Events for 11/16/2009 from all calendars
Departmental External Review
Time: 08:00AM - 8:00PM
Center for Approximation Theory Seminar
Time: 3:05PM - 4:00PM
Location: 317 Milner Hall
Speaker: Massimo Fornasier, Linz
Title: Mathematics enters the picture. An 'Italian touch' on mathematical image processing
Algebraic Geometry Seminar
Time: 3:30PM - 4:20PM
Location: MILN 216
Speaker: María-Cruz Fernández-Fernández, University of Seville, Spain
Title: Irregular hypergeometric D-modules
Abstract: Hypergeometric D-modules (also known as GKZ-systems) are systems of linear partial differential equations determinded by a matrix A with integer entries and a vector of complex parameters. We will describe how to construct their Gevrey solutions along coordinate subspaces in a combinatorial way. This type of formal solutions are closely related with the irregularity of a D-module.
URL: Link
Numerical Analysis Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 627
Speaker: Martin Kronbichler, Uppsala University
Title: A conservative level set approach to two-phase flow: error identification and corrections
Abstract: We discuss a conservative level set model for the simulation of two-phase flow based on a finite element discretization. The method consists of an incompressible Navier-Stokes solver to determine the fluid flow, coupled to an advection equation for the level set function that describes the position of the interface separating the two fluids. In our model, the level set function is set to be a smoothed indicator function, which provides a natural framework for discrete approximations of forces localized on the interface. Moreover, the (re-)initialization of the profile can be implemented such that the volume fractions of the individual fluids are conserved.
Numerical inaccuracies in our level set implementation can be traced back to errors in the approximation of normal vectors and curvature. The finite element spaces for approximating pressure and level set function need to match, in order not to introduce an additional imbalance between interface forces and pressure gradients. We analyze these inaccuracies on a drop in equilibrium, where numerical errors give rise to unphysical velocities.
A shortcoming of the level set model is its deficiency to model physics at contact lines, i.e., locations where the interface meets solids and aligns at material-dependent contact angles. We propose to tackle this problem by extending the level set model by a so-called phase field model close to boundaries, which does include a mechanism for setting oblique contact angles.