U-Net-based viscosity solver for incompressible newtonian fluids

Abstract

This study aims to accelerate incompressible Newtonian fluid simulation using U-Net based viscosity solver. The Affine Particle-In-Cell method, widely used for viscous fluid simulation in the field of computer graphics, has limitations in real-time simulation since it solves partial differential equations by iterative methods. Especially, the viscosity solver takes the longest time, accounting for half of the entire process. Therefore, we propose a U-Net-based convolutional neural network(CNN) viscosity solver that replaces the conventional variational viscosity solver. We implemented a U-Net-based solver to predict velocity changes due to viscosity through supervised learning. We propose a novel symmetric MAC grid for CNN to resolve the asymmetry of velocity and mass information in Eulerian MAC grid. We design the model for scenes with only fluid and scenes with rigid-fluid interaction in a box, respectively. In addition, the possibility of solving fluids of various viscosity coefficients as one model is shown by the model with the viscosity coefficient as a variable. Our model computes 10 times faster than the conventional solver and quantitatively shows that it effectively optimizes the minimization problem presented by the target viscosity solver. Finally, we show that our model is valid for both trained and unseen data by analyzing the realism of our simulation compared to the ground truth through user study.