Extended FEM for 3D two-phase incompressible flow problems

Decanato - Facoltà di scienze informatiche

Data d'inizio: 21 Settembre 2011

Data di fine: 22 Settembre 2011

The Faculty of Informatics is pleased to announce a seminar given by Sven Gross

DATE: Wednesday, September 21st, 2011
PLACE: USI Università della Svizzera italiana, room 251, Main building (Via G. Buffi 13)
TIME: 10.00

Two-phase systems play an important role in chemical engineering. Two examples are extraction columns where mass transport takes place between bubbles and a surrounding liquid (fluid-fluid system), or falling films which are e.g. used for cooling by heat transfer from a thin liquid layer to the gaseous phase (liquid-gas system). In this talk we consider 3D flow simulations of such two-phase systems on adaptive multilevel tetrahedral grids. We apply piecewise quadratic FE for the velocity and piecewise linear extended FE for the pressure. For capturing the interface we use a level set approach. The effect of surface tension is modeled by an interfacial force term (CSF model). Special care has to be taken of the numerical treatment of the interfacial force term and the pressure space, as otherwise very large artificial spurious velocities are induced at the interface.

The pressure is continuous in both phases, but has a jump across the interface due to surface tension. If the grid is not aligned to the interface, the approximation of such functions in standard finite element spaces yields poor results with an error of order 0.5 w.r.t. the

L2 norm. Second order approximations can be achieved by the introduction of an extended finite element space (XFEM) adding special basis functions incorporating a jump at the interface. We will discuss the optimal approximation order of the proposed pressure XFEM space.

Additionally, some stabilization strategies for the XFEM basis are presented which also offer the optimal approximation property. Numerical results for rising droplets and falling films obtained by our software package DROPS will be presented at the end of the talk.

Sven Gross:
2002: diploma thesis "Parallelisierung eines adaptiven Verfahrens zur numerischen Loesung partieller Differentialgleichungen", RWTH Aachen
2008: PhD thesis "Numerical methods for three-dimensional incompressible two-phase flow problems", RWTH Aachen, Prof. Reusken
2009-2010: PostDoc at Hausdorff Center for Mathematics, Uni Bonn, mentor Prof. Griebel
2011: book on two-phase flows (with A. Reusken) published by Springer

HOST: Prof. Rolf Krause, Robert Speck