Talks

After only two weeks of being able to get to know you in person, I will use this talk to introduce myself and talk about present and past work. My presentation will be divided into three parts. After shortly introducing myself (1), I'll cover the following topics related to my masters thesis (2) and my PhD research (3).

2. Amplitude dynamics of resonant Rossby wave triads in Nambu form:
Non-linear interactions play a fundamental role in the redistribution of energy amongst Rossby waves. For weakly interacting waves, geometric constraints govern the dynamics of forced and unforced resonant Rossby wave triads. These constraints allow to cast the dynamical equations in Nambu formulation.

3. How Semi-Implicit Spectral Deferred Correction (SISDC) can improve Numerical Weather Prediction (NWP) models and climate projections:
The multitude of time scales associated with atmospheric waves (e.g. Rossby-, gravity-, sound-waves) poses difficulties in modeling the full governing equations. The CFL condition usually requires the adaption of the time step to the fastest waves to prevent instabilities. However, the fastest waves (i.e. sound waves) in general transport a negligible amount of energy and therefore have minimal impact on the dynamics. By treating the fastest waves implicitly, instabilities can be prevented despite a CFL-number > 1. Using SISDC to integrate the linearized Boussinesq equations has proven to be valuable alternative to implicit-explicit Runge-Kutta and diagonally implicit Runge-Kutta methods. Applying SISDC to the full compressible governing equations may improve cost and accuracy of state of the art NWP models.

The presentations aims to give a rather short non-technical introduction in the general concept of a functional calculus including several examples and applications.

The presentation will (mostlikely) make use of the tool 'Zoom'. The audience will not have to do much but simply follow a link the speaker provides everybody with who asks in advance (jan.meichsner@tuhh.de). Members of the institute will get the link via the common email list.

Quite often, we wonder about the people around us but we are too shy to actually ask. On Thursday 27.02.2020, the Institute für Mathematik has organised a presentation about the one that is – up to the current date and not for very long – its latest “outstanding” acquisition.

During the presentation, you will finally be able to respond to the following questions:

- Why is he so fascinating?

- What was his last piece of work?

- What has he done during his first month?

These and any other question will be discussed during the meeting and who knows, maybe one day, in your closest cinema.

Moving-boundary flow simulations are an important design and analysis tool in many areas, including civil and biomedical engineering, as well as production engineering. Interface-capturing offers flexibility for complex free-surface motion, while interface-tracking is very attractive due to its mass conservation properties at low resolution. We focus on these alternatives in the context of flow simulations based on stabilized finite element discretizations of Navier-Stokes equations, including space-time formulations that allow extra flexibility concerning grid design at the interface.

Space-time approaches offer some not-yet-fully-exploited advantages; among them, the potential to allow some degree of unstructured space-time meshing. A method for generating simplex space-time meshes has been developed, allowing arbitrary temporal refinement in selected portions of space-time slabs. The method increases the flexibility of space-time discretizations, even in the absence of dedicated space-time mesh generation tools. The resulting tetrahedral and pentatope meshes are being used in the context of cavity filling flow simulations, such as those necessary to design injection molding processes.