A fast dynamic grid adaption scheme for meteorological flows

The continuous dynamic grid adaption (CDGA) technique is applied to a compressible, three-dimensional model of a rising thermal. The computational cost, "per grid point' per time step, of using CDGA instead of a fixed, uniform Cartesian grid is about 53% of the total cost of the model with CDGA. The use of general curvilinear coordinates contributes 11.7% to this total, calculating and moving the grid 6.1%, and continually updating the transformation relations 20.7%. Costs due to calculations that involve the gridpoint velocities (as well as some substantial unexplained costs) contribute the remaining 14.5%. A simple way to limit the cost of calculating the grid is presented. The grid is adapted by solving an elliptic equation for gridpoint coordinates on a coarse grid and then interpolating the full finite-difference grid. -from Authors