A Neural Network-Based Poisson Solver for Fluid Simulation

Abstract

The pressure Poisson equation is usually the most time-consuming problem in fluid simulation. To accelerate its solving process, we propose a deep neural network-based numerical method, termed Deep Residual Iteration Method (DRIM), in this paper. Firstly, the global equation is decomposed into multiple independent tridiagonal sub-equations, and DRIM is capable of solving all the sub-equations simultaneously. Moreover, we employed Residual Network and a correction iteration method to improve the precision of the solution achieved by the neural network in DRIM. The numerical results, including the Poiseuille flow, the backwards-facing step flow, and driven cavity flow, have proven that the numerical precision of DRIM is comparable to that of classic solvers. In these numerical cases, the DRIM-based algorithm is about 2–10 times faster than the conventional method, which indicates that DRIM has promising applications in large-scale problems.