A moving grid algorithm based on the deformation method

In this paper, a moving grid method based on a deformation method from differential geometry is presented. The node velocity is determined by a monitor function and a vector field which is calculated by a Poisson equation. It is proved that the cell volume is kept to be proportional to the monitor function when the grids are adapted to the solution at each time step. The moving grid method is then applied to a square cavity flow. Results show that the grid indeed follows the monitor function closely. Further research is required on constructing the monitor functions to make the method practical.