TWO-GRID METHOD FOR FLUID DYNAMIC PROBLEMS WITH DISPARATE TIME SCALES.

Abstract

For complicated time dependent fluid dynamic problems it is difficult to obtain good approximate solutions. Here we propose to obtain an approximation by solving the problem on two grids, a fine grid and a coarse grid. The solution on the fine grid will enable us to correct the truncation error on the coarse grid, where large time steps can be used without the full penalty of reduced resolution. The present method contains some of the elements of the multigrid 'frozen tau ' method but the motivation and justification are different. The present method is simple to implement and follows the correct physical transient. It allows for arbitrary mesh ratios and does not require storage of all time levels.