ADER scheme for incompressible Navier-Stokes equations on overset grids with a compact transmission condition

A space-time Finite Volume method is devised to simulate incompressible viscous flows in an evolving domain. Inspired by the ADER (based on a Finite-Element-prediction/Finite-Volume-correction approach), Navier-Stokes equations are discretized onto overset grid which able take into account both shape of possibly moving object and evolution compact transmission condition employed order mutually exchange information from one mesh other. The resulting second accurate space time for velocity pressure. accuracy efficiency tested through reference simulations.