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The group Mathematical Modeling and Analysis (MMA), headed by Prof. Dr. rer. nat. Dieter Bothe, represents an interdisciplinary group. It roots in the Department of Mathematics at Technische Universität Darmstadt with its research activities being embedded within the Profile Area “Thermofluids & Interfaces” at Technische Universität Darmstadt.

Research Areas

The research topics of MMA are substantially motivated by open problems in process and chemical engineering. The corresponding research areas are

Mathematical Modeling and Applied Analysis

  • Two-Phase Free Boundary/Interface Problems
  • Reaction-Diffusion(-Electromigration) Systems
  • Contact Line Dynamics
  • Phase Transition Problems
  • Viscoelastic Fluids

Our research is based on the continuum modeling of two-phase flows employing and further developing sharp-interface models based on Continuum Thermodynamics. These models correspond to increasing levels of physico-chemical interface properties, starting from capillary interfaces to the case when the interface is a phase on its own with surface tension, interfacial viscosities and adsorbed species. For the different levels the corresponding mathematical models are mathematically analysed regarding solvability and their qualitative properties.

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Computational Engineering

  • Two-Phase Flows and Free-Surface Flows
  • Transport Processes at Fluidic Interfaces
    • Interfacial Mass and Heat Transfer
    • Surfactant Mixtures
    • Reaction-Advection-Diffusion Systems
  • Contact Line Dynamics
  • Thermal and Solutal Marangoni-driven Flows
  • Viscoelastic Fluids
  • Hydrodynamics of Drops and Bubbles

Our research is focused on Computational Fluid Dynamics (CFD) by means of Direct Numerical Simulation (DNS) including the numerical modeling of interfacial transport processes and physico-chemical phenomena in two- and multiphase systems. For a deep understanding of elementary transport and transfer processes at fluid interfaces, we actively develop techniques for different numerical simulation methods. The central aim is to provide taylor-made high-fidelity methods which exhibit distinct advantages for the specific interfacial transport physics under consideration.

We develop and deploy Volume-Tracking, Interface-Tracking and Front-Tracking Methods and hybrid variants of those. The code bases used are Free-Surface 3D (FS3D), which is an in-house Fortran code, and Open Field Operation and Manipulation (OpenFOAM), which is an open source C++ library for computational continuum mechanics.

Free Surface 3D (FS3D)

Open Field Operation and Manipulation (OpenFOAM)