Oberseminar Numerische Mathematik / Scientific Computing
Arnold Reusken,
RWTH-Aachen
Numerical Simulation of Two-Phase Incompressible Flows
Abstract:
We consider a flow problem with two different immiscible incompressible newtonian phases (fluid-fluid or fluid-gas). A standard model for this consists of the Navier-Stokes equations with a viscosity and density that are discontinuous across the interface and with a localized force at the interface that describes surface tension effects. In this talk we present an overview of a solver for the numerical simulation of this class of problems that has been developed and implemented in our group. Important characteristics of the method are the following. For capturing the interface between the two phases the level set method is applied. The spatial discretization is based on a stable hierarchy of consistent tetrahedral grids. For discretization of velocity, pressure and the level set function we use conforming finite elements. For the pressure variable an extended linear finite element space (XFEM) is used which allows an accurate approximation of the pressure discontinuity across the interface. For the treatment of the surface tension force a special Laplace-Beltrami method has been developed. The time discretization is based on a variant of the fractional step theta-scheme. For solving the linearized discrete problems we use inexact Uzawa techniques and Krylov subspace methods combined with special preconditioners. We apply a variant of the Fast Marching method for the reparametrization of the level set function.We will discuss certain aspects of our solver in more detail. Results of numerical experiments for a three dimensional instationary two-phase fluid-fluid flow problem with and without mass transport are presented.
| Datum: | 07.01.08 | Zeit: | 16:15 | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | 032 im Erdgeschoss |