Mesh reconstruction is the key to the numerical simulation in CFD with large scale moving boundary which contains fast and stable mesh generation arithmetic. Firstly, this framework established efficient initial triangulation arithmetic based on directional edge theory which is fit for arbitrary polygon. Then it proved the arithmetic of longest edge division matches the divergence at some time and closes down the divergence with Delaunay edge swapping. Finally, the paper optimizes mesh with vertex spring model. The results indicate the way established in this study is efficient and stable.