Data-driven closures for turbulent free and porous media flows

PN 1-1 (II)

Project description

The main objective of this project is to create improved closure models for simulating turbulent flows in both free and porous media flows. These models are considered “optimized” when they are trained on high-fidelity simulation data, adhere to physical constraints, and account for the discretization aspects of the underlying PDE solver. We approach this task as a reinforcement learning (RL) problem, where the discretized PDE solver serves as the environment, the agent’s actions involve selecting and combining closure strategies, and the reward is based on relevant flow metrics. Our earlier work on RL-based closure models provided a promising proof of concept, but the challenge of applying them to non-standard flows remains an open research question that we aim to address in this project.

The project is structured into three primary goals, which also outline the work plan:

  • (A) Developing optimized closures for free flows, particularly those involving wall boundaries, by creating optimized eddy viscosity closures for free-flow situations.
  • (B) Extending the optimization process to turbulent flows at the pore scale, introducing complexity by considering flows within intricate pore geometries.
  • (C) Bridging the gap to the Representative Elementary Volume (REV) scale by expanding the

Large Eddy Simulation (LES) filtering concept to the Volume-averaged Navier-Stokes equations. Within the framework of this project, we aim to transfer the initial results obtained from RL-based closure strategies for canonical flows to real-world applications.

Project information

Project title Data-driven closures for turbulent free and porous media flows
Project leaders Andrea Beck (Rainer Helmig, Mathias Niepert)
Project staff Lukas Zech, doctoral researcher 
Project duration October 2022 - December 2025
Project number PN 1-1 (II)

Publications of PN 1-1 and PN 1-1 (II)

  1. 2023

    1. D. Appel, S. Jöns, J. Keim, C. Müller, J. Zeifang, and C.-D. Munz, “A narrow band-based dynamic load balancing scheme for the level-set ghost-fluid method,” in High Performance Computing in Science and Engineering ’21, W. E. Nagel, D. H. Kröner, and M. M. Resch, Eds., in High Performance Computing in Science and Engineering ’21. Cham: Springer International Publishing, 2023, pp. 305--320.
    2. D. Kempf et al., “Development of turbulent inflow methods for the high order HPC framework FLEXI,” in High Performance Computing in Science and Engineering ’21, W. E. Nagel, D. H. Kröner, and M. M. Resch, Eds., in High Performance Computing in Science and Engineering ’21. Cham: Springer International Publishing, 2023, pp. 289--304. doi: 10.1007/978-3-031-17937-2_17.
    3. M. Gao, D. Appel, A. Beck, and C.-D. Munz, “A high-order fluid–structure interaction framework with application to shock-wave/turbulent boundary-layer interaction over an elastic panel,” Journal of Fluids and Structures, vol. 121, p. 103950, Aug. 2023, doi: 10.1016/j.jfluidstructs.2023.103950.
    4. M. Kurz, P. Offenhäuser, and A. Beck, “Deep reinforcement learning for turbulence modeling in large eddy simulations,” International Journal of Heat and Fluid Flow, vol. 99, p. 109094, Feb. 2023, doi: 10.1016/j.ijheatfluidflow.2022.109094.
    5. P. Mossier, D. Appel, A. D. Beck, and C.-D. Munz, “An Efficient hp-Adaptive Strategy for a Level-Set Ghost-Fluid Method,” Journal of Scientific Computing, vol. 97, no. 2, Art. no. 2, Oct. 2023, doi: 10.1007/s10915-023-02363-7.

  2. 2022

    1. T. Wenzel, M. Kurz, A. Beck, G. Santin, and B. Haasdonk, “Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows,” in Large-Scale Scientific Computing, I. Lirkov and S. Margenov, Eds., in Large-Scale Scientific Computing. Cham: Springer International Publishing, 2022, pp. 410--418.
    2. D. Kempf and C.-D. Munz, “Zonal direct-hybrid aeroacoustic simulation of trailing edge noise using a high-order discontinuous Galerkin spectral element method,” Acta Acustica, vol. 6, p. 39, 2022, doi: 10.1051/aacus/2022030.
    3. P. Mossier, A. Beck, and C.-D. Munz, “A p-adaptive discontinuous Galerkin method with hp-shock capturing,” Joural of Scientific Computing, vol. 91, no. 4, Art. no. 4, 2022, doi: 10.1007/s10915-022-01770-6.
    4. A. Schwarz, P. Kopper, J. Keim, H. Sommerfeld, C. Koch, and A. Beck, “A neural network based framework to model particle rebound and fracture,” Wear, vol. 508–509, p. 204476, Nov. 2022, doi: 10.1016/j.wear.2022.204476.
    5. M. Kurz, P. Offenhäuser, D. Viola, O. Shcherbakov, M. Resch, and A. Beck, “Deep reinforcement learning for computational fluid dynamics on HPC systems,” Journal of Computational Science, vol. 65, p. 101884, Nov. 2022, doi: 10.1016/j.jocs.2022.101884.

  3. 2021

    1. S. Jöns, C. Müller, J. Zeifang, and C.-D. Munz, “Recent Advances and Complex Applications of the Compressible Ghost-Fl uid Method,” in Recent Advances in Numerical Methods for Hyperbolic PDE Systems, M. L. Muñoz-Ruiz, C. Parés, and G. Russo, Eds., in Recent Advances in Numerical Methods for Hyperbolic PDE Systems. Cham: Springer International Publishing, 2021, pp. 155--176.
    2. A. Beck et al., “Increasing the Flexibility of the High Order Discontinuous Galerkin Framework FLEXI Towards Large Scale Industrial Applications,” in High Performance Computing in Science and Engineering’20, in High Performance Computing in Science and Engineering’20. , Springer, 2021, pp. 343--358. doi: 10.1007/978-3-030-80602-6_22.
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