Data-driven multi-grid solver for accelerated pressure projection

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