Gudrun Thäter

For the 2D Oberbeck-Boussinesq system in an annulus we are looking for the critical Rayleigh number for which the (nonzero) basic flow loses stability. For this we consider the corresponding Euler-Lagrange equations and construct a precise functional analytical frame for the Laplace- and the Stokes problem as well as the Bilaplacian operator in this domain. With this frame and the right set of basis functions it is then possible to construct and apply a numerical scheme providing the critical Rayleigh number.

The phenomenon of distribution shift (DS) occurs when a dataset at test time differs from the dataset at training time, which can significantly impair the performance of a machine learning model in practical settings due to a lack of knowledge about the data's distribution at test time. To address this problem, we postulate that real-world distributions are composed of latent Invariant Elementary Distributions (I.E.D) across different domains. This assumption implies an invariant structure in the solution space that enables knowledge transfer to unseen domains. To exploit this property for domain generalization, we introduce a modular neural network layer consisting of Gated Domain Units (GDUs) that learn a representation for each latent elementary distribution. During inference, a weighted ensemble of learning machines can be created by comparing new observations with the representations of each elementary distribution. Our flexible framework also accommodates scenarios where explicit domain information is not present. Extensive experiments on image, text, and graph data show consistent performance improvement on out-of-training target domains. These findings support the practicality of the I.E.D assumption and the effectiveness of GDUs for domain generalisation.

A detailed knowledge of the influence of a particle’s shape on its settling behavior is useful for the prediction and design of separation processes. Models in the available literature usually fit a given function to experimental data. In this work, a constructive and data-driven approach is presented to obtain new drag correlations. To date, the only considered shape parameters are derivatives of the axis lengths and the sphericity. This does not cover all relevant effects, since the process of settling for arbitrarily shaped particles is highly complex. This work extends the list of considered parameters by, e.g., convexity and roundness and evaluates the relevance of each. The aim is to find models describing the drag coefficient and settling velocity, based on this extended set of shape parameters. The data for the investigations are obtained by surface resolved simulations of superellipsoids, applying the homogenized lattice Boltzmann method. To closely study the influence of shape, the particles considered are equal in volume, and therefore cover a range of Reynolds numbers, limited to [9.64, 22.86]. Logistic and polynomial regressions are performed and the quality of the models is investigated with further statistical methods. In addition to the usually studied relation between drag coefficient and Reynolds number, the dependency of the terminal settling velocity on the shape parameters is also investigated. The found models are, with an adjusted coefficient of determination of 0.96 and 0.86, in good agreement with the data, yielding a mean deviation below 5.5% on the training and test dataset.

The simulation of surface resolved particles is a valuable tool to gain more insights in the behaviour of particulate flows in engineering processes. In this work the homogenized lattice Boltzmann method as one approach for such direct numerical simulations is revisited and validated for different scenarios. Those include a 3D case of a settling sphere for various Reynolds numbers. On the basis of this dynamic case, different algorithms for the calculation of the momentum exchange between fluid and particle are evaluated along with different forcing schemes. The result is an updated version of the method, which is in good agreement with the benchmark values based on simulations and experiments. The method is then applied for the investigation of the tubular pinch effect discovered by Segré and Silberberg and the simulation of hindered settling. For the latter, the computational domain is equipped with periodic boundaries for both fluid and particles. The results are compared to the model by Richardson and Zaki and are found to be in good agreement. As no explicit contact treatment is applied, this leads to the assumption of sufficient momentum transfer between particles via the surrounding fluid. The implementations are based on the open-source C++ lattice Boltzmann library OpenLB.

It is shown that the anelastic Oberbeck–Boussinesq system is a small Mach, small Péclet and small Froude number limit of the complete Navier–Stokes–Fourier system for gases with large specific heat at constant volume. This result is obtained on an arbitrary large time interval. The proof allows an intrinsic view into the process of separation of fast oscillating acoustic waves, governed by a Lighthill-type equation, from the equations describing the slow fluid flows. This is a very useful information for numerical analysts.