Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples

We solve fluid flow problems through a space-time finite element method. The weak form of the Navier-Stokes equations is stabilized using the variational multi-scale formulation. The finite element problem is posed on the "full" space-time domain, considering time as another dimension. We apply this method on two benchmark problems in computational fluid dynamics, namely, lid-driven cavity flow and flow past a circular cylinder. We validate the current method with existing results from literature and show that very large space-time blocks can be solved using our approach.