An overlapping mesh based splitting method for the incompressible Navier-Stokes equations

Abstract: We present an overlapping mesh based splitting method for solving the incompressible Navier-Stokes equations on unfitted mesh settings. The developed method is based on Nitsche’s method for weakly imposing the interface condition between the overlapping meshes, and it uses a ghost penalty approach for stabilizing the cut elements produced by the mesh intersection. The developed method is tested on the Taylor-Green vortex problem for fluid flows in both the high and low regime of the Reynolds number. The numerical results show optimal order of convergence or higher for the considered space-time error norms in the low Reynolds regime. For the high Reynolds regime, the results are promising but inconclusive for concluding any final convergence rate in time. Suggestions for further studies are to consider a more physically realistic flow such as the benchmark test case of a channel flow around a cylinder, as well as adding some stabilization for convection dominated flows.