Shahbaz, Khosro, Paraschivoiu, Marius and Mostaghimi, Javad
(2003)
*Second order accurate volume tracking based on remapping for triangular meshes.*
Journal of Computational Physics, 188
(1).
pp. 100-122.
ISSN 0021-9991

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Official URL: http://dx.doi.org/doi:10.1016/S0021-9991(03)00156-...

## Abstract

This paper presents a second order accurate piecewise linear volume tracking based on remapping for triangular meshes. This approach avoids the complexity of extending unsplit second order volume of fluid algorithms, advection methods, on triangular meshes. The method is based on Lagrangian–Eulerian (LE) methods; therefore, it does not deal with edge fluxes and corner fluxes, flux corrections, as is typical in advection algorithms. The method is constructed of three parts: a Lagrangian phase, a reconstruction phase and a remapping phase. In the Lagrangian phase, the original, Eulerian, grid is projected along trajectories to obtain Lagrangian grids. In practice, this projection is handled through the time integration of velocity field for grid vertices at each time step. The reconstruction is based on truncating the volume material polygon for each Lagrangian mixed grid. Since in piecewise linear approximation, the interface is represented by a segment line, the polygon material truncation is mainly finding the segment interface. Finding the segment interface is calculating the line normal and line constant at each multi-fluid cell. Details of applying two normal calculation methods, differential and geometric least squares (GLS) methods, are given. While the GLS method exhibits second order accurate approximation in reproducing circular interfaces, the differential least squares (DLS) method results in a first order accurate representation of the interface. The last part of the algorithm which is remapping of the volume materials from the Lagrangian grid to the original one is performed by a series of polygon intersection procedures. The behavior of the algorithm is investigated for flow fields with constant interface topology and flow fields inducing large interfacial stretching and tearing. Second order accuracy is obtained if the velocity integration as well as the reconstruction steps are at least second order accurate.

Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical and Industrial Engineering |
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Item Type: | Article |

Refereed: | Yes |

Authors: | Shahbaz, Khosro and Paraschivoiu, Marius and Mostaghimi, Javad |

Journal or Publication: | Journal of Computational Physics |

Date: | June 2003 |

Digital Object Identifier (DOI): | 10.1016/S0021-9991(03)00156-6 |

ID Code: | 6751 |

Deposited By: | ANDREA MURRAY |

Deposited On: | 02 Jul 2010 16:33 |

Last Modified: | 18 Jan 2018 17:29 |

## References:

1. R. Scardovelli and S. Zaleski, Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech. 31 (1999), pp. 567–603.2. C.W. Hirt and B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981), p. 201.

3. B.D. Nichols, C.W. Hirt, R.S. Hotchkiss, SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries, Tech. Rep. LA-8355, Los Alamos National Laboratory, Augest 1980, unpublished

4. M.D. Torrey, L.D. Cloutman, R.C. Mjolsness, C.W. Hirt, NASA-VOF2D: A computer program for incompressible flows with free surfaces, Tech. Rep. LA-10612MS, Los Alamos National Laboratory, December 1985, unpublished

5. M.D. Torrey, R.C. Mjolsness, R.L. Stein, NASA-VOF3D: A three-dimensional computer program for incompressible flows with free surfaces, Tech. Rep. LA-11009MS, Los Alamos National Laboratory, July 1987, unpublished

6. D.B. Kothe and R.C. Mjolsness, Ripple: A new model for incompressible flows with free surfaces. AIAA J. 30 11 (1992), p. 2694.

7. D.B. Kothe, R.C. Mjolsness, M.D. Torrey, Ripple: A computer program for incompressible flows with free surfaces, Tech. Rep. LA-12007-MS, Los Alamos National Laboratory, 1991

8. C.W. Hirt, Flow3D Users Manual. , Flow Sciences, Inc. (1988).

9. N.V. Deshpande, Fluid mechanics of bubble growth and collapse in a thermal ink-jet printhead, in: in SPSE/SPIES Electronic Imaging Devices ans System Symposium, January 1989

10. P.A. Torpey, Prevention of air ingestion in a thermal ink-jet device, in: Proceedings of the 4th International Congress on Advances in Non-Impact Print Technology, March 1988

11. H. Liu, E.J. Lavernia and R.H. Rangel, Numerical investigation of micropore formation during substrate impact of molten droplets in plasma spray process. Atomization Sprays 4 (1994), p. 2694.

12. G. Trapaga, E.F. Matthys, J.J. Valencia and J. Szekely, Fluid flow, heat transfer, and solidification of molten deoplets impiging on substrates-comparison of numerical and experimental results. Metall. Trans. 23 6 (1992), p. 701.

13. D.L. Youngs, Time-dependent multi-material flow with large fluid distortion. In: K.W. Morton and M.J. Baines, Editors, Numerical Methods for Fluid Dynamics, Academic Press, New York (1982), p. 273.

14. D.L. Youngs, An interface tracking method for a 3d Eulerian hydrodynamics code, Tech. Rep. 44/92/35, Los Alamos National Laboratory, AWRE, 1984

15. M. Bussmann, S. Chandra and J. Mostaghimi, On a three-dimensional volume tracking model of droplet impact. Phys. Fluids 11 (1999), pp. 1406–1417.

16. M. Bussmann, S. Chandra and J. Mostaghimi, Modeling the splashing of a droplet impacting a solid surface. Phys. Fluids 12 (2000), pp. 3121–3132.

17. M. Pasandideh-Fard, S. Chandra and J. Mostaghimi, A three-dimensional model of droplet impact and solidification. Int. J. Heat Mass Transfer 45 (2002), pp. 2229–2242.

18. J.E. Pilliod, E.G. Pucket, Second-order accurate volume-of fluid algorithm for tracking material interfaces, Tech. Rep. LBNL-40744, Lawrence Berkeley National Laboratory

19. D.B. Kothe, Perspective on Eulerian finite volume methods for incompressible interfacial flows, Tech. Rep. LA-UR-97-3559, Los Alamos National Laboratory

20. W.J. Rider and D.B. Kothe, Reconstructing volume tracking. J. Comput. Phys. 141 (1998), pp. 112–152.

21. T.J. Barth, Aspects of unstructured grids and finite volume solvers for euler and navier-stokes equations, in: VKI/NASA/AGARD Special Courses on Unstrucured Grid methods for Advection Dominated Flows, AGARD Publications R-787, Los Alamos, NM, 1995

22. E.G. Pucket, A volume-of-fluid interface tracking algorithm with application to computing shock wave refraction, in: 4th International Synposium on Computational Fluid Dynamics, Davis, CA, 1991

23. G.H. Miller and E.G. Pucket, Edge effects on molybdenum-encapsulated molten silicate shock wave targets. J. Comput. Phys. 73 3 (1994), pp. 1426–1434.

24. G.H. Miller and E.G. Pucket, A high-order godonov method for multiple condensed phases. J. Comput. Phys. 128 (1996), pp. 134–164.

25. E.G. Pucket, L.F. Henderson and P. Colella, A general theory of anomalous refraction. In: R. Brun and L.Z. Dumitrescu, Editors, Shock Waves at Marsielles, Springer, Berlin (1995), pp. 139–144.

26. E.G. Pucket, L.F. Henderson, P. Colella, Computing surface tension with high-order kernels, in: K. Oshima (Ed.), Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Lake Tahoe, CA, 1995, pp. 6–13

27. E.G. Pucket, A.S. Almgren, J.B. Bell, D.L. Marcus and W.J. Rider, A high-order projection method for tracking fluid interfaces in variable density incompressible flows. J. Comput. Phys. 130 (1997), pp. 269–282.

28. D.K.S. Mosso, B. Swartz, C. Clancy, Recent enhancement of volume tracking algorithm for irregular grids, Tech. Rep. LA-cp-96-226, Los Alamos National Laboratory, Los Alamos, NM, 1996

29. D.K.S. Mosso, B. Swartz, R. Ferrel, A parallel volume-tracking algorithm for unstructured meshes, Tech. Rep. LA-UR-96-2420, Los Alamos National Laboratory, Los Alamos, NM, 1996

30. J.K. Dukowicz and J.R. Baumgardner, Incremental remapping as a transport/advection algorithm. J. Comput. Phys. 160 (2000), pp. 318–335.

31. C.W. Hirt, A.A. Amsden and J.L. Cook, An arbitrary Lagrangian–Eulerian computing method for all flow speed. J. Comput. Phys. 14 (1974), p. 227.

32. L.G. Margolin, Introduction to an arbitrary Lagrangian–Eulerian computing method for all flow speed. J. Comput. Phys. 135 (1997), pp. 198–202.

33. R.M. Darlington, T.L. McAbee and G. Rodrigue, A study of ALE simulations of Rayleigh-Taylor instability. Comput. Phys. Commun. 135 (2001), pp. 58–73.

34. M. Jaeger and M. Carin, The Front-Tracking ALE method: application to a model of the freezing of cell suspensions. J. Comput. Phys. 179 (2002), pp. 704–735.

35. P. Knupp, L.G. Margolin and M. Shashkov, Reference jacobian optimization-based rezoning strategies for arbitrary Lagrangian Eulerian methods. J. Comput. Phys. 176 (2002), pp. 93–128.

36. J.E. Pilliod, An analysis of piecewise linear interface reconstruction algorithms for volume-of-fluid methods, Master’s thesis, U.C Davis, September 1992

37. B.F.W. Press, S. Teukolsky and W. Vetterling, Numerical Recipes in C. , Cambridge University Press, Cambridge (1988).

38. J. O’Rourke, Computational Geometry in C. , Cambridge University Press, Cambridge (1993).

39. K. Schutte, An edge labeling approach to concave polygon clipping, in: ACM Transactions on Graphics (ftp://ftp.ph.tn.tudelft.nl/pub/klamer/clippoly.tar.gz), 1995

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