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XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications

HYP 2016: Theory, Numerics and Applications of Hyperbolic Problems II pp 291–304Cite as

A Particle-Based Multiscale Solver for Compressible Liquid–Vapor Flow

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 237))

Abstract

To describe complex flow systems accurately, it is in many cases important to account for the properties of fluid flows on a microscopic scale. In this work, we focus on the description of liquid–vapor flow with a sharp interface between the phases. The local phase dynamics at the interface can be interpreted as a Riemann problem for which we develop a multiscale solver in the spirit of the heterogeneous multiscale method (HMM) [7], using a particle-based microscale model to augment the macroscopic two-phase flow system. The application of a microscale model makes it possible to use the intrinsic properties of the fluid at the microscale, instead of formulating (ad hoc) constitutive relations.

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Notes

  1. 1.

    All simulations were performed on a single workstation equipped with an Intel® i7-6700 CPU at 3.4 GHz, 16GB RAM, and a Nvidia® GTX980 Ti GPU.

References

  1. R. Abeyaratne, J.K. Knowles, Kinetic relations and the propagation of phase boundaries in solids. Arch. Ration. Mech. Anal. 114(2) (1991)

    Article  MathSciNet  Google Scholar 

  2. D.M. Anderson, G.B. McFadden, A.A. Wheeler, Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30(1) (1998)

    Article  MathSciNet  Google Scholar 

  3. N. Bedjaoui, C. Chalons, F. Coquel, P.G. Lefloch, Non-monotonic traveling waves in van der waals fluids. Anal. Appl. 03(04) (2005)

    Article  MathSciNet  Google Scholar 

  4. C. Chalons, C. Rohde, M. Wiebe, A finite volume method for undercompressive shock waves in two space dimensions. ESAIM: M2AN 51(5), 1987–2015 (2017). https://doi.org/10.1051/m2an/2017027

    Article  MathSciNet  Google Scholar 

  5. I.A. Cosden, A hybrid atomistic-continuum model for liquid-vapor phase change. Ph.D. thesis, University of Pennsylvania, 2013

    Google Scholar 

  6. W. E, Principles of Multiscale Modeling (Cambridge University Press, 2011)

    Google Scholar 

  7. W. E, B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, Heterogeneous multiscale methods: a review. Commun. Comput. Phys. 2(3) (2007)

    Google Scholar 

  8. M. Herrmann, J.D.M. Rademacher, Riemann solvers and undercompressive shocks of convex FPU chains. Nonlinearity 23(2) (2010)

    Article  MathSciNet  Google Scholar 

  9. J.H. Irving, J.G. Kirkwood, The statistical mechanical theory of transport processes. iv. the equations of hydrodynamics. J. Chem. Phys. 18(6) (1950)

    Article  MathSciNet  Google Scholar 

  10. F. Kissling, C. Rohde, The computation of nonclassical shock waves in porous media with a heterogeneous multiscale method: the multidimensional case. Multiscale Model. Simul. 13(4) (2015)

    Article  MathSciNet  Google Scholar 

  11. X. Li, J.Z. Yang, W. E, A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks. J. Comput. Phys. 229(10) (2010)

    Article  MathSciNet  Google Scholar 

  12. C. Merkle, C. Rohde, The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques. ESAIM: M2AN 41(6) (2007)

    Article  MathSciNet  Google Scholar 

  13. W. Ren, Analytical and numerical study of coupled atomistic-continuum methods for fluids. J. Comput. Phys. 227(2) (2007)

    Article  MathSciNet  Google Scholar 

  14. C. Rohde, C. Zeiler, A relaxation Riemann solver for compressible two-phase flow with phase transition and surface tension. Appl. Numer. Math. 95 (2015)

    Article  MathSciNet  Google Scholar 

  15. I. Steinwart, A. Christmann, Support Vector Machines (Springer, 2008)

    Google Scholar 

  16. L. Truskinovsky, Kinks versus shocks, in Shock Induced Transitions and Phase Structures in General Media, IMA Vol. Math. Appl. vol. 52 (Springer, New York, 1993)

    Chapter  Google Scholar 

  17. L. Verlet, Computer "experiments" on classical fluids. i. thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103 (1967)

    Article  Google Scholar 

  18. D. Wirtz, N. Karajan, B. Haasdonk, Surrogate modeling of multiscale models using kernel methods. Int. J. Numer. Methods Eng. 101(1) (2015)

    Article  MathSciNet  Google Scholar 

  19. C. Zeiler, Liquid vapor phase transitions: modeling, Riemann solvers and computation. Ph.D. thesis, Universität Stuttgart (2015)

    Google Scholar 

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Acknowledgements

The work was supported by the German Research Foundation (DFG) through SFB TRR 75 “Droplet dynamics under extreme ambient conditions.”

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Authors and Affiliations

  1. Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Germany

    Jim Magiera & Christian Rohde

Authors
  1. Jim Magiera
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  2. Christian Rohde
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Corresponding author

Correspondence to Jim Magiera .

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Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Magiera, J., Rohde, C. (2018). A Particle-Based Multiscale Solver for Compressible Liquid–Vapor Flow. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_23

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