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Mathematisches Kolloquium

Datum Gastredner Thema Ort
Im Rahmen des Mathematischen Kolloquiums
Im Rahmen der Vortragsreihe Angewandte Numerik und Simulation
13.05.2014
14 Uhr
Prof. Alexander Panchenko
Washington State University, USA
Nonlocal continuum models of particle systems

Zusammenfassung


The main question addressed in the talk is how to obtain continuum equations for spatial averages from the ODEs of classical particle dynamics. Balance equations for the average density, linear momentum, and energy were derived by Irving and Kirkwood, Noll, Hardy, Murdoch and others. These equations are exact, but not in closed form since fluxes are given as functions of particle positions and velocities. Evaluating the exact fluxes requires solving the full ODE system which can be prohibitively expensive. We present a closure approximation that leads to continuum models in the true sense of the word. The fluxes in these models are given by operators acting on the average density and velocity. The closure construction is based on the use of regularized deconvolution. In the discrete setting, characterized by a finite non-improvable resolution, the error associated with deconvolution closure can be further reduced by incorporating a priori knowledge of empirical statistics of fluctuations. At the end of the talk we briefly discuss connections with large eddy simulation and quasi-continuum method. Results of numerical experiments and partial error estimates are presented as well.
[Abstract]
Mathematikgebäude, Seminarraum M614/616 (6. Etage)
Vortrag in der Reihe
Im Rahmen des Mathematischen Kolloquiums
14.05.2014
16.15 Uhr
Amin Safi, M.Sc.
Fakultät für Mathematik, TU Dortmund
Was ist Lattice Boltzmann? [WWW] Mathematikgebäude, Seminarraum E19
Im Rahmen des Mathematischen Kolloquiums
Im Rahmen der Vortragsreihe Angewandte Numerik und Simulation
27.05.2014
14 Uhr
Prof. Ilya Timofeyev
University of Houston, USA
From Microscopic to Coarse-Grained PDE Models of Pedestrian Traffic

Zusammenfassung


Microscopic rules for pedestrian traffic in a narrow street are discussed and the corresponding stochastic lattice system modeling the pedestrian bi-directional flow is introduced. Then the mesoscopic and macroscopic PDE models for the pedestrian density are derived. The macroscopic PDE model is a system of conservation laws which can change type depending on the strength of interaction between the pedestrian flows and initial conditions. Behavior of the stochastic and coarse-grained models is compared numerically for several different regimes and initial conditions. Finally, nonlinear diffusive corrections to the PDE model are derived systematically. Numerical simulations show that the diffusive terms can play a crucial role when the conservative coarse-grain PDE model becomes non-hyperbolic.
[Abstract]
Mathematikgebäude, Seminarraum M614/616 (6. Etage)
Vortrag in der Reihe
Im Rahmen des Mathematischen Kolloquiums
10.06.2014
16.15 Uhr
PD Dr. Frank Klinker
Fakultät für Mathematik, TU Dortmund
Was ist Supersymmetrie? [WWW] Mathematikgebäude, Seminarraum E19
Im Rahmen des Mathematischen Kolloquiums
Im Rahmen der Vortragsreihe Angewandte Numerik und Simulation
04.07.2014
14 Uhr
Dr. Mikhail Shashkov
Los Alamos National Laboratory, USA
Multimaterial Moment-of-Fluid Interface Reconstruction [PDF] Mathematikgebäude, Seminarraum M614/616 (6. Etage)
Vortrag in der Reihe
Im Rahmen des Mathematischen Kolloquiums
09.07.2014
16.15 Uhr
Dr. Amir Nasseri
Bergische Universität Wuppertal
Was ist Chaos? [WWW] Mathematikgebäude, Seminarraum E19