A spatially adaptive linear space-time finite element solution procedure for incompressible flows with moving domains

A linear solution strategy for the finite element simulation of incompressible fluid flows with moving domains is outlined in the context of a fully Lagrangian space-time GLS formulation using low-order elements. This linear solution strategy is achieved by assuming that the incompressibility condition is enforced although it is relaxed in the GLS formulation. The approach has a distinct advantage over the non-linear Newton-Raphson solution approach in a sense that it can not only significantly reduce the computing costs in terms of computer CPU time and memory requirements but also preserve the solution accuracy if a sufficiently small time-step size is applied. Its applicability is further demonstrated through a wave propagation and breaking problem. For this type of problems, adaptive re-meshing techniques are essential to achieve a successful simulation. A mesh adaptive procedure developed earlier for simulation of large deformation solid mechanics problems is appropriately modified and employed in simulation of flows of incompressible fluids with moving domains.