Transformer based deep learning accelerated numerical simulation for incompressible flow

Numerical simulation of fluid plays an important role in the research of engineering, weather, and climate; the classical methods solve incompressible Navier–Stokes equations, providing the most detailed flow information in many cases. However, an increase in the number of grids causes the computing cost to increase significantly. In this paper, we propose a deep learning-based numerical solver for incompressible flow to improve the accuracy of numerical simulation on coarse-resolution grids. The solver uses the Swin Transformer—a hierarchical vision transformer using shifted windows—to build independent subnetworks and learn the interpolating coefficients for the variable values on the cell edge and, thus, to obtain fluxes in different directions. Numerical experiments show that our proposed solver can perform better than the traditional numerical scheme, predicting the solution well and maintaining long-term computational stability.