News & Events 2017
Activities of the RTG

Weekly Seminar
Semiclassical Computation of High Frequency Waves in Heterogeneous Media
Shi Jin (University of Wisconsin-Madison (U.S.A.))
Thu, 14 Dec 2017 • 10:15-11:15h • Schinkelstraße 2, Room 328


In this talk we will study kinetic equations with multiple scales and random uncertainties from initial data and/or collision kernel. Here the multiple scales, characterized by the Knudsen number, will lead the kinetic equations to hydrodynamic (Euler, incompressible Navier-Stokes or diffusion) equations as the Knudsen number goes to zero. Asymptotic-preserving schemes, which minic the asymptotic transitions from the microscopic to the macroscopic scales at the discrete level, have been shown to be effective to deal with multiscale problems in the deterministic setting.

We first extend the paradigm of asymptotic-preserving schemes to random kinetic equations, and show how it can be constructed in the setting of stochastic Galerkin approximations. We then extend the hypocoercivity theory, developed for deterministic kinetic equations, to the random case, and establish in the random space regularity, long-time sensitivity analysis, and uniform (in Knudsen number) spectral convergence of the stochastic Galerkin methods, for general lienar and nonlinear random kinetic equations in various asymptotic–including the diffusion, incompressible Navier-Stokes, high-field, and acoustic–regimes.

Weekly Seminar
Variational formulation and limits of evolution equations possessing a gradient structure
André Schlichting (RWTH Aachen University (Germany))
Thu, 07 Dec 2017 • 10:15-11:15h • Schinkelstraße 2, Room 328


In this talk, we consider evolution equations possessing a gradient structure, that is they are the gradient flow of a free energy functional with respect to some metric. We review a variational framework, which allows to pass to the limit from one gradient structure to another.

In particular, we apply the method to gradient structures of a discrete coagulation-fragmentation model, the Becker-Böring equation, and its macroscopic limit. We show that the convergence result obtained by Niethammer (J. Nonlinear Sci.) can be extended to proof the convergence not only for solutions of the Becker-Döring equation towards the Lifshitz-Slyozov-Wagner equation of coarsening, but also the convergence of the associated gradient structures.

Weekly Seminar
Relative entropy for hyperbolic conservation laws and related systems
Jan Giesselmann (RWTH Aachen University (Germany))
Thu, 30 Nov 2017 • 10:15-11:15h • Schinkelstraße 2, Room 328


We will review the relative entropy framework for systems of hyperbolic conservation laws. It provides a stability theory which allows to compare solutions to different initial data, and, in particular, to prove weak-strong uniqueness. We will discuss how it can be extended to a variety of models for compressible fluid flows that have a (nearly) Hamiltonian structure such as the isothermal Euler-Korteweg and Euler-Poisson systems. In this context the relative entropy can be used, for example, to show that the Euler-Korteweg model converges to the Cahn-Hilliard equation in a large friction limit.

For the Euler-Kortweg model a particular feature is the interest in non-convex energy functionals and we will discuss whether the relative entropy framework can be extended to that case.

Weekly Seminar
Two-Phase Flows with Phase Transition
Maren Hantke (RWTH Aachen University (Germany))
Thu, 16 Nov 2017 • 10:15-11:15h • Schinkelstraße 2, Room 328


Zur Modellierung von Zwei-Phasen-Strömungen wird nicht selten das Baer-Nunziato-Modell verwendet. Dieses wurde 1986 von Baer und Nunziato für Deflagrations- / Detonationsprozesse eingeführt und später von zahllosen Autoren zur Simulation von zwei-komponentigen Gemischen aufgegriffen. Eine Erweiterung des Modells auf mehrere Komponenten ist nicht trivial und bedarf besonderer Sorgfalt. Durch Modellierung geeigneter Quellterme lässt sich das Baer-Nunziato-Modell auch zur Beschreibung von Phasenübergangsprozessen verwenden.

Wir diskutieren Schließungsbedinungen für eine Verallgemeinerung des Baer-Nunziato-Modells auf n Komponenten, Relaxationsterme zur Modellierung von Austauschprozessen und numerische Verfahren zur Handhabung dieser Austauschterme.

DFG to fund Research Training Group

The German Research Foundation (DFG) has approved funding for our Research Training Group in applied mathematics, titled Energy, Entropy, and Dissipative Dynamics. The RTG will start in October 2017.

It combines analysis, modeling, and numerics of nonlinear partial differential equations coming from physics, materials science, and geometry. A common theme among the research projects is the use of energy and entropy functionals and their dissipation mechanisms as a tool for the investigation of the qualitative and quantitative behavior of solutions.

Eight RWTH professors will contribute to the Research Training Group and ten doctoral researchers are financed by the German Research Foundation, which will provide a total of 3.4 million Euros.

Prof. Dr. Michael Westdickenberg
Deputy Speaker
Prof. Dr. Michael Herty
DFG Press Release