An Efficient CUDA Implementation of Fast Algorithms for Computing Particle Interactions in Vortex Particle Method for 2D Flow Simulating
DOI:
https://doi.org/10.14529/cmse260302Keywords:
CFD, vortex particle method, fast algorithm, particle interaction, Barnes–Hut method, LBVH tree, GPU computing, nearest neighborsAbstract
This work addresses the problem of improving the computational efficiency of calculating mutual interactions between vortex particles in vortex particle methods for simulating 2D incompressible flows. Direct computation, with its quadratic complexity, becomes infeasible when the number of particles exceeds several tens of thousands, whereas achieving results that are quantitatively consistent with experiments requires introducing up to several million vortex particles. We have adapted and optimized a hybrid fast algorithm for GPUs, which combines the principles of the Barnes—Hut method and the Multipole method. This algorithm achieves quasi-linear computational complexity by constructing an LBVH-tree and employing multipole expansions to approximate the influence of distant particle clusters. Based on this core algorithm, we have also developed and implemented auxiliary GPU routines for nearest neighbor searches and for preventing particles from penetrating solid boundaries. The developed algorithms are integrated into the VM2D code. Computational experiments simulating flow around a system of airfoils were performed on NVIDIA GPUs (H100, Titan V, GeForce RTX 5080), confirming the high performance of the implementation. The optimizations resulted in a threefold speedup of the most time-consuming computational operations, while maintaining a very low level of error in calculating vortex particle velocities. This research opens up prospects for the use of optimized GPU algorithms and high-performance GPUs in resource-intensive calculations within the vortex particle method framework for computational fluid dynamics.
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