Parallel Implicit Methods for an Unstructured CFD Simulator on GPU

The advancement of GPU technology has revolutionized Computational Fluid Dynamics (CFD) by enabling efficient generation of high-precision flow field data. However, a critical challenge lies in reconciling the fast convergence of data-dependent implicit schemes with GPU parallelism, as existing methods struggle to strike a balance between computational efficiency and convergence accuracy. This study systematically evaluates four implicit approaches implemented in the industrial solver FlowStar, focusing on efficiency-convergence trade-offs stemming from serial dependencies that limit GPU utilization. To address these limitations, a balanced coloring and hyperplane method is proposed to optimize hardware resource allocation, while a unified evaluation framework quantifies performance across five unstructured grid configurations. Experimental results demonstrate that the balanced coloring and hyperplane implementations achieve comprehensive speedups of 2.33× and 1.15× against the conventional level-set parallelization. This work provides actionable insights for designing parallel CFD algorithms that harmonize parallelism with numerical stability.