An effective convergence accelerator of fluid simulations via generative diffusion probabilistic model

Developing effective methods to computational fluid dynamics (CFD) convergence acceleration has been a central focus for nearly a century, vital for driving technological advancements across various industries. Deep learning-based strong nonlinear modeling methods are currently empowering traditional CFD simulations from various perspectives. In this paper, we propose a novel non-intrusive method for accelerating convergence in fluid simulations, achieving further acceleration in an open-source CFD solver. This is the first application of the diffusion probabilistic model for convergence acceleration in flow simulations. By strategically integrating diffusion probabilistic model throughout the simulation process, the proposed method significantly reduced the number of CFD iterations while exhibiting strong stability. Leveraging a generative probabilistic model, this method successfully achieves a many-to-one mapping from unconverged flow fields at various accuracies to a converged flow field. It effectively addresses the challenge of input generalization caused by differences in convergence processes of various flow conditions, thereby preventing mapping failures. The verification is conducted on transonic shock flows with variable shapes through perturbation of the RAE2822 airfoil. The results indicate that this acceleration method can achieve a speedup of 2.4 times on the CFD solver with LU-SGS. Remarkably, it also significantly enhances sample convergence, attaining high-accuracy solutions for samples that cannot fully converge previously.