Julius Reiss

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.

Philipp Schulze, Julius Reiss, Volker Mehrmann

We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance of classical methods like the proper orthogonal decomposition (POD) for transport-dominated phenomena. This is achieved by identifying the transport directions and velocities and by shifting the modes in space to track the transports. Our new algorithm carries out a residual minimization in which the main computational cost arises from solving a nonlinear optimization problem scaling with the snapshot dimension. We apply the algorithm to snapshot data from the simulation of a pulsed detonation combuster and observe that very few sPOD modes are sufficient to obtain a good approximation. For the same accuracy, the common POD needs ten times as many modes and, in contrast to the sPOD modes, the POD modes do not reflect the moving front profiles properly.

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.