A Characteristic Mapping method for the two-dimensional incompressible Euler equations

We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. The new approach evolves flow map using gradient-augmented level set (GALSM). Since can be decomposed into submaps (each over finite time interval), error controlled by choosing remapping times appropriately. This leads to numerical scheme that has exponential resolution in linear time. Error estimates are provided and conservation properties analyzed. computational efficiency of illustrated vortex merger four mode random flow. Comparisons Cauchy-Lagrangian also presented.