×

zbMATH — the first resource for mathematics

A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. (English) Zbl 1047.76085
Summary: We present a coupled level set/volume-of-fluid method for computing growth and collapse of vapor bubbles. The liquid is assumed incompressible and the vapor is assumed to have constant pressure in space. Second order algorithms are used for finding ”mass conserving” extension velocities, for discretizing the local interfacial curvature and also for the discretization of the cell-centered projection step. Convergence studies are given that demonstrate this second order accuracy. Examples are provided that apply to cavitating bubbles.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76T10 Liquid-gas two-phase flows, bubbly flows
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Software:
PROST
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] I. Aleinov, E.G. Puckett, Computing surface tension with high-order kernels, in: Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Lake Tahoe, CA, 1995
[2] A.S. Almgren, J.B. Bell, P. Colella, T. Marthaler, A cell-centered cartesian grid projection method for the incompressible Euler equations in complex geometries, in: Proceedings of the 12th AIAA Computational Fluid Dynamics Conference, San Diego, CA, June 19-22 1995 · Zbl 0910.76040
[3] Armfield, S.W.; Street, R., Fractional step methods for the navier – stokes equations on non-staggered grids, Anziam j., 42, E, C134-C156, (2000) · Zbl 1008.76058
[4] J.B. Bell, P. Colella, H.M. Glaz, A second-order projection method for viscous, incompressible flow, in: Proceedings of the 8th AIAA Computational Fluid Dynamics Conference, Honolulu, June 9-11, 1987
[5] Bell, J.B.; Colella, P.; Glaz, H.M., A second-order projection method for the incompressible navier – stokes equations, J. comput. phys., 85, 257-283, (1989) · Zbl 0681.76030
[6] Bell, J.B.; Marcus, D.L., A second-order projection method for variable-density flows, J. comput. phys., 101, 334-348, (1992) · Zbl 0759.76045
[7] Best, J., The formation of toroidal bubbles upon the collapse of transient cavities, J. fluid mech., 251, 79-107, (1993) · Zbl 0784.76011
[8] Brackbill, J.U.; Kothe, D.B.; Zemach, C., A continuum method for modeling surface tension, J. comput. phys., 100, 335-353, (1992) · Zbl 0775.76110
[9] Caiden, R.; Fedkiw, R.; Anderson, C., A numerical method for two phase flow consisting of separate compressible and incompressible regions, J. comput. phys., 166, 1-27, (2001) · Zbl 0990.76065
[10] Chan, R.; Street, R., A computer study of finite-amplitude water waves, J. comput. phys., 6, 68-94, (1970) · Zbl 0207.27403
[11] Chen, S.; Johnson, D.; Raad, P., Velocity boundary conditions for the simulation of free surface fluid flow, J. comput. phys., 116, 262-276, (1995) · Zbl 0823.76051
[12] Chopp, D., Some improvements of the fast marching method, SIAM J. sci. comput., 23, 1, 230-244, (2001) · Zbl 0991.65105
[13] Chorin, A.J., Curvature and solidification, J. comput. phys., 57, 472-490, (1985) · Zbl 0555.65085
[14] N.V. Deshpande, Fluid mechanics of bubble growth and collapse in a thermal ink-jet printer, in: SPSE/SPIES Electronic Imaging Devices and Systems Symposium, January 1989
[15] Enright, D.; Fedkiw, R.; Ferziger, R.; Mitchell, I., A hybrid particle level set method for improved interface capturing, J. comput. phys., 183, 83-116, (2002) · Zbl 1021.76044
[16] D. Enright, S. Marschner, R. Fedkiw, Animation and rendering of complex water surfaces, in: SIGGRAPH 2002, 2002, pp. 736-744
[17] Gibou, F.; Fedkiw, R.; Cheng, L.-T.; Kang, M., A second order accurate symmetric discretization of the Poisson equation on irregular domains, J. comput. phys., 176, 205-227, (2002) · Zbl 0996.65108
[18] Helenbrook, B.T.; Martinelli, L.; Law, C.K., A numerical method for solving incompressible flow problems with a surface of discontinuity, J. comput. phys., 148, 366-396, (1999) · Zbl 0931.76058
[19] J. Helmsen, P. Colella, E.G. Puckett, Non-convex profile evolution in two dimensions using volume of fluids, LBNL Technical Report LBNL-40693, Lawrence Berkeley National Laboratory, 1997
[20] Juric, D.; Tryggvason, G., Computations of boiling flows, Int. J. multiphase flow, 24, 3, 387-410, (1998) · Zbl 1121.76455
[21] Martin, D.; Colella, P., A cell-centered adaptive projection method for the incompressible Euler equations, J. comput. phys., 163, (2000) · Zbl 0991.76052
[22] Minion, M.L., A projection method for locally refined grids, J. comput. phys., 127, (1996) · Zbl 0859.76047
[23] Poo, J.Y.; Ashgriz, N., A computational method for determining curvatures, J. comput. phys., 84, 483-491, (1989) · Zbl 0682.65006
[24] Puckett, E.G.; Almgren, A.S.; Bell, J.B.; Marcus, D.L.; Rider, W.G., A high-order projection method for tracking fluid interfaces in variable density incompressible flows, J. comput. phys., 130, 269-282, (1997) · Zbl 0872.76065
[25] Renardy, Y.; Renardy, M., Prost: a parabolic reconstruction of surface tension for the volume-of-fluid method, J. comput. phys., 183, 400-421, (2002) · Zbl 1057.76569
[26] W.J. Rider, D.B. Kothe, S. Jay Mosso, J.H. Cerutti, J.I. Hochstein, Accurate solution algorithms for incompressible multiphase flows, AIAA paper 95-0699, October 30, 1994
[27] Shu, C.-W., Total-variation-diminishing time discretizations, SIAM J. sci. stat. comput., 9, 6, 1073-1084, (1988) · Zbl 0662.65081
[28] Son, G.; Dhir, V.K., Numerical simulation of film boiling near critical pressures with a level set method, J. heat transfer, 120, 183-192, (1998)
[29] Sussman, M.; Almgren, A.; Bell, J.; Colella, P.; Howell, L.; Welcome, M., An adaptive level set approach for incompressible two-phase flows, J. comput. phys., 148, 81-124, (1999) · Zbl 0930.76068
[30] Sussman, M.; Puckett, E.G., A coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two-phase flows, J. comput. phys., 162, 301-337, (2000) · Zbl 0977.76071
[31] Sussman, M.; Smereka, P., Axisymmetric free boundary problems, J. fluid mech., 341, 269-294, (1997) · Zbl 0892.76090
[32] Sussman, M.; Smereka, P.; Osher, S.J., A level set approach for computing solutions to incompressible two-phase flow, J. comput. phys., 114, 146-159, (1994) · Zbl 0808.76077
[33] Szymczak, W.G.; Rogers, J.; Solomon, J.; Berger, A.E., A numerical algorithm for hydrodynamic free boundary problems, J. comput. phys., 106, 319-336, (1993) · Zbl 0770.76047
[34] van Leer, B., Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov’s method, J. comput. phys., 32, 101-136, (1979) · Zbl 1364.65223
[35] M. Williams, D. Kothe, E.G. Puckett, Convergence and accuracy of kernel-based continuum surface tension models, in: Proceedings of the Thirteenth US National Congress of Applied Mechanics, Gainesville, FL, June 16-21, 1998 · Zbl 0979.76014
[36] Zhang, Y.L.; Yeo, K.; Khoo, B.C.; Wang, C., 3d jet impact and toroidal bubbles, J. comput. phys., 166, 336-360, (2001) · Zbl 1030.76040
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.