Deep learning accelerated numerical simulation for three-dimensional compressible fluids

Abstract

Numerical simulation of fluid flow is a long-standing challenge across many physical application domains, including engineering, climate, and the physical science. There has been a surge of interest in high order schemes aimed at improving simulation accuracy on coarse grids. However, for high-dimensional fluids, the computational cost escalates with the number of dimensions involved. In this paper, we propose a deep learning-based approach to accelerate the numerical computation and further improve the accuracy in simulating three-dimensional (3D) compressible fluids which can be described by Eulerian equations. The proposed work utilizes 3D Euler transformer networks to learn the interpolation coefficients for cell boundaries, which are applied to approximate the boundary fluxes of fluid on coarser grids. Benefiting from learning features of high-resolution fluid flow, our learned interpolation method yields finer performance on coarse grids, thereby accelerating the fluid simulations and improving the numerical accuracy. The numerical experiments confirm that the proposed method improves performance in inference of coarse-grained dynamics.