ADAPTIVE MESH REFINEMENT FOR SINGULAR SOLUTIONS OF THE INCOMPRESSIBLEEULER EQUATIONS

The occurrence of a finite time singularity in the incompressible Eule r equations in three dimensions is studied numerically using the techn ique of adaptive mesh refinement. As opposed to earlier treatments, a prescribed accuracy is guaranteed over the entire integration domain. A singularity in the vorticity could he traced down to five levels of refinement which corresponds to a resolution of 2048(3) mesh points in a nonadaptive treatment. The growth of vorticity fits a power law beh avior proportional to 1/(T - t) where T* denotes the time when the si ngularity occurs.