HGS MathComp Curriculum & Events

A numerical model for simulating a three-dimensional flow bounded by a fully-nonlinear, free-surface boundary is developed. The free-surface boundary conditions are satisfied on the free-moving surface exactly without any approximation or linearization. The governing equations and the boundary conditions on the time-dependent, physical domain are transformed onto a regular domain for numerical computations. The solenoidal condition of the velocity field is satisfied by solving the transformed pressure Poisson equation. A modified secant method is used to accelerate the iterative solution of the non-separable Poisson equation. We first apply the numerical model to study the development and evolution of parasitic capillary ripples on a two-dimensional gravity-capillary wave. The simulation results reveal that strong vortices are shed from the troughs of the capillary ripples, convected backward, and form a strong boundary layer. As a result, energy dissipation is enhanced with the generation of parasitic capillaries. The model capabilities for resolving nonlinear interactions among the surface waves are then demonstrated by simulating the three-dimensional evolutions of the short-crested waves and the crescent waves. Finally, the developed model is applied to simulate a wind-driven turbulent boundary layer bounded by a dynamic water surface. The simulation results reveal fine surface structures, including parasitic capillary waves developed from the front face near the crest of the dominant gravity wave and streamwise velocity streaks on the back gravity-wave surface, which have been observed in the laboratory and field experiments.

Abstract:
Motivated by the requirements of today’s archaeologists we are developing a system for documentation of daily finds of excavations using 3D-acquisition. The most widespread finds are fragments of ceramics, shortly called sherds. As ceramics have been produced for millenniums and found in vast numbers, their fragments are important for archaeological research, because their shape leads to information about ancient cultures.

We show the use of 3D-Scanners based on the principle of structured light for documentation. This enables an accurate and efficient way of in-situ acquisition. Using the common feature of rotational symmetry of ceramics typically produced on rotational wheels, we can automatically estimate proper orientated cross-sections (profiles) of the acquired sherds for archaeological publications and classification. Having 3D-models of ceramics we can also determine additional information about the manufacturing process, quality features or volume estimations for further classification.

Beside geometric features, ceramics and other objects of our Cultural Heritage have painted decoration and today’s 3D-scanners are able to acquire coloured (textured) surfaces. Future work requires to add texture-analysis and pattern recognition methods for 3D-documentation as well as high-resolution texture mapping and handling techniques e.g. from multi-spectral imaging. Pattern recognition will also help to organize the 3D-documenation using Semantics and Digital Libraries. We will show examples from several inter-disciplinary projects with archaeological partners in Austria, Israel, Italy, Germany and Peru.

Samarium Doped Ceria (SDC) electrodes are currently of great interest for SOFC
applications. For example, ceria-containing anodes can be operated directly on
hydrocarbons without coking, and in addition can be used at lower temperatures than
Ni/YSZ. In order to design, optimize, and characterize electrodes, it is very useful to have
models to aid in interpreting experimental results. In this work, we present a linear, timeindependent
model for the study of SDC. This model allows us to compute species
concentrations, electric potential and currents under small bias conditions. A regular
perturbation of the drift diffusion equations and Poisson’s equation is used to derive the
model for the behavior of bulk of the material. We also include the kinetics of reactions
occurring at the SDC-gas surface where the SDC is exposed to a spatially uniform
hydrogen-water-argon mixture at fixed total pressure. The linear response to a small
voltage input is computed at various hydrogen and water partial pressures.
The numerical procedure allows for fast computations and for the direct determination of
fast and rate limiting steps. Polarization resistance curves are computed in the two
dimensional case and a quantitative comparison between experimental (symmetric cell)
and numerical results computations is presented.
The model can be naturally extended to the non-symmetric case, i.e. the case under which
the two sides of the SDC assemblies are exposed to different atmospheres.

Samarium Doped Ceria (SDC) electrodes are currently of great interest for SOFC applications. For example, ceria-containing anodes can be operated directly on hydrocarbons without coking, and in addition can be used at lower temperatures than Ni/YSZ. In order to design, optimize, and characterize electrodes, it is very useful to have models to aid in interpreting experimental results. In this work, we present a linear, time-independent model for the study of SDC. This model allows us to compute species concentrations, electric potential and currents under small bias conditions. A regular perturbation of the drift diffusion equations and Poisson’s equation is used to derive the model for the behavior of bulk of the material. We also include the kinetics of reactions occurring at the SDC-gas surface where the SDC is exposed to a spatially uniform hydrogen-water-argon mixture at fixed total pressure. The linear response to a small voltage input is computed at various hydrogen and water partial pressures.
The numerical procedure allows for fast computations and for the direct determination of fast and rate limiting steps. Polarization resistance curves are computed in the two dimensional case and a quantitative comparison between experimental (symmetric cell) and numerical results computations is presented.
The model can be naturally extended to the non-symmetric case, i.e. the case under which the two sides of the SDC assemblies are exposed to different atmospheres.

Modeling of elastic shell structures coupled with acoustics in a way
that is suitable for optimization poses a multitude of challenges. For
the exterior problem, it is convenient to use shell elements in
conjunction with boundary elements so that shape updates can be
performed without modifying the mesh. In order to do so, the shell
code must be free of the so-called locking phenomenon, and the
boundary element code must be robust and reasonably fast. With the aim
of making the implementation of the coupling and adjoint equations as
simple as possible, we describe a scheme satisfying these criteria,
and present some numerical results.

In this talk, I will discuss some applications of dynamic optimisation techniques to problems arising in the (bio)chemical industry. The employed techniques involve a combination of both direct and indirect approaches. The (bio)chemical processes under study are, e.g., tubular reactors and fed-batch fermentors. Special attention will be paid to how to efficiently deal with dynamic optimisation problems with multiple objectives.

The workshop is addressed to students and PhD students of mathematics, physics
and computer science, who want to visualize their own numerical results using
the advantages of virtual reality for a better understanding of three dimensional
processes. We explain the possibilities of importing data and how to extend them
to own data formats. Furthermore the workshop gives insight in available possibilities
of visualizing these data with COVISE and how to adjust them on own needs.
Emphasis is put on working with virtual reality and how this technology can be
sucsessfully used. This will be explained with several examples to demonstrate to
the participants how they can present their own numerical results interactively and
easy to understand. Every participant will be guided how to adapt the existing scope
of operations and established interactions for own requirements.