Jörn Sesterhenn

Julius Reiss, Philipp Schulze, Jörn Sesterhenn et al.

Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind of systems. It extends the proper orthogonal decomposition (POD) by introducing time-dependent shifts of the snapshot matrix. The approach, called shifted proper orthogonal decomposition (sPOD), features a determination of the {\it multiple} transport velocities and a separation of these. One- and two-dimensional test examples reveal the good performance of the sPOD for transport-dominated phenomena and its superiority in comparison to the POD.

Jörn Sesterhenn, Amir Shahirpour

Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models and define either spatial structures in time or temporal structures in space. On the contrary, convecting phenomena pose a major problem to those decompositions. A structure traveling with a certain group velocity will be perceived as a plethora of modes in time or space respectively. This manifests itself for example in poorly decaying singular values when using a POD. The poor decay is counter-intuitive, since a single structure is expected to be represented by a few modes. The intuition proves to be correct and we show that in a properly chosen reference frame along the characteristics defined by the group velocity, a POD or DMD reduces moving structures to a few modes, as expected. Beyond serving as a reduced model, the resulting entity can be used to define a constant or minimally changing structure in turbulent flows. This can be interpreted as an empirical counterpart to exact coherent structures. We present the method and its application to a head vortex of a compressible starting jet.

Julius Reiss, Mathias Lemke, Jörn Sesterhenn

A method to calculate the adjoint solution for a large class of partial differential equations is discussed. It differs from the known continuous and discrete adjoint, including automatic differentiation. Thus, it represents an alternative, third method. It is based on a modal representation of the linearized operator of the governing (primal) system. To approximate the operator an extended version of the Arnoldi factorization, the dynamical Arnoldi method (DAM) is introduced. The DAM allows to derive approximations for operators of non-symmetric coupled equations, which are inaccessible by the classical Arnoldi factorization. The approach is applied to the Burgers equation and to the Euler equations on periodic and non-periodic domains. Finally, it is tested on an optimization problem.

Steffen Büchholz, Mathias Lemke, Julius Reiss et al.

Monitoring active volcanos is an ongoing and important task helping to understand and predict volcanic eruptions. In recent years, analysing the acoustic properties of eruptions became more relevant. We present an inexpensive, lightweight, portable, easy to use and modular acoustic data acquisition system for field measurements that can record data with up to 100~kHz. The system is based on a Raspberry Pi 3 B running a custom build bare metal operating system. It connects to an external analog - digital converter with the microphone sensor. A GPS receiver allows the logging of the position and in addition the recording of a very accurate time signal synchronously to the acoustic data. With that, it is possible for multiple modules to effectively work as a single microphone array. The whole system can be build with low cost and demands only minimal technical infrastructure. We demonstrate a possible use of such a microphone array by deploying 20 modules on the active volcano \textit{Stromboli} in the Aeolian Islands by Sicily, Italy. We use the collected acoustic data to indentify the sound source position for all recorded eruptions.