Stefan Turek
University of Dortmund
Department of Mathematics
Germany
We present numerical simulation techniques for incompressible fluids with complex rheology due to 'extreme' changes of the viscosity which may vary significantly by several orders of magnitude, for instance due to non-isothermal behavior and pressure, resp., shear dependency. Such fluids may include viscoplastic as well as viscoelastic effects which is typical for biological fluids, yield-stress fluids, granular material as well as polymer melts and rubber (caoutchouc). We discuss special discretization and solver techniques in which case the coupling between the velocity, pressure and additional variables for the stresses, which leads to restrictions for the choice of the FEM approximation spaces, and the (often) hyperbolic nature of the problem are handled with special Finite Element techniques including stabilization methods. The resulting linearized systems inside of outer Newton-type solvers are (special) nonsymmetric saddle point problems which are solved via geometrical multigrid approaches. We illustrate and analyze numerically the presented methodology for well-known benchmark configurations as well as protoypical industrial and biomechanical applications for several nonlinear flow models.