Experimental Report on Accelerating Numerical Computation of Simple Navier-Stokes Equations Using Generalized Mapping Theory

Numerical simulation of Navier-Stokes (NS) equations is a core tool in fluid dynamics research, but traditional methods face challenges of high computational time and memory consumption, especially for high-Reynolds-number turbulence simulations that are difficult to implement on ordinary equipment. This experiment is based on Generalized Mapping Theory (GMT), which decomposes the NS equations into independent operators (convection, viscosity, pressure projection, etc.) to construct a modular solution framework, aiming to verify the acceleration effect of GMT on NS numerical computations. Two cases were designed: 2D flow around a cylinder at Re=1000 and 3D lid-driven cavity flow at Re=5000. Results show that the 2D experiment successfully captured the formation of Karman vortex street and laminar-turbulent transition, with operator contributions quantifying energy transfer mechanisms. The 3D experiment completed high-Reynolds-number turbulence simulation on a personal computer in only 23.52 seconds, clearly presenting 3D vortex evolution and energy cascade, with the turbulent energy spectrum conforming to the Kolmogorov k⁻⁵/³ law. This experiment verified the efficiency and stability of the GMT framework, achieving the first high-Reynolds-number 3D NS equation simulation on a personal computer, providing a feasible solution for low-cost fluid dynamics research.