Communications on Applied Mathematics and Computation >

2024 , Vol. 6 >Issue 4: 2265 - 2294

DOI: https://doi.org/10.1007/s42967-023-00349-8

ORIGINAL PAPERS

A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

Expand
  • Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Received date: 2023-04-26

  Revised date: 2023-09-03

  Accepted date: 2023-10-29

  Online published: 2024-12-20

Supported by

B. Dong is partially supported by the National Natural Science Foundation of China (Grant No. 12261070) and the Ningxia Key Research and Development Project of China (Grant No. 2022BSB03048). Z. Li is partially supported by the Simons (Grant No. 633724) and by Fundación Séneca grant 21760/IV/22. J. Ruiz is partially supported by the Spanish national research project PID2019-108336GB-I00 and by Fundación Séneca grant 21728/EE/22. (Este trabajo es resultado de las estancias (21760/IV/22) y (21728/EE/22) financiadas por la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia con cargo al Programa Regional de Movilidad, Colaboración Internacional e Intercambio de Conocimiento “Jiménez de la Espada”. (Plan de Actuación 2022)).

Fold

Abstract

Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of the compressible two-component flow and propose a heterogeneous multiscale method (HMM) to describe the flow fields accurately. The multiscale approach combines a hyperbolic system of balance laws on the continuum scale with molecular-dynamics (MD) simulations on the microscale level. Notably, the multiscale approach is necessary to compute the interface dynamics because there is-at present-no closed continuum-scale model. The basic HMM relies on a moving-mesh finite-volume method and has been introduced recently for the compressible one-component flow with phase transitions by Magiera and Rohde in (J Comput Phys 469:111551, 2022). To overcome the numerical complexity of the MD microscale model, a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argonmethane mixtures in several space dimensions. To our knowledge, such compressible twophase dynamics accounting for microscale phase-change transfer rates have not yet been computed.

Key words： Phase transition; Hyperbolic balance laws for multi-component fluids; Multiscale modeling; Moving-mesh methods; Deep neural networks

Cite this article

Jim Magiera, Christian Rohde . A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate[J]. Communications on Applied Mathematics and Computation, 2024 , 6(4) : 2265 -2294 . DOI: 10.1007/s42967-023-00349-8

References

1. Alkämper, M., Magiera, J.: Interface preserving moving mesh (Code). DaRUS (2021). https:// doi. org/ 10. 18419/ darus- 1671
2. Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids, 2nd edn. Oxford University Press Inc, Oxford (2017)
3. Anderson, D.M., McFadden, G.B., Wheeler, A.A.: Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30(1), 139-165 (1998)
4. Andrianov, N., Warnecke, G.: The Riemann problem for the Baer-Nunziatio model of two-phase flows. J. Comput. Phys. 195, 434-464 (2004)
5. Berthelot, D.: Sur le mélange des gaz. Comptes rendus hebdomadaires des séances de l’Académie des Sciences 126, 1703-1706 (1898)
6. Bothe, D., Dreyer, W.: Continuum thermodynamics of chemically reacting fluid mixtures. Acta Mech. 226(6), 1757-1805 (2023)
7. Chalons, C., Rohde, C., Wiebe, M.: A finite volume method for undercompressive shock waves in two space dimensions. Math. Model. Numer. Anal. 51, 1987-2015 (2017)
8. Colombo, R.M., Priuli, F.S.: Characterization of Riemann solvers for the two phase p-system. Commun. Partial Differ. Equ. 28(7/8), 1371-1389 (2003)
9. Dreyer, W., Giesselmann, J., Kraus, C.: A compressible mixture model with phase transition. Physica D 273/274, 1-13 (2014)
10. Engquist, B., Li, X., Ren, W., Vanden-Eijnden, E.: Heterogeneous multiscale methods: a review. Commun. Comput. Phys. 2(3), 367-450 (2007)
11. Faccanoni, G., Kokh, S., Allaire, G.: Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium. ESAIM Math. Model. Numer. Anal. 46(5), 1029-1054 (2012)
12. Fechter, S., Munz, C.-D., Rohde, C., Zeiler, C.: A sharp interface method for compressible liquidvapor flow with phase transition and surface tension. J. Comput. Phys. 336, 347-374 (2017)
13. Frezzotti, A., Barbante, P.: Simulation of shock induced vapor condensation flows in the Lennard-Jones fluid by microscopic and continuum models. Phys. Fluids 32(12), 122106 (2020)
14. Ghazi, H., James, F., Mathis, H.: A nonisothermal thermodynamical model of liquid-vapor interaction with metastability. Discrete Contin. Dyn. Syst. Ser. B 26(5), 2371-2409 (2021)
15. Gross, J., Sadowski, G.: Perturbed-Chain SAFT: an equation of state based on a perturbation theory for chain molecules. Ind. Eng. Chem. Res. 40(4), 1244-1260 (2001)
16. Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration illustrated by the Störmer-Verlet method. Acta Numer. 12, 399-450 (2003)
17. Han, E., Hantke, M., Warnecke, G.: Criteria for nonuniqueness of Riemann solutions to compressible duct flows. Z. fur Angew. Math. Phys. Mech. 93(6/7), 465-475 (2013)
18. Hantke, M., Matern, C., Warnecke, G., Yaghi, H.: A new method to discretize a model for isothermal flow with a multi-component equation of state. J. Comput. Appl. 422, 114876 (2023)
19. Hantke, M., Müller, S.: Analysis and simulation of a new multi-component two-phase flow model with phase transitions and chemical reactions. Q. Appl. Math. 76(2), 253-287 (2018)
20. Hantke, M., Müller, S., Richter, P.: Closure conditions for non-equilibrium multi-component models. Contin. Mech. Thermodyn. 28, 1157-1189 (2016)21. Hantke, M., Thein, F.: On the impossibility of first-order phase transitions in systems modeled by the full
Euler equations. Entropy 21(11), 1039 (2019)
22. Hitz, T., Jöns, S., Heinen, M., Vrabec, J., Munz, C.-D.: Comparison of macro- and microscopic solutions of the Riemann problem II. Two-phase shock tube. J. Comput. Phys. 429, 110027 (2020)
23. Janzen, T.: On diffusion coefficients of multicomponent liquid mixtures predicted by equilibrium molecular dynamics simulation. Doctoral thesis, Technische Universität Berlin, Berlin (2019)
24. Keim, J., Munz, C.-D., Rohde, C.: A relaxation model for the non-isothermal Navier-Stokes-Korteweg equations in confined domains. J. Comput. Phys. 474, 111830 (2023)
25. Krishna, R., Wesselingh, J.A.: The Maxwell-Stefan approach to mass transfer. Chem. Eng. Sci. 52(6), 861-911 (1997)
26. Lorentz, H.A.: Ueber die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase. Annalen der Physik 248(1), 127-136 (1881)
27. Ma, P.C., Lv, Y., Ihme, M.: An entropy-stable hybrid scheme for simulations of transcritical real-fluid flows. J. Comput. Phys. 340, 330-357 (2017)
28. Magiera, J.: A molecular-continuum multiscale solver for liquid-vapor flow: modeling and numerical simulation. PhD thesis, University of Stuttgart, Stuttgart (2021)
29. Magiera, J.: Data sets for a molecular-continuum multiscale solver for liquid-vapor flow: modeling and numerical simulation. DaRUS (2021). https:// doi. org/ 10. 18419/ darus- 1258
30. Magiera, J., Ray, D., Hesthaven, J.S., Rohde, C.: Constraint-aware neural networks for Riemann problems. J. Comput. Phys. 409, 109345 (2020)
31. Magiera, J., Rohde, C.: A particle-based multiscale solver for compressible liquid-vapor flow. In: Klingenberg, C., Westdickenberg, M. (eds.) Theory, Numerics and Applications of Hyperbolic Problems II, pp. 291-304. Springer, Cham (2018)
32. Magiera, J., Rohde, C.: A molecular-continuum multiscale model for inviscid liquid-vapor flow with sharp interfaces. J. Comput. Phys. 469, 111551 (2022)
33. Magiera, J., Rohde, C.: Analysis and numerics of sharp and diffuse interface models for droplet dynamics. In: Schulte, K., Tropea, C., Weigand, B. (eds.) Droplet Dynamics Under Extreme Ambient Conditions. Fluid Mechanics and Its Applications, pp. 67-86. Springer, Cham (2022)
34. Mitchell, D.P.: Spectrally optimal sampling for distribution ray tracing. In: Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH 91, pp. 157-164. ACM, New York (1991)
35. Ponte, M., Streett, W.B., Miller, R.C., Staveley, L.A.K.: An experimental study of the equation of state of liquid (argon + methane), and the effect of pressure on their excess thermodynamic functions. J. Chem. Thermodyn. 13(8), 767-781 (1981)
36. Rohde, C., Zeiler, C.: On Riemann solvers and kinetic relations for isothermal two-phase flows with surface tension. Z. fur Angew. Math. Phys. 69(3), 76 (2018)
37. Saurel, R., Abgrall, R.: A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150(2), 425-467 (2023)
38. Saurel, R., Petitpas, F., Abgrall, R.: Modelling phase transition in metastable liquids: application to cavitating and flashing flows. J. Fluid Mech. 607, 313-350 (2008)
39. Shen, Y., Ren, Y., Ding, H.: A 3D conservative sharp interface method for simulation of compressible two-phase flows. J. Comput. Phys. 403, 109107-10919 (2020)
40. Truskinovsky, L.: Kinks versus shocks. In: Shock Induced Transitions and Phase Structures in General Media. IMA Volumes in Mathematics and Its Applications, vol. 52, pp. 185-229. Springer, New York (1993)
41. Vrabec, J., Fischer, J.: Vapour liquid equilibria of mixtures from the NpT plus test particle method. Mol. Phys. 85(4), 781-792 (1995)
42. Vrabec, J., Lotfi, A., Fischer, J.: Vapour liquid equilibria of Lennard-Jones model mixtures from the NpT plus test particle method. Fluid Phase Equilib. 112(2), 173-197 (1995)
43. Zein, A., Hantke, M., Warnecke, G.: Modeling phase transition for compressible two-phase flows applied to metastable liquids. J. Comput. Phys. 229(8), 2964-2998 (2010)
Options
Outlines

/

〈 〉

Copyright © Editorial By Communications on Applied Mathematics and Computation
沪ICP备09014157