An efficient moving grid method

The deformation method, one of the moving grid methods was originated from differential geometry. An efficient deformation method which is based on least-squares finite element method (LS-FEM) was investigated in the present paper. The div-curl system is solved by using LSFEM. The nodes will cluster in regions where the solution error is large and the size of the new grid cell can be directly controlled by specifying the monitor function with a suitable value. The location of any node, whether it is on a boundary or not, can be specified. Four numerical examples were presented. The first one is on moving grid for shock reflection problem, the second adaptive grid obtained from the image of Mona Lisa, the third grid on a square deformed to a circle and inner nodes adapted to a small circle, the fourth one is a grid on a cube deformed to a hexahedron with complex surfaces and inner nodes adapted to a small spherical surface. These examples indicate that the presented method is efficient.