High order ghost-FEM for incompressible Navier-Stokes equations on moving domains
Please login to view abstract download link
We develop a new technique to approximate the solution of Navier-Stokes equations in arbitrary moving domains. We use a space discretization based on ghost finite element method (ghost-FEM) and a high order IMplicit-EXplicit (IMEX) scheme in time. When working with moving domains, the computational region may evolve during the simulation, and it is often necessary to extend a function from the region where it is defined to a region where it is not. We follow the Aslam technique, first introduced for finite difference schemes, and here tailored to finite element framework. When dealing with high-order in space and arbitrary domains, since the boundary conditions are not applied on the true boundary, it is essential to preserve the accuracy of their evaluation. To prevent any loss of accuracy, we follow the strategy proposed in the Shifted Boundary Method, and correct the boundary conditions via Taylor expansions. We provide numerical results to verify the accuracy of the numerical scheme and test it against benchmarks.
