### Applied Mathematics Seminar

Department of Mathematics, University of Texas at Arlington

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__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.