Data-Driven Multi-Grid Solver for Accelerated Pressure Projection

TL;DR

This paper introduces a data-driven multi-grid method that significantly accelerates pressure projection in fluid simulations by leveraging neural network techniques, achieving 2-3x speedup without accuracy loss.

Contribution

It develops a novel data-driven smoother for multi-grid pressure projection, enhancing efficiency and robustness in unsteady incompressible flow simulations.

Findings

Accelerates classic multi-grid methods by 2-3 times

Maintains accuracy across diverse 2D and 3D flow cases

Effectiveness remains high with increasing resolution

Abstract

Pressure projection is the single most computationally expensive step in an unsteady incompressible fluid simulation. This work demonstrates the ability of data-driven methods to accelerate the approximate solution of the Poisson equation at the heart of pressure projection. Geometric Multi-Grid methods are identified as linear convolutional encoder-decoder networks and a data-driven smoother is developed using automatic differentiation to optimize the velocity-divergence projection. The new method is found to accelerate classic Multi-Grid methods by a factor of two to three with no loss of accuracy on eleven 2D and 3D flow cases including cases with dynamic immersed solid boundaries. The optimal parameters are found to transfer nearly 100% effectiveness as the resolution is increased, providing a robust approach for accelerated pressure projection of unsteady flows.