Abstract: In order to reduce the computational cost of solving partial differential equation (PDE), whose solution has strong singularity or drastic change in a small local area, a moving mesh method based on equation solution is proposed and applied to solve the two-dimensional incompressible Navier-Stokes equations. Different from the most existing moving mesh methods, the moving distance of the nodes is obtained by solving a variable-coefficient diffusion equation, which avoids regional mapping and does not need to smooth the monitoring function, so the algorithm is easier to program and implement. Numerical examples show that the proposed algorithm can refine the mesh in the position where the gradient of the solution changed drastically, which can save a lot of computation time on the premise of improving the resolution of the numerical solution. Due to the typicality of the Navier-Stokes equations, the proposed algorithm can be generalized to solve many similar partial differential equations numerically.

Key words: moving mesh method, finite element method, Navier-Stokes equation