A GPU-accelerated algorithm for solving Navier-Stokes equations

Real-time fluid engineering simulations require significant computational power and high-resolution grids to ensure accuracy. This paper proposes a novel CUDA-C-based simulation algorithm nemesys that leverages GPU devices to solve the Na vier-Stokes equations with precision and speed. The algorithm uses a Successive Over Relaxation (SOR) iterative process on a multi-dimensional CUDA core to accelerate solving speed. The co-located Rhie and Chow interpolation scheme is applied to unstructured grids to solve the equations using an implicit finite volume method. Benchmark simulations are performed on two problems aimed to validate the effectiveness of the proposed methodology: the classical lid-driven cavity and closed-channel flow. Results exhibit a significant advantage of the proposed method in terms of convergence rate compared to state-of-the-art techniques using varying grid resolutions and Reynolds numbers. Specifically, the strategy is nearly 850 times faster than parallel CPU-based code when utilizing an RTX 3090 Nvidia graphics card. Furthermore, the algorithm's performance is investigated on an airfoil simulation, confirming the approach's effectiveness. The findings highlight that GPU-based parallel programming is a promising approach for achieving real­time simulations, and the proposed algorithm presents a significant improvement over CPU-based techniques.