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.