Mathematikgebäude, M1011

In this talk we present a robust methodology for solving incompressible, immiscible two-phase flows modeled by the Navier-Stokes equations. All the equations are solved using continuous Galerkin finite elements. We start by describing the general algorithm, which employs a splitting operator technique that considers a velocity field to advect the material interface via a phase conservative level-set method. Afterwards, the new interface location is used to reconstruct the material parameters and to solve the Navier-Stokes equations to obtain a new velocity field. Most of the presentation will be devoted to the representation and time evolution of the interface. There is an extensive list of methodologies to treat material interfaces. Popular choices include the volume of fluid and level-set methods. We propose a novel level-set like model for multiphase flow that preserves the initial mass of each phase. The model combines and reconciles ideas from the volume of fluid and level-set methods by solving a non-linear conservation law for a regularized Heaviside function of the level-set function. By doing this, we guarantee conservation of the volume enclosed by the interface. Our level-set model contains a term that penalizes deviations from the distance function. The result is a non-linear monolithic model for a phase conservative level-set with embedded redistancing. To solve the Navier-Stokes equations we use a second order projection scheme. Using ideas for solving hyperbolic PDEs via continuous Galerkin finite elements, we propose a robust and parameter free stabilization for the momentum equations. This stabilization is suitable for unstructured meshes and has been tested for multiple refinement levels. We present several numerical examples to demonstrate the behavior of this method under different scenarios.

Dr. Manuel Quezada de Luna

KAUST: King Abdullah University of Science and Technology (Thuwal, Saudi Arabien)