two innovative coloring strategies: (1) a hierarchical parallelization method utilizing the matrix's directed acyclic graph (DAG) topology for dependency sorting, and (2) an enhanced multicolor ordering algorithm derived from red-black Gauss-Seidel principles. Experimental validation using both motorBike benchmark and 3D lid-driven cavity cases demonstrates the proposed methods' computational efficacy. Comparative analysis reveals that our GPU-accelerated implementation achieves 5× speedup for standalone DILU/DIC preconditioners and 4-10× acceleration for hybrid DILU-Gauss-Seidel configurations compared to conventional CPU-based approaches. The developed framework maintains numerical accuracy while significantly enhancing solution efficiency, providing a robust acceleration paradigm for large-scale CFD simulations in heterogeneous computing environments.