A multiscale framework for multiphase flow based on the compressible Navier-Stokes-Korteweg system

PN 1-2 A

Project description

Multiphase flow simulations become difficult due to the occurrence of strongly interacting physical phenomena on different space and time scales.  In this project, we develop numerical methods, in which multi-X continua models can be included covering a wide range of length/time scales. As the basic mathematical model we consider the Navier-Stokes-Korteweg (NSK) system that describes the compressible motion of a homogeneous fluid in a liquid and a vapour phase with phase transition. For the direct numerical solution of the NSK system we rely on our open-source  software framework FLEXI: A high-order discontinuous Galerkin method on curved hexahedral grid cells, allowing non-conform grid refinement and a local sub-cell treatment of interfaces  enhancing locality and robustness. The novel simulation code FLEXI-NSK is first applied to the direct numerical simulation of droplets. In the second part of the project, we will extend FLEXI-NSK to control uncertainties concerning the choice of free energy potentials and geometries in case of confined domains. In the third part of the project, we intend to develop a simple multi-domain and multi-scale approach to pave the way towards a holistic NSK approach for coupled free and porous media flow.  In this way, we cover different flow regimes contributing to the EXC-2075 Vision on Engineered Geosystems. Data-driven surrogates handle the computationally expensive sub-scale or sub-domain problems.

Project information

Project title A multiscale framework for multiphase flow based on the compressible Navier-Stokes-Korteweg system
Project leaders

Claus-Dieter Munz (Christian Rohde)
Project duration February 2019 - July 2022
Project number PN 1-2 A

Publications of PN 1-2 A

  1. 2024

    1. M. Gao, P. Mossier, and C.-D. Munz, “Shock capturing for a high-order ALE discontinuous Galerkin method with applications to fluid flows in time-dependent domains,” Computers & fluids, vol. 269, p. 106124, Jan. 2024, doi: 10.1016/j.compfluid.2023.106124.

  2. 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., 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., Cham: Springer International Publishing, 2023, pp. 289–304. doi: 10.1007/978-3-031-17937-2_17.
    3. S. Jöns and C.-D. Munz, “Riemann solvers for phase transition in a compressible sharp-interface method,” Applied mathematics and computation, vol. 440, p. 127624, 2023, doi: 10.1016/j.amc.2022.127624.
    4. J. Keim, C.-D. Munz, and C. Rohde, “A Relaxation Model for the Non-Isothermal Navier-Stokes-Korteweg Equations in Confined Domains,” J. Comput. Phys., vol. 474, p. 111830, 2023, doi: https://doi.org/10.1016/j.jcp.2022.111830.
    5. 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.
    6. C. Müller, P. Mossier, and C.-D. Munz, “A sharp interface framework based on the inviscid Godunov-Peshkov-Romenski equations : Simulation of evaporating fluids,” Journal of computational physics, vol. 473, p. 111737, 2023, doi: 10.1016/j.jcp.2022.111737.
    7. 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, Art. no. 2, Oct. 2023, doi: 10.1007/s10915-023-02363-7.

  3. 2022

    1. 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.
    2. P. Mossier, A. Beck, and C.-D. Munz, “A p-adaptive discontinuous Galerkin method with hp-shock capturing,” Joural of Scientific Computing, vol. 91, Art. no. 4, 2022, doi: 10.1007/s10915-022-01770-6.
    3. M. Gao, T. Kuhn, and C.-D. Munz, “On the investigation of oblique shock‐wave/turbulent boundary‐layer interactions with a high‐order discontinuous Galerkin method,” International Journal for Numerical Methods in Fluids, vol. 94, Art. no. 8, Apr. 2022, doi: 10.1002/fld.5091.
    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.

  4. 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., 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, Springer, 2021, pp. 343–358. doi: 10.1007/978-3-030-80602-6_22.
    3. T. Hitz, S. Jöns, M. Heinen, J. Vrabec, and C.-D. Munz, “Comparison of macro- and microscopic solutions of the Riemann problem II. Two-phase shock tube,” Journal of Computational Physics, vol. 429, p. 110027, Mar. 2021, doi: 10.1016/j.jcp.2020.110027.
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