Maxim Olshanskii: [WS] The cause and cure of spurious boundary forces in an Eulerian finite element method for moving…

Speaker
Maxim Olshanskii, University of Houston

Abstract
We discuss the causes and remedies for spurious temporal oscillations in boundary forces within an immersed boundary method for the incompressible Navier–Stokes equations on time-dependent domains. The immersed boundary method of interest is an Eulerian unfitted finite element method, combining cutFEM with standard BDF time-stepping schemes, facilitated by a discrete implicit extension of the numerical solution into a neighborhood of the physical domain. We demonstrate that the presence of spurious boundary forces can be mathematically attributed to the lack of unconditional stability estimates in the $L^\infty(L^2)$ norm for the finite element pressure and velocity time derivative. We further examine how the magnitude of these spurious oscillations depends on physical and discretization parameters. Finally, we propose an oscillation-free variant of the unfitted FEM.