Shahbaz, Khosro and Paraschivoiu, Marius and Mostaghimi, Javad (2003) Second order accurate volume tracking based on remapping for triangular meshes. Journal of Computational Physics, 188 (1). pp. 100122. ISSN 00219991

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Official URL: http://dx.doi.org/doi:10.1016/S00219991(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 multifluid 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 > Faculty of Engineering and Computer Science > Mechanical and Industrial Engineering 

Item Type:  Article 
Refereed:  Yes 
Authors:  Shahbaz, Khosro and Paraschivoiu, Marius and Mostaghimi, Javad 
Journal or Publication:  Journal of Computational Physics 
Date:  June 2003 
ID Code:  6751 
Deposited By:  ANDREA MURRAY 
Deposited On:  02 Jul 2010 16:33 
Last Modified:  08 Dec 2010 23:11 
References:  1. R. Scardovelli and S. Zaleski, Direct numerical simulation of freesurface 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, SOLAVOF: A solution algorithm for transient fluid flow with multiple free boundaries, Tech. Rep. LA8355, Los Alamos National Laboratory, Augest 1980, unpublished 4. M.D. Torrey, L.D. Cloutman, R.C. Mjolsness, C.W. Hirt, NASAVOF2D: A computer program for incompressible flows with free surfaces, Tech. Rep. LA10612MS, Los Alamos National Laboratory, December 1985, unpublished 5. M.D. Torrey, R.C. Mjolsness, R.L. Stein, NASAVOF3D: A threedimensional computer program for incompressible flows with free surfaces, Tech. Rep. LA11009MS, 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. LA12007MS, 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 inkjet printhead, in: in SPSE/SPIES Electronic Imaging Devices ans System Symposium, January 1989 10. P.A. Torpey, Prevention of air ingestion in a thermal inkjet device, in: Proceedings of the 4th International Congress on Advances in NonImpact 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 substratescomparison of numerical and experimental results. Metall. Trans. 23 6 (1992), p. 701. 13. D.L. Youngs, Timedependent multimaterial 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 threedimensional 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. PasandidehFard, S. Chandra and J. Mostaghimi, A threedimensional model of droplet impact and solidification. Int. J. Heat Mass Transfer 45 (2002), pp. 2229–2242. 18. J.E. Pilliod, E.G. Pucket, Secondorder accurate volumeof fluid algorithm for tracking material interfaces, Tech. Rep. LBNL40744, Lawrence Berkeley National Laboratory 19. D.B. Kothe, Perspective on Eulerian finite volume methods for incompressible interfacial flows, Tech. Rep. LAUR973559, 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 navierstokes equations, in: VKI/NASA/AGARD Special Courses on Unstrucured Grid methods for Advection Dominated Flows, AGARD Publications R787, Los Alamos, NM, 1995 22. E.G. Pucket, A volumeoffluid 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 molybdenumencapsulated molten silicate shock wave targets. J. Comput. Phys. 73 3 (1994), pp. 1426–1434. 24. G.H. Miller and E.G. Pucket, A highorder 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 highorder 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 highorder 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. LAcp96226, Los Alamos National Laboratory, Los Alamos, NM, 1996 29. D.K.S. Mosso, B. Swartz, R. Ferrel, A parallel volumetracking algorithm for unstructured meshes, Tech. Rep. LAUR962420, 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 RayleighTaylor instability. Comput. Phys. Commun. 135 (2001), pp. 58–73. 34. M. Jaeger and M. Carin, The FrontTracking 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 optimizationbased 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 volumeoffluid 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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