Monolithic Newton-multigrid solution techniques for incompressible nonlinear flow models ⋆

We present special Newton-multigrid techniques for stationary incompressible nonlinear flow models discretised by the high order LBB-stable Q2P1 element pair. We treat the resulting nonlinear and the corresponding linear discrete systems by a fully coupled monolithic approach to maintain high accuracy and robustness, particularly with respect to different rheological behaviour but also regarding different problem sizes and type of nonlinearity. Here, local pressure Schur complement (PSC) techniques are presented as a generalization of the classical Vanka smoother. The discussed methodology is implemented for the well-known flow around cylinder benchmark configuration [1–4] for generalised Newtonian as well as non-Newtonian flows including non-isothermal, shear/pressure dependent and viscoelastic effects.