Skip to main content
Log in

A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

We present a new solver for massively parallel simulations of fully three-dimensional multiphase flows. The solver runs on a variety of computer architectures from laptops to supercomputers and on 262144 threads or more (limited only by the availability to us of more threads). The code is wholly written by the authors in Fortran 2008 and uses a domain decomposition strategy for parallelization with MPI. The fluid interface solver is based on a parallel implementation of the LCRM hybrid front tracking/level set method designed to handle highly deforming interfaces with complex topology changes. We discuss the implementation of this interface method and its particular suitability to distributed processing where all operations are carried out locally on distributed subdomains. We have developed parallel GMRES and Multigrid iterative solvers suited to the linear systems arising from the implicit solution of the fluid velocities and pressure in the presence of strong density and viscosity discontinuities across fluid phases. Particular attention is drawn to the details and performance of the parallel Multigrid solver. The code includes modules for flow interaction with immersed solid objects, contact line dynamics, species and thermal transport with phase change. Here, however, we focus on the simulation of the canonical problem of drop splash onto a liquid film and report on the parallel performance of the code on varying numbers of threads. The 3D simulations were run on mesh resolutions up to 10243 with results at the higher resolutions showing the fine details and features of droplet ejection, crown formation and rim instability observed under similar experimental conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. Tryggvason, R. Scardovelli and S. Zaleski, Direct numerical simulations of gas-liquid multiphase flows, Cambridge University Press, Cambridge, England (2011).

    Book  MATH  Google Scholar 

  2. C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comp. Phys., 39 (1981) 201–225.

    Article  MATH  Google Scholar 

  3. S. Osher and R. P. Fedkiw, Level set methods: An overview and some recent results, J. Comp. Phys., 169 (2001) 463–502.

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Jamet, O. Lebaigue, N. Coutris and J. M. Delhaye, The second gradient method for the direct numerical simulation of liquid-vapor flows with phase change, J. Comp. Phys., 169 (2001) 624–651.

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas and Y.-J. Jan, A fronttracking method for the computations of multiphase flow, J. Comp. Phys., 169 (2001) 708–759.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. L. George and J. A. Warren, A parallel 3D dendritic growth simulator using the phase-field method, J. Comp. Phys., 177 (2002) 264–283.

    Article  MATH  Google Scholar 

  7. K. Wang, A. Chang, L. V. Kale and J. A. Dantzig, Parallelization of a level set method for simulating dendritic growth, J. Parallel Distrib. Comput., 66 (2006) 1379–1386.

    Article  MATH  Google Scholar 

  8. M. Sussman, A parallelized, adaptive algorithm for multiphase flows in general geometries, Comput. and Struct., 83 (2005) 435–444.

    Article  Google Scholar 

  9. O. Fortmeier and H. M. Bücker, A parallel strategy for a level set simulation of droplets moving in a liquid medium, Lect. Notes Comput. Sci., 6449 (2011) 200–209.

    Article  MATH  Google Scholar 

  10. D. Zuzio and J. L. Estivalezes, An efficient block parallel AMR method for two phase interfacial flow simulations, Computers & Fluids, 44 (2011) 339–357.

    Article  MathSciNet  MATH  Google Scholar 

  11. V. Aggarwal, V. H. Gada and A. Sharma, Parallelization methodology and performance study for Level-Set-Method based simulation of a 3-D transient two-phase flow, Numerical Heat Transfer, Part B, 63 (2013) 327–356.

    Article  Google Scholar 

  12. A. Banari, C. Janßen, S. T. Grilli and M. Krafczyk, Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios, Computers & Fluids, 93 (2014) 1–17.

    Article  MathSciNet  Google Scholar 

  13. S. Popinet, Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries, J. Comp. Phys., 190 (2003) 572–600.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Popinet, An accurate adaptive solver for surface-tensiondriven interfacial flows, J. Comp. Phys., 228 (2009) 5838–5866.

    Article  MathSciNet  MATH  Google Scholar 

  15. M. J. Thoraval, K. Takehara, T. Goji Etoh, S. Popinet, P. Ray, C. Josserand, S. Zaleski and S. T. Thoroddsen, von Kármán vortex street within an impacting drop, Phys. Rev. Lett., 108 (2012) 264506.

  16. C. Kuan, J. Sim and W. Shyy, Adaptive thermos-fluid moving boundary computations for interfacial dynamics, Acta Mechanica Sinica., 28 (4) (2012) 99–1021.

    Article  MathSciNet  MATH  Google Scholar 

  17. E. Uzgoren, R. Singh, J. Sim and W. Shyy, Computational modelling for multiphase flows with spacecraft application, Progress in Aerospace Science, 43 (4) (2007) 138–192.

    Article  Google Scholar 

  18. B. Bunner and G. Tryggvason, Direct numerical simulations of three-dimensional bubbly flows, Phys. Fluids, 11 (1999) 1967–1969.

    Article  MATH  Google Scholar 

  19. S. Shin and D. Juric, Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity, J. Comp. Phys., 180 (2002) 427–470.

    Article  MATH  Google Scholar 

  20. S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, Accurate representation of surface tension using the level contour reconstruction method, J. Comp. Phys., 203 (2005) 493–516.

    Article  MATH  Google Scholar 

  21. S. Shin and D. Juric, High order level contour reconstruction method, Journal of Mechanical Science and Technology, 21 (2) (2007) 311–326.

    Article  Google Scholar 

  22. S. Shin, Computation of the curvature field in numerical simulation of multiphase flow, J. Comp. Phys., 222 (2007) 872–878.

    Article  MathSciNet  MATH  Google Scholar 

  23. S. Shin and D. Juric, A hybrid interface method for threedimensional multiphase flows based on front-tracking and level set techniques, Int. J. Num. Meth. Fluids, 60 (2009) 753–778.

    Article  MATH  Google Scholar 

  24. S. Shin and D. Juric, Simulation of droplet impact on a solid surface using the level contour reconstruction method, Journal of Mechanical Science and Technology, 23 (2009) 2434–2443.

    Article  Google Scholar 

  25. S. Shin, I. Yoon and D. Juric, The Local Front Reconstruction Method for direct simulation of two-and threedimensional multiphase flows, J. Comp. Phys., 230 (2011) 6605–6646.

    Article  MATH  Google Scholar 

  26. M. Sussman and E. G. Puckett, A coupled level set and volume-of-fluid method computing 3D and axisymmetric incompressible two-phase flows, J. Comp. Phys., 162 (2000) 301–337.

    Article  MathSciNet  MATH  Google Scholar 

  27. E. Coyajee and B. J. Boersma, Numerical simulation of drop impact on a liquid-liquid interface with a multiple marker front-capturing method, J. Comp. Phys., 228 (2009) 4444–4467.

    Article  MATH  Google Scholar 

  28. D. Enright, R. Fedkiw, J. Ferziger and I. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comp. Phys., 183 (2002) 83–116.

    Article  MathSciNet  MATH  Google Scholar 

  29. E. Aulisa, S. Manservisi and R. Scardovelli, A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows, J. Comp. Phys., 188 (2003) 611–639.

    Article  MATH  Google Scholar 

  30. C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comp. Phys., 25 (1977) 220–252.

    Article  MathSciNet  MATH  Google Scholar 

  31. A. J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput., 22 (1968) 745–762.

    Article  MathSciNet  MATH  Google Scholar 

  32. F. H. Harlow and J. E. Welch, Numerical calculation of time dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8 (1965) 2182–2189.

    Article  MathSciNet  MATH  Google Scholar 

  33. W. L. Briggs, S. McCormick and V. Henson, A Multigrid Tutorial. SIAM, Second Edition (2000).

    Book  MATH  Google Scholar 

  34. M. Francois, E. Uzgoren, J. Jackson and W. Shyy, Multigrid computations with the immersed boundary technique for multiphase flows, International Journal of Numerical Methods for Heat & Fluid Flow, 14 (1) (2004) 98–115.

    Article  MATH  Google Scholar 

  35. D. Y. Kwak and J. S. Lee, Multigrid algorithm for cellcentred finite difference method II: Discontinuous coefficient case, Department of Mathematics, KAIST, Daejon, Korea (2003) 305–701.

    Google Scholar 

  36. P. Wesseling, Cell-centred multigrid for interface problems, J. Comp. Phys., 79 (1097) 85–91.

    Article  MathSciNet  MATH  Google Scholar 

  37. N. Nikolopoulos, A. Theodorakakos and G. Bergeles, Three-dimensional numerical investigation of a droplet impinging normally onto a wall film, J. Comp. Phys., 225 (2007) 322–341.

    Article  MATH  Google Scholar 

  38. M. Rieber and A. Frohn, A numerical study on the mechanism of splashing, International Journal of Heat and Fluid Flow, 20 (1999) 455–461.

    Article  Google Scholar 

  39. T. Okawa, T. Shiraishi and T. Mori, Production of secondary drops during the single water drop impact onto a plane water surface, Exp. Fluids, 41 (2006) 965–974.

    Article  Google Scholar 

  40. H. E. Edgerton, Stopping Time: The Photographs of Harold Edgerton, Abrams, New York (1977).

    Google Scholar 

  41. F. H. Harlow and J. P. Shannon, The splash of a liquid drop, J. Appl. Phys., 38 (1967) 3855–3866.

    Article  Google Scholar 

  42. R. Krechetnikov and G. M. Homsy, Crown-forming instability phenomena in the drop splash problem, J. Colloid and Interface Science, 331 (2009) 555–559.

    Article  Google Scholar 

  43. L. V. Zhang, P. Brunet, J. Eggers and R. Deegan, Wavelength selection in the crown splash, Phys. Fluids, 22 (2010) 122105.

    Article  Google Scholar 

  44. R. D. Deegan, P. Brunet and J. Eggers, Complexities of splashing, Nonlinearity, 21 (2008) C1–C11.

    Article  MathSciNet  MATH  Google Scholar 

  45. S. Mukherjee and J. Abraham, Crown behavior in drop impact on wet walls, Phys. Fluids, 19 (2007) 052103.

    Article  MATH  Google Scholar 

  46. J. M. Fullana and S. Zaleski, Stability of a growing end rim in a liquid sheet of uniform thickness, Phys. Fluids, 11 (1999) 952.

    Article  MATH  Google Scholar 

  47. D. Gueyffier and S. Zaleski, Finger formation during droplet impact on a liquid film, C.R. Acad. Sci., Ser. IIc: Chim, 326 (1998) 839.

    Google Scholar 

  48. C. Josserand and S. Zaleski, Droplet splashing on a thin liquid film, Phys. Fluids, 15 (2003) 1650.

    Article  MATH  Google Scholar 

  49. G. Agbaglah, C. Josserand and S. Zaleski, Longitudinal instability of a liquid rim, Phys. Fluids, 25 (2013) 022103.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Seungwon Shin.

Additional information

Recommended by Associate Editor Gihun Son

Seungwon Shin received his B.S. and M.S. degrees in Mechanical Engineering from Seoul National University, Korea, in 1995 and 1998, respectively. He then received his Ph.D. degree from Georgia Tech. in 2002. Dr. Shin is currently a Professor at the School of Mechanical and System Design Engineering at Hongik University in Seoul, Korea. Dr. Shin’s research interests include computational fluid dynamics, multiphase flow, surface tension effect, phase change process.

Jalel Chergui received his B.S. and M.S. degrees in Applied Fluid Mechanics from Tunis University of Science in 1982 and 1984, respectively and his Ph.D. degree from the University of Pierre and Marie Curie of Paris 6 in 1989. Dr. Chergui has worked in Academia and Government and is currently Ingénieur de Recherche at the CNRS in Orsay, France. His main research interests are in Parallel computational Fluid Dynamics for Multiphase Flows.

Damir Juric received his B.S. and M.S. degrees in Mechanical Engineering from Worcester Polytechnic Institute in 1987 and 1990, respectively and his Ph.D. degree from the University of Michigan in 1996. Dr. Juric has worked in industry, academia and government and is currently Chargé de Recherche at the CNRS in Orsay, France. His research interests are in computational physics, fluid dynamics and interface methods for multiphase flow.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shin, S., Chergui, J. & Juric, D. A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows. J Mech Sci Technol 31, 1739–1751 (2017). https://doi.org/10.1007/s12206-017-0322-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-017-0322-y

Keywords

Navigation