Applied Mathematics Seminar

Department of Mathematics, University of Texas at Arlington

Date/Time/Room: Thursday (11/2/2000) at 3:30 pm in 487 Pickard Hall (Refreshments served at 3:00 pm)

Speaker: Gary C. dela Pena, Department of Mathematics, University of Texas at Arlington

``The deformation method applied to the Incompressible Navier-Stokes Equations''

Abstract: A moving grid method based on a deformation method from differential geometry is presented. As the calculation proceeds, the nodes of an initial grid are moved in real time according to the solution through a set of deformation ODEs. The node velocity is determined by a monitor function constructed from physical variables through a scalar Poisson equation on the computational domain. It is proved mathematically 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. In particular, the moving grid has positive Jacobian and will not fold into itself. The moving grid method is then applied to a driven cavity flow. The results are compared to a benchmark for this problem. It is shown that the grid indeed follows the monitor function closely and that the method appears to have achieved the same accuracy with far less nodes. Further research is required on constructing the monitor functions to make the method practical.