Numerical Techniques for Multiphase Flow with Liquid-Solid Interaction

In many fluid applications, particularly in multiphase flow problems with liquidsolid interaction based on the incompressible Navier-Stokes equations, the mathematical description and the numerical schemes have to be designed in such a way that quite complicated constitutive relations and interactions between fluid and solids can be incorporated into existing flow solvers in an accurate and robust manner. In the following sections, first of all we describe finite-element discretization strategies and corresponding solver techniques (approximate Newton methods, multilevel pressure Schur complement techniques, operator-splitting approaches) for the resulting discrete systems of equations. The need for the development of robust and efficient iterative solvers for implicit high-resolution discretization schemes is emphasized and the numerical treatment of extensions of the NavierStokes equations (Boussinesq approximation, Κ-ε turbulence model) is addressed which is evaluated by simulation results for prototypical applications including multiphase and granular flows. In the second part, a fully monolithic finite-element approach is described for fluid-structure interactions with elastic materials which is applied to several benchmark configurations. In the third part, the concept of FEM fictitious-boundary techniques, together with operator-splitting approaches for particulate flow, is introduced which allows the efficient simulation of systems with many solid particles of different shape and size.