Large scale flow simulations

Barbara Wohlmuth
TU München
Thursday 3rd March 2016
Aula Seminari
Large scale flow problems play an important role in many multi-physics applications. In this talk, we consider different aspects such as the role of local mass conservation in a weak or strong setting and non-linear solution techniques in case of inequality constraints. Many natural pairings of conforming discrete spaces do not satisfy a uniform inf-sup condition and thus do have either to be stabilized or the velocity space has to be enriched. Quite often these standard techniques result in discrete velocities which do not yield strongly the divergence free condition. Here we propose easy to realize local a posteriori corrections which allow us to lift the $H^1$-conforming velocity onto a $H(\text{div})$-conforming mixed finite element, e.g. of Raviart--Thomas type. By doing so we achieve a significantly improved accuracy in case of coupled transport terms where, e.g., the velocity enters into the advective part of an energy equation. Secondly we consider an example from porous media flow and discuss the role of inequality constraints on the saturation. In contrast, to simple contact laws where a non-linear complementarity condition can be defined in terms of the max-function and affine terms, non-linear constitutive relations also enters. Thus the realizations of active set strategies are more involved. Nevertheless, robust numerical results can be obtained if combined with an adaptive time stepping scheme. contact: