Thematic Einstein Semester on

Energy-based mathematical methods for reactive multiphase flows

Winter Semester 2020/21

Organizers

Matthias Liero (WIAS Berlin)
Volker Mehrmann (TU Berlin)
Alexander Mielke (HU Berlin / WIAS)
Dirk Peschka (WIAS)
Marita Thomas (WIAS)
Barbara Wagner (WIAS)

Note

In the course of the current COVID-19 situation, we have decided to take some precautions and organize the semester program online. In particular, it will be possible to present and attend the lectures of the kick-off conference via an online platform, where we strive to making interactive discussions as engaging as possible.

The semester is organized within the framework of the Berlin Mathematics Research Center Math+ and supported by the Einstein Foundation Berlin.

We are committed to fostering an atmosphere of respect, collegiality, and sensitivity. Please read our MATH+ Collegiality Statement.

Scope of the Semester

Since the early works of Lagrange and Hamilton for classical mechanics and Rayleigh and Helmholtz for dissipative processes, energetic variational methods for fluids and solids have been developed extensively. The relation to underlying microscopic stochastic models was pioneered by Onsager leading to his celebrated reciprocal relations. However, most systematic developments concerned either purely conservative Hamiltonian systems or purely dissipative gradient systems. In the last two decades, a unification of these two extremes was addressed by developing concepts for systems combining both systems. More recently, these topics evolved into mathematical theories such as GENERIC and port-Hamiltonian structures. Corresponding thermodynamical structures are advantageous from the modeling point-of-view and for the design of efficient numerical schemes. However, different communities have developed own languages and specific mathematical methods that are not always accessible for non-experts.

This Thematic Einstein Semester will bring together scientists from different communities to develop synergies between the different approaches. The mathematical community could contribute (to) the structural analysis of flowing systems concerning, for example, the geometry of thermodynamic systems, functional analytical frameworks for partial differential equations, description of bulk-interface coupling, connection to microscopic/stochastic models, construction of structure-preserving numerical schemes, model reduction or modular modeling. Communication with applied material research communities in mathematics, physics and engineering will cover diverse material systems such as, for example, reactive flows, porous medium flow, hydrogels, electrolytes, colloidal and non-colloidal suspensions, nematic materials, and beyond, where thermodynamic descriptions play an important role.

TES-Seminar on Energy-based Mathematical Methods and Thermodynamics

The seminar is held online in Zoom. In order to receive the Zoom-links to attend the talks, please register using the button below.

Next seminar: November 19, 2020
Speaker: Christian Wieners (KIT)
Title of the talk: A discontinuous Galerkin method for phase field approximations of dynamic fracture

Abstract: We present a new numerical method for dynamic fracture at small strains which is based on a discontinuous Galerkin approximation of a first order formulation for elastic waves and where the fracture is approximated by a phase field driven by a stress based fracture criterion.
The staggered algorithm in time combines the implicit midpoint rule for the wave propagation followed by an implicit Euler step for the phase field evolution. Then, driven by a stress based fracture criterion, the material is degradated, and the waves are reflected at the diffusive interface.
Then method is evaluated in detail in one dimension, and then we demonstrate in a 2D application the fracture evolution with multiple fractures initiated by reflections.
This is joint work with Kerstin Weinberg, Siegen.

Upcoming workshops

Scope: This workshop is devoted to recent aspects regarding the analysis of mathematical problems arising in the continuum mechanics of solids.
It features 20 presentations by invited speakers and will be held as an online format. Registration is required and open till November 20, 2020.
In particular, please note that the links to the online-presentation sessions will be available for registered participants, only.

Past events

TES Kick-Off Conference

Scope: For this conference, we combine daily invited presentations (40 minutes including discussion) with other interactive discussion formats. In particular, we have parallel discussion sessions that are supposed to create the interactive discussion type of a poster presentation. We also have moderated discussion sessions (round table) on given topics, where we discuss promising research topics in the field of energetic- variational mathematical methods with the participants of the conference. The talks on Friday Oct 30 are organized in cooperation with the DFG CRC 910. All parts of the conference (invited talks, discussions and round table) are available online. If you plan to contribute a talk or a discussion contribution, please indicate this during the registration procedure (and we will provide additional information & extended abstract template afterwards).

TES Student Compact Course

Scope: The course will give an in-depth background on the topics of the Thematic Einstein Semester Energy-based Mathematical Methods for Reactive Multiphase Flows. In particular, the focus is on evolutionary systems whose mathematical formulation exhibits advantageous structures such as port-Hamiltonian, gradient, or GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling) structures.