A novel moving mesh method for solving fluid dynamic equations

In this article, a novel moving finite elements method has been presented and applied to solve two typical fluid dynamic equations. Different from the existing methods, the moving direction and the distance of the nodes were obtained by solving a variable coefficient diffusion equation. By this method, neither the mapping of the region nor the smoothing of the monitoring function is needed. Therefore, the proposed method is easy to be implemented. Numerical examples show that the proposed method can move the nodes to the position where the solution changed drastically, and the resolution of numerical solutions has improved distinctly.