The Viscous Vortex Domains (VVD) method is a powerful fully Lagrangian approach for simulating two-dimensional viscous incompressible flows. However, its computational efficiency is severely hampered by the high cost of calculating the diffusive velocity field, which is crucial for modeling viscous effects. Specifically, the evaluation of contour integrals for terms accounting for the influence of solid boundaries becomes the most time-consuming part of the algorithm, consuming up to 70% of the total simulation time, since N -body-type fast methods that allow for a “dramatic” speedup of the rest of the algorithm turn out to be inefficient for this operation. This paper presents a novel approach to accelerate this calculation by replacing the direct numerical integration with a fast approximation using a pre-trained multilayer perceptron (MLP). The neural network approximates two dimensionless functions, which are universal for all panels, based on three normalized geometric parameters. The model was trained on a high-accuracy dataset generated in Wolfram Mathematica. Implemented within the VM2D code using NVIDIA’s cuDNN library for GPU acceleration, this approach demonstrates a significant performance improvement. The computation time for the diffusive velocity terms was reduced by approximately 85%, leading to a 1. 75x overall speedup of the simulation time step. Furthermore, the new method provides higher accuracy, resulting in a cleaner, more periodic force signal and improved simulation quality, as demonstrated for flow around an impulsively started cylinder at Re = 1000.
Sukhova et al. (Fri,) studied this question.