NUMERICAL EXPERIMENTS WITH A TWO-DIMENSIONAL HORIZONTAL VARIABLE GRID

Abstract

A two-dimensional horizontal variable grid is derived that has maximum resolution at the center and minimum resolution near the boundaries of the grid. By using the analytic transformation that defines the variable grid, the equations of motion for a free-surface model are transformed in terms of new independent space variables in a computational domain with constant resolution. Numerical experiments utilize the variable grid to (1) increase the domain size with a fixed resolution at the center and (2) increase the resolution at the center with a fixed domain size. Several finite-difference analogs and three time-integration schemes are tested. For a given domain size and number of grid points, several variable grid experiments show superior results in the mass and momentum fields compared to constant grid results. Most variable grid experiments, however, show a small (less than 1 percent) increase in total energy after 2000 time steps due apparently to the presence of additional nonlinear terms in the forecast equations. The results show that, although care must be taken with the nonlinear terms, the variable grid may be effectively used in certain physical problems to economically gain resolution at the center of the domain.