Data-integrated two-scale modelling of compressible multiphase flow

PN 1-9

Project description

Compressible liquid-vapour flow with phase change appears in many natural and technical processes providing a paradigm for multi-scale modelling approaches. By now there are reliable but very expensive Navier-Stokes-type models on a microscopic, detailed-scale level with full resolution of phase boundaries. On the other hand, first-order and thus computationally cheap Baer-Nunziato-type models have been developped to describe the mixture evolution on an averaged scale. However, they loose accuracy for phase-change problems. As a remedy we develop a two-scale model that acts on the averaged scale but incorporates a diffuse-interface model as cell problem. This approach exploits a novel homogenization technique based on Wentzel-Kramers-Brillouin expansions for the detailed-scale flow field. A particular feature of this ansatz is its flexibility to substitute the cell-problem solver by a machine-learned surrogate solver. To ensure essential flow properties like mass/momentum/energy conservation or thermodynamical consistency we will adapt constraint-aware neural networks, in particular the previously developped constraint-resolving layer method that allows an analytical treatment of side conditions. Finally, the implementation will be validated using the FLEXI open-source frameworks.

Project information

Project title Data-integrated two-scale modelling of compressible multiphase flow
Project leader Christian Rohde (Andrea Beck, Bernhard Weigand)
Project staff Florian Wendt, doctoral researcher
Project duration October 2022 - December 2025
Project number PN 1-9

Publications of PN 1-9

  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. J. Magiera and C. Rohde, “A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate,” Communications in Applied Mathematics and Computation, 2024, doi: 0.1007/s42967-023-00349-8.
    3. M. Hörl and C. Rohde, “Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture,” Networks and Heterogeneous Media, vol. 19, Art. no. 1, 2024, doi: 10.3934/nhm.2024006.
    4. Y. Miao, C. Rohde, and H. Tang, “Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities,” Stochastic Partial Differential Equations: Analysis & Computation, vol. 12, Art. no. 1, 2024, doi: 10.1007/s40072-023-00291-z.
    5. M. Alkämper, J. Magiera, and C. Rohde, “An Interface-Preserving Moving Mesh in Multiple Space Dimensions,” ACM Transactions in Mathematical Software, vol. 50, Art. no. 1, Mar. 2024, doi: 10.1145/3630000.

  2. 2023

    1. J. Keim, A. Schwarz, S. Chiocchetti, C. Rohde, and A. Beck, “A Reinforcement Learning Based Slope Limiter for Two-Dimensional Finite Volume Schemes,” in Finite volumes for complex applications X. Vol. 2. Hyperbolic and related problems, in Springer Proc. Math. Stat., vol. 433. Springer, Cham, 2023, pp. 209–217. doi: 10.13140/RG.2.2.18046.87363.
    2. J. Keim, C.-D. Munz, and C. Rohde, “A relaxation model for the non-isothermal Navier-Stokes-Korteweg equations in confined domains,” Journal of Computational Physics, vol. 474, p. 111830, 2023, [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0021999122008932?via%3Dihub
    3. S. Burbulla, M. Hörl, and C. Rohde, “Flow in Porous Media with Fractures of Varying Aperture,” SIAM J. Sci. Comput, vol. 45, Art. no. 4, 2023, doi: 10.1137/22M1510406.
    4. M. J. Gander, S. B. Lunowa, and C. Rohde, “Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations,” SIAM J. Sci. Comput., vol. 45, Art. no. 1, 2023, doi: 10.1137/21M1415005.
    5. 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.

  3. 2022

    1. J. Magiera and C. Rohde, “A molecular–continuum multiscale model for inviscid liquid–vapor flow with sharp interfaces,” Journal of Computational Physics, p. 111551, 2022, doi: https://doi.org/10.1016/j.jcp.2022.111551.

  4. 2021

    1. C. Rohde and H. Tang, “On a stochastic Camassa-Holm type equation with higher order nonlinearities,” J. Dynam. Differential Equations, vol. 33, pp. 1823–1852, 2021, doi: https://doi.org/10.1007/s10884-020-09872-1.
    2. D. Alonso-Orán, C. Rohde, and H. Tang, “A local-in-time theory for singular SDEs with applications to fluid models with transport noise,” Journal of Nonlinear Science, vol. 31, p. Paper No. 98, 55, 2021.
    3. C. Rohde and H. Tang, “On the stochastic Dullin-Gottwald-Holm equation: global existence and wave-breaking phenomena,” Nonlinear Differential Equations and Applications, vol. 28, Art. no. 1, 2021, doi: 10.1007/s00030-020-00661-9.

  5. 2020

    1. T. Hitz, J. Keim, C.-D. Munz, and C. Rohde, “A parabolic relaxation model for the Navier-Stokes-Korteweg equations,” Journal of Computational Physics, vol. 421, p. 109714, 2020, doi: https://doi.org/10.1016/j.jcp.2020.109714.

  6. 2019

    1. T. Kuhn, J. Dürrwächter, F. Meyer, A. Beck, C. Rohde, and C.-D. Munz, “Uncertainty quantification for direct aeroacoustic simulations of cavity flows,” J. Theor. Comput. Acoust., vol. 27, Art. no. 1, 2019, doi: https://doi.org/10.1142/S2591728518500445.
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