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Building a Numerical Framework to Model Gas-Liquid-Solid Interactions Using Meshfree Interpolation Methods

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Meshfree Methods for Partial Differential Equations VIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 115))

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Abstract

In this work, we present a numerical framework that can model and simulate gas-liquid-solid three-phase interactions. A non-boundary-fitted approach is developed to simultaneously accommodate the moving gas-liquid interfaces and deforming solid. The connectivity-free front tracking method (CFFT) is adopted to track the gas-liquid interface, where an approximation-correction step is used to construct an indicator field without requiring the connectivity of the interfacial points. Therefore, topological change such as free surfaces with bubble breaking up and coalescing can be handled more easily and robustly. The fluid-solid interactions are modeled using the modified immersed finite element method (mIFEM). A more realistic and accurate solid movement and deformation are achieved by solving the solid dynamics, rather than been imposed as in the original IFEM. The coupling of the two algorithms is achieved using a meshfree interpolation function, the reproducing kernel particle method. The concept of constructing the indicator function to distinguish gas from liquid and fluid from solid naturally combines the CFFT and mIFEM algorithms together, and simulate the complex 3-phase physical system in a cohesive manner.

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References

  1. S. Aliabadi, T.E. Tezduyar, Stabilized-finite-element/interface-capturing technique for parallel computation of unsteady flows with interfaces. Comput. Methods Appl. Mech. Eng. 190 (3–4), 243–261 (2000)

    Article  MATH  Google Scholar 

  2. J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335–354 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Cervone, S. Manservisi, R. Scardovelli, Simulation of axisymmetric jets with a finite element Navier-Stokes solver and a multilevel VOF approach. J. Comput. Phys. 229 (19), 6853–6873 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. J.-B. Dupont, D. Legendre, Numerical simulation of static and sliding drop with contact angle hysteresis. J. Comput. Phys. 229 (7), 2453–2478 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. M.M. Francois, S.J. Cummins, E.D. Dendy, D.B. Kothe, J.M. Sicilian, M.W. Williams, A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213 (1), 141–173 (2006)

    Article  MATH  Google Scholar 

  6. M. Gay, L.T. Zhang, W.K. Liu, Stent modeling using immersed finite element method. Comput. Methods Appl. Mech. Eng. 195 (33–36), 4358–4370 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Herrmann, A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids. J. Comput. Phys. 227 (4), 2674–2706 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225 (1981)

    Article  MATH  Google Scholar 

  9. H.H. Hu, N.A. Patankar, M.Y. Zhu, Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J. Comput. Phys. 169 (2), 427–462 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Hua, J.F. Stene, P. Lin, Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method. J. Comput. Phys. 227 (6), 3358–3382 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Huerta, W.K. Liu, Viscous flow with large free surface motion. Comput. Methods Appl. Mech. Eng. 69 (3), 277–324 (1988)

    Article  MATH  Google Scholar 

  12. T.J.R. Hughes, W.K. Liu, T.K. Zimmermann, Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Eng. 29 (3), 329–349 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  13. B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti, Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113 (1), 134–147 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. Y. Liu, W.K. Liu, Rheology of red blood cell aggregation by computer simulation. J. Comput. Phys. 220 (1), 139–154 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. W.K. Liu, D.C. Ma, Computer implementation aspects for fluid-structure interaction problems. Comput. Methods Appl. Mech. Eng. 31 (2), 129–148 (1982)

    Article  MATH  Google Scholar 

  16. W.K. Liu, H. Chang, J.-S. Chen, T. Belytschko, Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua. Comput. Methods Appl. Mech. Eng. 68 (3), 259–310 (1988)

    Article  MATH  Google Scholar 

  17. W.K. Liu, S. Jun, S. Li, J. Adee, B. Belytschko, Reproducing kernel particle methods for structural dynamics. Int. J. Numer. Methods Eng. 38 (10), 1655–1679 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  18. W.K. Liu, S. Jun, Y.F. Zhang, Reproducing kernel particle methods. Int. J. Numer. Methods Fluids 20 (8–9), 1081–1106 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Liu, S. Koshizuka, Y. Oka, A hybrid particle-mesh method for viscous, incompressible, multiphase flows. J. Comput. Phys. 202 (1), 65–93 (2005)

    Article  MATH  Google Scholar 

  20. W.K. Liu, Y. Liu, D. Farrell, L.T. Zhang, X.S. Wang, Y. Fukui, N. Patankar, Y. Zhang, C. Bajaj, J. Lee, J. Hong, X. Chen, H. Hsu, Immersed finite element method and its applications to biological systems. Comput. Methods Appl. Mech. Eng. 195 (13–16), 1722–1749 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. W.K. Liu, D.W. Kim, S. Tang, Mathematical foundations of the immersed finite element method. Comput. Mech. 39 (3), 211–222 (2007) (English)

    Article  MathSciNet  MATH  Google Scholar 

  22. M.F. McCracken, C.S. Peskin, A vortex method for blood flow through heart valves. J. Comput. Phys. 35 (2), 183–205 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  23. M. Muradoglu, G. Tryggvason, A front-tracking method for computation of interfacial flows with soluble surfactants. J. Comput. Phys. 227 (4), 2238–2262 (2008)

    Article  MATH  Google Scholar 

  24. C.S. Peskin, Numerical analysis of blood flow in the heart. J. Comput. Phys. 25 (3), 220–252 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  25. C.S. Peskin, D.M. McQueen, A three-dimensional computational method for blood flow in the heart I. Immersed elastic fibers in a viscous incompressible fluid. J. Comput. Phys. 81 (2), 372–405 (1989)

    MATH  Google Scholar 

  26. C.S. Peskin, D.M. McQueen, Mechanical equilibrium determines the fractal fiber architecture of aortic heart valve leaflets. Am. J. Phys. 266 (1), 319–328 (1994)

    Google Scholar 

  27. Y. Renardy, M. Renardy, PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. J. Comput. Phys. 183 (2), 400–421 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  28. S. Shin, I. Yoon, D. Juric, The local front reconstruction method for direct simulation of two- and three-dimensional multiphase flows. J. Comput. Phys. 230 (17), 6605–6646 (2011)

    Article  MATH  Google Scholar 

  29. E. Shirani, N. Ashgriz, J. Mostaghimi, Interface pressure calculation based on conservation of momentum for front capturing methods. J. Comput. Phys. 203 (1), 154–175 (2005)

    Article  MATH  Google Scholar 

  30. D.J. Torres, J.U. Brackbill, The point-set method: front-tracking without connectivity. J. Comput. Phys. 165 (2), 620–644 (2000)

    Article  MATH  Google Scholar 

  31. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, Y.-J. Jan, A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169 (2), 708–759 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  32. S.O. Unverdi, G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100 (1), 25–37 (1992)

    Article  MATH  Google Scholar 

  33. C. Wang, Numerical modeling of three-phase (gas-liquid-solid) flows with connectivity-free multi-fluid interface treatment and non-boundary-fitted techniques for fluid-structure interactions. Ph.D. thesis, Rensselaer Polytechnic Institute (2013)

    Google Scholar 

  34. X. Wang, L.T. Zhang, Interpolation functions in the immersed boundary and finite element methods. Comput. Mech. 45, 321–334 (2010)

    Article  MATH  Google Scholar 

  35. C. Wang, L.T. Zhang, Numerical modeling of gas-liquid-solid interactions: gas-liquid free surfaces interacting with deformable solids. Comput. Methods Appl. Mech. Eng. 286, 123–146 (2013)

    Article  MathSciNet  Google Scholar 

  36. C. Wang, X. Wang, L. Zhang, Connectivity-free front tracking method for multiphase flows with free surfaces. J. Comput. Phys. 241, 58–75 (2013)

    Article  MATH  Google Scholar 

  37. J.A.S. Witteveen, B. Koren, P.G. Bakker, An improved front tracking method for the Euler equations. J. Comput. Phys. 224 (2), 712–728 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  38. J.-J. Xu, Z. Li, J. Lowengrub, H. Zhao, A level-set method for interfacial flows with surfactant. J. Comput. Phys. 212 (2), 590–616 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  39. K. Yokoi, Efficient implementation of THINC scheme: a simple and practical smoothed VOF algorithm. J. Comput. Phys. 226 (2), 1985–2002 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  40. L.T. Zhang, M. Gay, Immersed finite element method for fluid-structure interactions. J. Fluids Struct. 23 (6), 839–857 (2007)

    Article  Google Scholar 

  41. L.T. Zhang, G.J. Wagner, W.K. Liu, Modeling and simulation of fluid structure interaction by meshfree and FEM. Commun. Numer. Methods Eng. 19 (8), 615–621 (2003)

    Article  MATH  Google Scholar 

  42. L.T. Zhang, A. Gerstenberger, X. Wang, W.K. Liu, Immersed finite element method. Comput. Methods Appl. Mech. Eng. 193 (21–22), 2051–2067 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Convergent Science, Madison, WI, USA

    Chu Wang

  2. Rensselaer Polytechnic Institute, Troy, NY, USA

    Lucy T. Zhang

Authors
  1. Chu Wang
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  2. Lucy T. Zhang
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Correspondence to Lucy T. Zhang .

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Editors and Affiliations

  1. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Michael Griebel

  2. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Marc Alexander Schweitzer

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Wang, C., Zhang, L.T. (2017). Building a Numerical Framework to Model Gas-Liquid-Solid Interactions Using Meshfree Interpolation Methods. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations VIII . Lecture Notes in Computational Science and Engineering, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-319-51954-8_11

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