×

A volume-tracking method for incompressible multifluid flows with large density variations. (English) Zbl 0915.76060

Summary: A numerical technique for solving the time-dependent incompressible Navier-Stokes equations in fluid flows with density large variations is presented for staggered grids. Mass conservation is based on a volume tracking method and incorporates a piecewise-linear interface reconstruction on a grid twice as fine as the velocity-pressure grid. It also uses a special flux-corrected transport algorithm for momentum advection, a multigrid algorithm for solving a pressure-correction equation and a surface tension algorithm that is robust and stable. In principle, the method conserves both mass and momentum exactly, and maintains extremely sharp fluid interfaces. Applications of the numerical method to prediction of two-dimensional bubble rise in an inclined channel and a bubble bursting through an interface are presented.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] , and , ’The MAC method. A computing technique for solving viscous, incompressible, transient fluid-flow problems involving free surfaces’, LASL Report LA - 3425, Los Alamos, NM, 1965.
[2] and , ’Computer study of finite amplitude water waves’, Tech. Report 104, Dept. Civil Engineering, Stanford University, CA, 1969.
[3] Nichols, J. Comput. Phys. 12 pp 234– (1973)
[4] Wang, Int. J. Numer. Methods Fluids 18 pp 669– (1994)
[5] and , ’SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries’, Los Alamos Scientific Laboratory Report, LA-8355, Los Alamos, NM, 1980.
[6] Unverdi, J. Comput. Phys. 100 pp 25– (1992)
[7] Pericleous, Numer. Heat Transfer, Part B 27 pp 487– (1995)
[8] ’A multilevel adaptive projection method for unsteady incompressible flow’, 6th Copper Mountain Conference on Multigrid Methods, Copper Mountain, Co, April 4-9, 1993.
[9] Bell, J. Comput. Phys. 101 pp 334– (1992)
[10] , , and , ’Accurate solution algorithms for incompressible multiphase flows’, AIAA Paper No. 95-0699, 33rd Aerospace Sciences Meeting, Reno, NV, 1995.
[11] and , ’Second order volume-of-fluid interface tracking algorithms’, Unpublished manuscript, to be submitted to J. Comput. Phys. (1996).
[12] Tau, J. Comput. Phys. 115 pp 147– (1994)
[13] Chorin, Math. Comput. 22 pp 745– (1968)
[14] ’Time-dependent multi-material flow with large fluid distortion’, in and (eds.), Numerical Methods for Fluid Dynamics, Academic Press, New York, 1982, pp. 273-285.
[15] Rudman, Int. J. Numer. Methods Fluids 24 pp 671– (1979)
[16] Zalesak, J. Comput. Phys. 31 pp 335– (1979)
[17] Li, Numer. Heat Transfer. Part B 27 pp 1– (1995)
[18] Brackbill, J. Comput. Phys. 100 pp 335– (1992)
[19] and , ’Computing surface tension with high-order kernels’, in K. Oshima (ed.), Proc. 6th International Symposium on Computational Dynamics, Lake Tahoe, CA, September 4-8 1995.
[20] Monaghan, Ann. Rev. Astrophys. 30 pp 543– (1992)
[21] LaFaurie, J. Comput. Phys. 113 pp 134– (1994)
[22] ’A variational approach to deriving smeared-interface surface tension models’, Preprint (1997).
[23] An Introduction to Multigrid Methods, John Wiley and Sons, Chichester, UK, 1992. · Zbl 0760.65092
[24] Che, Trans. IChemE 69 pp 25– (1991)
[25] Maneri, Int. J. Multiphase Flow 1 pp 623– (1974)
[26] Maxworthy, J. Fluid Mech. 229 pp 659– (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.