Experimental Report on Progress in Solving Numerical Solutions of NS Equations by Completely Replacing Poisson Equation with Generalized Mapping

This paper focuses on the experimental research of solving numerical solutions of Navier-Stokes (NS) equations by completely replacing the Poisson equation with the Generalized Mapping Technique (GMT). In traditional numerical solution of NS equations, solving the pressure Poisson equation is a core step, but its complex calculation and high demand for hardware resources severely restrict applications in resource-constrained environments. The first experiment successfully solved the NS equations on a personal PC with a running time of only tens of seconds, but it avoided using the Poisson equation solver [1]. On this basis, the second experiment adopted the GMT method to completely replace the traditional pressure projection of the Poisson equation, successfully achieving the numerical solution of a simple three-dimensional NS equation (Re=5000) on a personal PC with 360,000 grids, 98M memory and a running time of tens of seconds. Compared with the first experiment, the second experiment has made significant progress in pressure processing, obstacle handling, algorithm stability and performance monitoring. The accuracy of the output results is not much different from the industrial level and can automatically generate graphs, verifying the feasibility and superiority of the GMT method in replacing the Poisson equation for solving NS equations, and providing a new path for numerical solution of NS equations in resource-constrained environments.