Composite Grid Method and Its Application on Welding Modeling

In order to increase the accuracy of the approximate solution of singularity problems on specific local region, a new algorithm-composite grid method (CGM) was proposed in this paper. Two different scale grids were adopted, a coarse mesh for the whole area without considering the impact of singularity and a fine mesh for the local singular area considering the impact of singularity respectively. Equations on coarse and fine grids were solved iteratively for the final result. Calculated results in coarse grid were mapped into boundary of fine grid through interpolation matrix. Then those results in coarse grid were corrected by residuals calculated in fine grid. The non-conforming error was introduced in case of non-matching of two grids. The method to reduce such error was introduced. Numerical experiments of partial differential equation in singular problems were performed, whose results agree well with analytical solution. In the numerical simulation of the laser welding, reasonable agreement was achieved and efficiency of CGM for such kind of problem was displayed.