Uncertainty Quantification in Direct Noise Computations of Cavity Feedback

Principal Investigator:
Andrea Beck(1), Claus-Dieter Munz(1), Christian Rohde(2)

(1) Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, (2) Institute of Applied Analysis and Numerical Simulation, University of Stuttgart

Local Project ID:

HPC Platform used:
Hazel Hen of HLRS

Date published:

In addition to wind tunnel experiments, the deterministic numerical simulation has become an indispensable tool for the aerodynamic research both in academia and industry. Large improvements of the available algorithms and an increase in present computer resources have lead to a great improvement in the accuracy of simulation results and to a reduction of numerical errors. Therefore, numerical simulation results often provide a good agreement with experimental data. However, whenever uncertainty about the experimental setting or uncertainties due to unknown model parameters enter the non-linear governing equations, larger deviations between numerical and experimental results can occur. In order to address these deviations and to capture the whole picture in a numerical simulation, the quantification of the influence of uncertain model input is necessary. This leads to the research field of Uncertainty Quantification (UQ) which provides different mathematical tools to uncover the influence of random input on numerical simulation results and derived quantities.

In the current project, researchers of the Institute of Aerodynamics and Gas Dynamics at the University of Stuttgart develop an efficient UQ framework to capture the influence of uncertainties at minimal computational cost. This framework contains both an intrusive as well as a non-intrusive forward uncertainty propagation environment. The intrusive solver is based on the Stochastic Galerkin method which was implemented into the high-order Discontinuous Galerkin solver FLEXI. FLEXI is developed within the Numerics Research Group of Prof. Munz at the IAG Stuttgart. For the non-intrusive UQ software POUNCE has been developed, which is specifically designed for queue-based HPC systems such as the Hazel Hen or the Hawk system and for HPC file systems such as Lustre.

With the newly developed UQ framework, the researchers investigate the influence of uncertain input onto the highly-nonlinear aeroacoustic feedback of cavity flows. To perform such an aeroacoustic cavity simulation at high Reynolds number with a direct simulation approach already necessitates a large amount of computational resources in a deterministic setting. Hence, in combination with UQ the computational resources get over-exceeded. Therefore, the researchers developed an efficient simulation framework which includes a turbulent inflow method as well as a wall-model approach. In multiple deterministic simulations of an open rectangular cavity, the modeling assumptions have been verified with experimental results.

An example of such an aeroacoustic cavity simulation combined with the UQ framework is shown in Fig. 1. In this specific simulation, the uncertainty of an uncertain boundary layer thickness of the incoming turbulent boundary layer has been studied. The left plot shows an instantaneous snapshot of the wall-bounded turbulence and the radiated sound wave from the cavity. The right figure represents the corresponding sound spectrum measured inside the cavity. Apart from the experimental result, mean and variance of the acoustic spectrum are given.

For the setup shown above, a 7th order ansatz in space and a 5th order ansatz in the stochastic domain was chosen, leading to a total of 181 million degrees of freedom. All computations were run on the Cray HPC System Hazel Hen at HLRS. The simulation costs per deterministic simulation sample were about 38,400 CPU hours with 9,600 cores. Similar simulations with the same setup are currently running on Hawk.

Research Team (Principal Investigators)

Dr. Andrea Beck1, Prof. Dr. Claus Dieter Munz1, Prof. Dr. Christian Rohde2

1Institute of Aerodynamics and Gas Dynamics (IAG), University of Stuttgart
2Institute of Applied Analysis and Numerical Simulation (IANS), University of Stuttgart


[1] J. Giesselmann, F. Meyer, and C. Rohde, “A posteriori error analysis for random scalar conservation laws using the stochastic Galerkin method”, IMA J. Numer. Anal., 2019. doi: 10.1093/imanum/drz004. [Online]. Available:

[2] J. Dürrwächter, T. Kuhn, F. Meyer, L. Schlachter, and F. Schneider, “A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations”, Journal of Computational and Applied Mathematics, p. 112 602, 2019, issn: 0377-0427. doi:

[3] J. Dürrwächter, F. Meyer, T. Kuhn, A. Beck, C.-D. Munz, and C. Rohde, “A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations”, In review at Computers and Fluids, 2019.

[4] A. Beck, J. Dürrwächter, T. Kuhn, F. Meyer, C.-D. Munz, and C. Rohde, “Hp-Multilevel Monte Carlo methods for uncertainty quantification of compressible flows”, In review at SIAM Scientific Computing, 2018. [Online]. Available:

[5] T. Kuhn, J. Dürrwächter, F. Meyer, A. Beck, C. Rohde, and C.-D. Munz, “Uncertainty quantification for direct aeroacoustic simulations of cavity flows”, Journal of Theoretical and Computational Acoustics, vol. 27, 2019, issn: 2591-7811 and 2591-7285. doi:

[6] T. Kuhn, J. Dürrwächter, A. Beck, and C.-D. Munz, “Zonal large eddy simulation of active open cavity noise using a high order discontinuous Galerkin method”, AIAA Conference Paper, 2019. [Online]. Available:

[7] J. Giesselmann, F. Meyer, and C. Rohde, “An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws”, Proceedings of HYP2018, 2019. [Online]. Available:

[8] J. Giesselmann, F. Meyer, and C. Rohde, “A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws”, In review at BIT Numerical Mathematics, 2019. [Online]. Available:

[9] A. Beck, J. Dürrwächter, T. Kuhn, F. Meyer, C.-D. Munz, and C. Rohde, “Uncertainty quantification in high performance computational fluid dynamics”, In review for High Performance Computing in Science and Engineering ’19, 2019.

Scientific Contact

Prof. Dr. rer. nat. Claus-Dieter Munz
Institute of Aerodynamics and Gas Dynamics (IAG)
University of Stuttgart
Pfaffenwaldring 21, D-70569 Stuttgart (Germany)
e-mail: munz [@]

HLRS project ID: SEAL

May 2020


Tags: HLRS Universität Stuttgart IAG