Fakultät für Mathematik — Lehrstuhl 3 für Angewandte Mathematik

Vogelpothsweg 87

44227 Dortmund

- Computerorientiertes Problemlösen WS10/11
- Computerorientiertes Problemlösen WS08/09
- PhD topics
- Eindrücke vom Hochschulstaffellauf 2005
- Eindrücke vom Hochschulstaffellauf 2003
- Eindrücke vom Hochschulstaffellauf 2002
- Eindrücke vom Hochschulstaffellauf 2001
- Vorbesprechung WS 2023/24

Supervisors: Prof. Dr. S. Turek / Prof. Dr. H. Blum

**Multiscale Diffusion Surface Techniques in FEM Simulation **

One of the central problems in the Finite Element (FEM) simulation of realistic problem configurations, particularly in structural mechanics and fluid dynamics for complex 3D geometries, is the generation of a sequence of hierarchical meshes in combination with multilevel adaptivity and solvers. Using fast multigrid solvers, one usually starts with coarse grids which however are based on the available CAD description of the full geometry so that these coarse meshes are often too large since they contain too many details which are not corresponding to the coarse character of this initial mesh. Moreover, additional problems occur if moving objects or even dynamic breakup or coalescence effects occur since in that case, permanent remeshing and import of new CAD data is necessary for the use of standard meshing tools.
The aim of this project is the development, analysis and realization of new techniques which describe surfaces in 3D geometries as volumes with a special "thickness" which can be controlled in relation to the underlying multiscale phenomena, that means the mesh width of the actual computational grid. Since implicit representations of such objects are required, Level-Set techniques are candidates which shall be applied together with special filtering techniques for the numerical treatment of Dirichlet boundary conditions in PDE simulation tools. In addition, these techniques have to be combined with the special `fictitious boundary` methods which have been developed in the FEM package FEATFLOW and which have been successfully tested in CFD simulations. Additionally, special adaptivity concepts which are based on local hanging nodes together with mesh deformation techniques are the central points in this project such that a flexible and efficient FEM simulation tool can be developed. The derived methodology shall be implemented in FEATFLOW and applications are taken from structural and fluid mechanics. Therefore, deepened knowledge in numerics of partial differential equations (theory and applications of FEM discretizations, multigrid methods), computational fluid dynamics and experience with mathematical simulation tools (FEATFLOW) are demanded. In addition, there has to be basic knowledge of continuum mechanics and experience in problems of engineering science.

**Contact:**

Prof. Dr. Stefan Turek (ture@featflow.de)

Department of Mathematics

Chair of Applied Mathematics and Numerics

Supervisors: Prof. Dr. Stefan Turek / Prof. Dr. Herbert Koch / Prof. Dr.-Ing. Sebastian Engell:

The aim of this project is the development and numerical analysis of coupling mechanisms for kinetic equations with CFD solvers, for instance FEATFLOW for incompressible and compressible flow simulations. Possible examples for this project can include population balance models which are typical in liquid-liquid and gas-liquid multiphase flows or in multiphase polymerization processes. In that case, a set of reaction-transport PDEs has to be coupled with the Navier-Stokes equations which requires appropriate discretization techniques in space and time. Moreover, the coupling mechanisms (implicit vs. explicit) and methods for data reduction are key aspects in this example. Another example is the coupling of CFD methods with simplified Boltzmann equations, for instance in the case of particulated flows. In that case, a huge number of objects has to be treated together with the surrounding fluid which requires special techniques for collision modelling and high performance computing techniques for efficient simulation software. Additionally, discrete breakup and coalescence can occur, for instance for thermal spraying or liquid-liquid phases, which shall be treated by special discrete rules. All methods have to analyzed and realized in the FEATFLOW package and applications are taken from chemical engineering processes. Therefore, deepened knowledge in numerics of partial differential equations (theory and applications of FEM discretizations, multigrid methods), computational fluid dynamics and experience with mathematical simulation tools (FEATFLOW) are demanded. In addition, there has to be basic knowledge of continuum mechanics and experience in problems of engineering science.

Prof. Dr. Stefan Turek (ture@featflow.de)

Department of Mathematics

Chair of Applied Mathematics and Numerics

Supervisors: Prof. Dr. S. Turek / Prof. Dr. H. Koch / Prof. Dr. rer. nat B. Svendsen

In the production of metallic and semiconductive materials the melt is the initial state in more than 90% of all production processes. Therefore detailed knowledge of physical properties of melts and detailed understanding of physical processes during solidification and superficially fusing are the basis to develop mathematical models, which can quantitatively describe the structure of the product, and hence the physical and chemical properties of the material. The description of solidification processes on a scale, which includes the formation of microstructures, is of crucial importance if one intends to develop materials with desired properties on the computer, that means `Virtual Material Design` for the forecast of microstructures. Based on the Heterogeneous Multi-Scale Method (HMM), the aim of this project is the coupling of microscopic effects (microstructures) with macroscopic processes for the solidification and melting of metallic and semiconductive materials which include solid, mush and fluid phases. Corresponding FEM simulation techniques for the prediction of microstructures as a function of controllable macroscopic process parameters have to realized and analyzed on the basis of the FEM package FEATFLOW. Therefore, deepened knowledge in numerics of partial differential equations (theory and applications of FEM discretizations, multigrid methods), computational fluid dynamics and experience with mathematical simulation tools (FEATFLOW) are demanded. In addition, there has to be basic knowledge of continuum mechanics and experience in problems of engineering science.

Prof. Dr. Stefan Turek (ture@featflow.de)

Department of Mathematics

Chair of Applied Mathematics and Numerics

Supervisors: Prof. Dr. S. Turek / Prof. Dr. H. Koch / Prof. Dr. W. Tillmann

The aim of this project is the mathematical modelling and the numerical simulation of coating processes via thermal spraying which consists of 2 parts. First of all, the flight phase of the particles, resp., droplets, can be described via a multiphase flow model which consists of the compressible Navier-Stokes equations together with an appropriate turbulence model. Moreover, models for the melting process and the multiphase flow behaviour have to be developed and analyzed, and the influence of the plasma inlet and the geometries have to be examined. Another aspect of this project is the building of the substrate by the impinging droplets including temperature effects and hence solidification. Here, the underlying model are the incompressible Navier-Stokes equations with level-set techniques for capturing the free surface. First of all, the impact of single droplets and their interaction with the underground consisting of older droplets, which have already formed "splats", have to be analysed. Based on these "microscopic" configurations, a statistical model for a macroscopic description has to be developed and realized. The derived methodology shall be implemented on the basis of the FEM package FEATFLOW which provides discretization and solver components for compressible as well as incompressible flow problems. Therefore, deepened knowledge in numerics of partial differential equations (theory and applications of FEM discretizations, multigrid methods), computational fluid dynamics and experience with mathematical simulation tools (FEATFLOW) are demanded. In addition, there has to be basic knowledge of continuum mechanics and experience in problems of engineering science.

Prof. Dr. Stefan Turek (ture@featflow.de)

Department of Mathematics

Chair of Applied Mathematics and Numerics

Supervisor: Prof. Dr.-Ing. S. Engell, Co-Supervisors: Prof. Dr. H. Koch, Prof. Dr. S. Turek

When polymerizations are performed on the technical scale, i.e. in large reactors, perfect mixing can no longer be assumed, in contrast to laboratory scale reactors, so there are concentration gradients in the reaction mixture that lead to different reaction velocities. Also the particle density may vary locally. Modelling of such processes is a multiscale problem, where on the macroscopic level, a flow pattern is established which influences the local mixing and thus the progress of the reaction. In turn, the resulting inhomogeneous distribution of the polymer in the reactor influences the flow pattern.The goal of the project is to predict the polymer properties in non-ideal technical reactors using first principles models. The solution approach will be to perform a CFD simulation of the flow pattern in the reactor with a certain amount of polymer particles, to discretize the reactor volume into larger compartments, and to solve the reaction model in the compartments. This process is repeated after the particle content in the reactor has changed enough to necessitate a re-computation of the flow pattern. The polymerisation process will be a semi-batch emulsion co-polymerisation of two monomers with different reaction rates so that the spatial distribution of the monomers significantly influences the composition of the polymer.

Prof. Dr.-Ing. Sebastian Engell (sebastian.engell@bci.uni-dortmund.de) Department of Bio- and Chemical Engineering Chair of Process Control www.bci.uni-dortmund.de/ast/de/index.html

Further details concerning the PhD Topics are available at Graduate School of Production Engineering and Logistics

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