CutFEM and ghost stabilization techniques for space?time discretizations of the Navier?Stokes equations

We propose and analyze computationally a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of nonstationary, incompressible Navier–Stokes equations evolving domains. The physical is embedded into fixed computational mesh such that arbitrary intersections moving domain's boundaries with background occur. potential cut techniques methods has rarely been studied in literature so far deserves further elucidation. key ingredients approach are weak formulation Dirichlet boundary conditions by Nitsche's flexible efficient integration over all types cells spatial extension discrete quantities to entire including (ghost) subdomains fluid flow. Thereby, an expensive remeshing adaptation sparse matrix data structure avoided computations accelerated. To prevent spurious oscillations caused irregular cells, penalization, defining also implicitly ghost domains, added. These order, discontinuous Galerkin discretization time variable inf-sup stable variables. parallel implementation assembly described. optimal convergence properties algorithm illustrated numerical experiment domain. well-known 2d benchmark flow around cylinder as well obstacles arising domains considered further.