Local Mesh Refinement and Penalty Methods Dedicated to the Direct Numerical Simulation of Incompressible Multiphase Flows

Recent advances in numerical methods for the direct numerical simulation (DNS) of multiphase flows are presented. The mathematical formulation is based on an eulerian discretisation of the navier-stokes equations on fixed staggered curvilinear grids where the media are located thanks to volume of fluid functions. An adaptative and local mesh refinement method (AMR) is proposed to allow multi-space scale solutions in three dimensions and a tensorial penalty (or fictious domain) approach is detailed for the numerical modelling of incompressibility, velocity/pressure coupling and liquid/solid interactions in multi fluid flows. The article is focussed on three-dimensional applications of the direct numerical simulation. The DNS tool is applied to the mould filling under unstable viscous jet conditions, the stoke’s flow induced by a solid particle in a tube and the turbulent wave breaking in deep water. These flows are chosen to highlight the abilities of the numerical model for characterising unsteady incompressible multiphase flows.