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Zhang, Qinghai; Liu, Philip L.-F.

HyPAM: A hybrid continuum-particle model for incompressible free-surface flows. (English) Zbl 1330.76106

J. Comput. Phys. 228, No. 4, 1312-1342 (2009).
Summary: Three major issues associated with numerical simulations of complex free-surface flows, viz. interface tracking, fragmentation and large physical jumps, are addressed by a new hybrid continuum-particle model (HyPAM). The new model consists of three parts: (1) the Polygonal Area Mapping method [Q. Zhang and P. L. F. Liu, J. Comput. Phys. 227, No. 8, 4063–4088 (2008; Zbl 1135.76041)]; (2) a new algorithm that decomposes the interested (water) phase into a continuum zone, a buffer zone and a particle zone, based on material topology and graph theory; (3) a ‘passive-response’ assumption, in which the air phase is assumed to respond passively to the continuum part of the water phase. The incompressible inviscid Euler equations and the equations describing the free fall of rigid bodies are used as the governing equations for the continuum-buffer zone and the particle zone, respectively, and separately. A number of examples, including water droplet impact, solitary wave propagation, and dam-break problems, are simulated for the illustration and validation of HyPAM. It is shown that HyPAM is more accurate and versatile than a continuum-based Volume-of-Fluid model. One major contribution of this work is the single-phase decomposition algorithm, useful for many other hybrid formulations. Neglecting surface tension, viscosity and particle interactions, HyPAM is currently limited to mildly-fragmented free-surface flows with high Reynolds and Weber numbers.

Cited in 3 Documents

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76M28 Particle methods and lattice-gas methods
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

Keywords:

free-surface flow; interface tracking; polygonal area mapping method; 2-connectedness; material topology graph; single-phase decomposition; passive-response assumption; hybrid continuum-particle method; pressure-incremental projection method; droplet impact; dam-break problem; solitary wave propagation

Citations:

Zbl 1135.76041

Software:

Boost C++ Libraries; BGL; RIPPLE; Boost
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Full Text: DOI

References:

[1] Aho, A. V.; Hopcroft, J. E.; Ullman, J. D., Data Structures and Algorithms (1983), Addison-Wesley · Zbl 0257.68065
[2] Almgren, A. S.; Bell, J. B.; Colella, P.; Howell, L. H.; Welcome, M. L., A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations, J. Comput. Phys., 142, 1, 1-46 (1998) · Zbl 0933.76055
[3] Ataie-Ashtiani, B.; Farhadi, L., A stable moving-particle semi-implicit method for free surface flows, Fluid Dynamics Research, 38, 241-256 (2006) · Zbl 1178.76291
[4] Baase, S., Computer Algorithms: Introduction to Design and Analysis (1983), Addison-Wesley
[5] Bell, J. B.; Colella, P.; Glaz, H. M., A second-order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., 85, 2, 257-283 (1989) · Zbl 0681.76030
[6] Bender, C. M.; Orszag, S. A., Advanced Mathematical Methods for Scientists and Engineers. Advanced Mathematical Methods for Scientists and Engineers, WKB Theory (1978), McGraw-Hill Book Company, (Chapter 10) · Zbl 0417.34001
[7] Berthelsen, P. A.; Faltinsen, O. M., A local directional ghost cell approach for incomopressible viscous flow problems with irregular boundaries, J. Comput. Phys., 227, 4354-4397 (2008) · Zbl 1388.76199
[8] Brocchini, M.; Peregrine, D. H., The dynamics of strong turbulence at free surface. Part 1. Description, J. Fluid Mech., 449, 225-254 (2001) · Zbl 1007.76027
[9] Brown, D. L.; Cortez, R.; Minion, M. L., Accurate projection methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 168, 2, 464-499 (2001) · Zbl 1153.76339
[10] Chan, R. K.C.; Street, R. L., A computer study of finite amplitude water waves, J. Comput. Phys., 6, 68-94 (1970) · Zbl 0207.27403
[11] Chanson, H., Air Bubble Entrainment in Free-surface Turbulent Shear Flows (1996), Academic Press: Academic Press London, UK
[12] Chen, S.; Johnson, D. B.; Raad, P. E., Velocity boundary conditions for the simulation of free surface fluid flow, J. Comput. Phys., 116, 2, 262-276 (1995) · Zbl 0823.76051
[13] Chorin, A. J., Numerical solution of the Navier-Stokes equations, Math. Comput., 22, 104, 745-762 (1968) · Zbl 0198.50103
[14] Chorin, A. J., On the convergence of discrete approximations to the Navier-Stokes equations, Math. Comput., 23, 106, 341-353 (1969) · Zbl 0184.20103
[15] Colagrossi, A.; Landrini, M., Numerical simulation of interfacial flows by smoothed particle hydrodynamics, J. Comput. Phys., 191, 448-475 (2003) · Zbl 1028.76039
[16] Cristini, V.; Blawzdziewicz, J.; Loewenberg, M., An adaptive mesh algorithm for evolving surfaces: Simulations of drop breakup and coalescence, J. Comput. Phys., 168, 2, 445-463 (2001) · Zbl 1153.76382
[17] Cui, J.; He, G. W.; Qi, D., A constrained particle dynamics for continuum-particle hybrid method in micro- and nano-fluidics, Acta Mech. Sin., 22, 503-508 (2006) · Zbl 1202.76113
[18] Dai, M.; Schmidt, D. P., Adaptive tetrahedral meshing in free-surface flow, J. Comput. Phys., 208, 228-252 (2005) · Zbl 1114.76333
[19] Dean, R. G.; Dalrymple, R. A., Water Wave Mechanics for Engineers and Scientists (1991), World Scientific: World Scientific Singapore
[20] Delgado-Buscalioni, R.; Coveney, P. V., Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow, Phys. Rev. E, 67, 4, 046704 (2003)
[21] Diestel, R., Graph Theory (2005), Springer-Verlag: Springer-Verlag Heidelberg, New York · Zbl 1074.05001
[22] Enright, D.; Fedkiw, R.; Ferziger, J.; Mitchell, I., A hybrid particle level set method for improved interface tracking, J. Comput. Phys., 183, 83-116 (2002) · Zbl 1021.76044
[23] Enright, D.; Marschner, S.; Fedkiw, R., Animation and rendering of complex water surfaces, ACM Trans. Graph., 21, 3, 736-744 (2002)
[24] Flack, K. A.; Sylor, J. R.; Smith, G. B., Near-surface turbulence for evaporative convection at an air/water interface, Phys. Fluids, 13, 11, 3338 (2001) · Zbl 1184.76165
[25] N. Foster, R. Fedkiw. Practical animation of liquids, in: SIGGRAPH 2001 Annual Conference, 2001, pp. 15-22.; N. Foster, R. Fedkiw. Practical animation of liquids, in: SIGGRAPH 2001 Annual Conference, 2001, pp. 15-22.
[26] J. Fukai, Z. Zhao, D. Poulikakos, C.M. Megaridis, O. Miyatake. Modeling of the deformation of a liquid droplet impinging upon a flat surface, J. Comput. Phys. 5(11), Phys. Fluids A - Fluid Dynam., 1993.; J. Fukai, Z. Zhao, D. Poulikakos, C.M. Megaridis, O. Miyatake. Modeling of the deformation of a liquid droplet impinging upon a flat surface, J. Comput. Phys. 5(11), Phys. Fluids A - Fluid Dynam., 1993. · Zbl 0807.76022
[27] Ginzburg, I.; Steiner, K., Lattice Boltzmann model for free-surface flow and its application to filling process in casting, J. Comput. Phys., 185, 61-99 (2003) · Zbl 1062.76554
[28] Gonzalez, D.; Cueto, E.; Chinesta, F.; Doblare, M., A natural element updated lagrangian strategy for free-surface fluid dynamics, J. Comput. Phys., 223, 127-150 (2007) · Zbl 1108.76053
[29] Gorokhovski, M.; Herrmann, M., Modeling primary atomization, Annu. Rev. Fluid Mech., 40, 343-366 (2008) · Zbl 1232.76058
[30] Grimshaw, R., The solitary wave in water of variable depth. part 2, J. Fluid Mech., 46, 3, 611-622 (1971) · Zbl 0222.76017
[31] Gross, J. L.; Yellen, J., Graph Theory and its Applications (2006), Chapman & Hall/CRC: Chapman & Hall/CRC Boca Raton, London, New York · Zbl 1082.05001
[32] Hirt, C. W.; Nichols, B. D., Volume of fluid (vof) method for the dynamics of free boundaries, J. Comput. Phys., 39, 1, 201-225 (1981) · Zbl 0462.76020
[33] Hu, H. H.; Patankar, N. A.; Zhu, M. Y., Direct numerical simulations of fluid-solid systems using the arbitrary lagrangian-eulerian technique, J. Comput. Phys., 169, 2, 427-462 (2001) · Zbl 1047.76571
[34] Hunt, J. C.R.; Graham, J. M.R., Free-stream turbulence near plane boundaries, J. Fluid Mech., 84, 2, 209-235 (1978) · Zbl 0365.76056
[35] Inamuro, T.; Ogata, T.; Tajima, S.; Konishi, N., A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys., 198, 628-644 (2004) · Zbl 1116.76415
[36] Kim, J.; Moin, P., Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59, 2, 308-323 (1985) · Zbl 0582.76038
[37] Koshizuka, S.; Nobe, A.; Oka, Y., Moving-particle semi-implicit method for fragmentation of incompressible fluids, Int. J. Numer. Meth. Fluids, 26, 751-769 (1998) · Zbl 0928.76086
[38] Koshizuka, S.; Oka, Y., Moving-particle semi-implicit method for fragmentation of incompressible fluids, Nucl. Sci. Eng., 123, 421-434 (1996)
[39] Kothe, D. B.; Mjolsness, R. C., Ripple: A new model for incompressible flows with free surfaces, AIAA J., 30, 11, 2694-2700 (1992) · Zbl 0762.76074
[40] Koumoutsakos, P., Multiscale flow simulations using particles, Annu. Rev. Fluid Mech., 37, 457-487 (2005) · Zbl 1117.76054
[41] Lemos, C. M., Wave Breaking: A Numerical Study, Lecture Notes in Engineering, vol. 71 (1992), Springer-Verlag: Springer-Verlag Berlin, New York · Zbl 0753.76119
[42] Leveque, R. J.; Li, Z., Immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31, 4, 1019-1044 (1994) · Zbl 0811.65083
[43] Leveque, R. J.; Li, Z., Immersed interface methods for stokes flow with elastic boundaries or surface tension, SIAM J. Sci. Comput., 18, 3, 709-735 (1997) · Zbl 0879.76061
[44] Li, Z.; Lai, M.-C., The immersed interface method for the navier-stokes equations with singular forces, J. Comput. Phys., 171, 2, 822-842 (2001) · Zbl 1065.76568
[45] Lin, P.; Liu, P. L.-F., Numerical study of breaking waves in the surf zone, J. Fluid Mech., 359, 239-264 (1998) · Zbl 0916.76009
[46] Liu, D.; Lin, P., A numerical study of three-dimensional liquid sloshing in tanks, J. Comput. Phys., 227, 3921-3939 (2008) · Zbl 1317.76061
[47] Liu, J.; Chen, S.; Nie, X.; Robbins, M. O., A continuum-atomistic simulation of heat transfer in micro- and nano-flows, J. Comput. Phys., 227, 279-291 (2007) · Zbl 1130.80010
[48] Liu, J.; Koshizuka, S.; Oka, Y., A hybrid particle-mesh method for viscous, incompressible, multiphase flows, J. Comput. Phys., 202, 65-93 (2005) · Zbl 1061.76069
[49] Liu, X.-D.; Fedkiw, R. P.; Kang, M., A boundary condition capturing method for poisson’s equation on irregular domains, J. Comput. Phys., 160, 151-178 (2000) · Zbl 0958.65105
[50] Lo, D. C.; Young, D. L., Arbitrary lagrangian-eulerian finite element analysis of free surface flow using a velocity-vorticity formulation, J. Comput. Phys., 195, 175-201 (2004) · Zbl 1087.76066
[51] Longuet-Higgins, M. S., Mass transport in water waves, Phil. Trans. R. Soc. Lond. A, 245, 903, 535-581 (1953) · Zbl 0050.20304
[52] Longuet-Higgins, M. S., Mass transport in the boundary layer at a free oscillating surface, J. Fluid Mech., 8, 293-306 (1960) · Zbl 0096.21604
[53] Longuet-Higgins, M. S., Capillary rollers and bores, J. Fluid Mech., 240, 659-679 (1992) · Zbl 0759.76021
[54] F. Losasso, J.O. Talton, N. Kwatra, R. Fedkiw, Two-way coupled sph and particle level set fluid simulation, IEEE Trans. Vis. Comput. Graph. (2008), doi:10.1109/TVCG.2008.37; F. Losasso, J.O. Talton, N. Kwatra, R. Fedkiw, Two-way coupled sph and particle level set fluid simulation, IEEE Trans. Vis. Comput. Graph. (2008), doi:10.1109/TVCG.2008.37
[55] Mei, C. C.; Stiassnie, M.; Yue, D. K.-P., Theory and Applications of Ocean Surface Waves, Part 1: Linear Aspects (2005), World Scientific: World Scientific Singapore · Zbl 1113.76001
[56] Melville, W. K., The role of surface-wave breaking in air-sea interaction, Annu. Rev. Fluid Mech., 28, 279-321 (1996)
[57] Minion, M. L., A projection method for locally refined grids, J. Comput. Phys., 127, 1, 158-178 (1996) · Zbl 0859.76047
[58] Monaghan, J. J., Smoothed particle hydrodynamics, Annu. Rev. Astron. Astrophys., 30, 543-574 (1992)
[59] Monaghan, J. J., Simulating free surface flows with sph, J. Comput. Phys., 110, 399-406 (1994) · Zbl 0794.76073
[60] O’Connell, S. T.; Thompson, P. A., Molecular dynamics-continuum hybrid computations: a tool for studying complex fluid flows, Phys. Rev. E, 52, 6, 5792-5795 (1995)
[61] Oger, G.; Doring, M.; Alessandrini, B.; Ferrant, P., An improved sph method: towards higher order convergence, J. Comput. Phys., 225, 1472-1492 (2007) · Zbl 1118.76050
[62] O’Rourke, J., Computational Geometry in C (1998), Cambridge University Press: Cambridge University Press New York · Zbl 0912.68201
[63] Panton, R. L., Incompressible Flow (1996), John Wiley & Sons INC.: John Wiley & Sons INC. New York
[64] Parau, E. I.; Vanden-Broeck, J.-M.; Cooker, M. J., Nonlinear three-dimensional interfacial flows with a free surface, J. Fluid Mech., 591, 481-494 (2007) · Zbl 1169.76338
[65] Perot, B.; Nallapati, R., A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows, J. Comput. Phys., 184, 192-214 (2003) · Zbl 1118.76307
[66] Peskin, C. S., Flow patterns around heart valves: a numerical method, J. Comput. Phys., 10, 252-271 (1972) · Zbl 0244.92002
[67] Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25, 220-252 (1977) · Zbl 0403.76100
[68] Sarpkaya, T., Vorticity, free surface, and surfactants, Annu. Rev. Fluid Mech., 28, 83-128 (1996)
[69] Scardovelli, R.; Zaleski, S., Direct numerical simulation of free-surface and interfacial flow calculations, Ann. Rev. Fluid Mech., 31, 567-603 (1999)
[70] Schaffer, S., A semi-coarsening multigrid method for elliptic partial differential equations with highly discontinuous and anisotropic coefficients, SIAM J. Sci. Comput., 20, 1, 228-242 (1998) · Zbl 0913.65111
[71] Schwartzentruber, T. E.; Scalabrin, L. C.; Boyd, I. D., A modular particle-continuum numerical method for hypersonic non-equilibrium gas flows, J. Comput. Phys., 225, 1159-1174 (2007) · Zbl 1343.76057
[72] Scott, J. C., The preparation of water for surface-clean fluid mechanics, J. Fluid Mech., 69, 2, 339-351 (1975)
[73] Selle, A.; Rasmussen, N.; Fedkiw, R., A vortex particle method for smoke water and explosions, ACM Trans. Graph., 24, 3, 910-914 (2005)
[74] Sethian, J. A.; Smereka, P., Level-set methods for fluid interfaces, Ann. Rev. Fluid Mech., 35, 341-372 (2003) · Zbl 1041.76057
[75] Shen, L.; Triantafyllou, G. S.; Yue, D. K.P., Turbulent diffusion near a free surface, J. Fluid Mech., 407, 145-166 (2000) · Zbl 0966.76038
[76] Shen, L.; Yue, D. K.P.; Triantafyllou, G. S., Effect of surfactants on free-surface turbulent flows, J. Fluid Mech., 506, 79-115 (2004) · Zbl 1073.76047
[77] Shen, L.; Zhang, X.; Yue, D. K.P.; Triantafyllou, G. S., the surface layer for free-surface turbulent flows, J. Fluid Mech., 386, 167-212 (1999) · Zbl 0938.76044
[78] Shigematsu, T.; Liu, P. L.-F.; Oda, K., Modelisation numerique des etapes initiales de l’onde de rupture de barrage; numerical modeling of the initial stages of dam-break waves, J. Hydraul. Res., 42, 2, 183-195 (2004)
[79] J.G. Siek, L.-Q. Lee, A. Lumsdaine. The Boost Graph Library, C++ In-depth Series, Addison-Wesley, 2002, ISBN 0-201-72914-8.; J.G. Siek, L.-Q. Lee, A. Lumsdaine. The Boost Graph Library, C++ In-depth Series, Addison-Wesley, 2002, ISBN 0-201-72914-8.
[80] Stansby, P. K.; Chegini, A.; Barnes, T. C.D., Initial stages of dam-break flow, J. Fluid Mech., 374, 407-424 (1998) · Zbl 0941.76515
[81] Sugioka, K.-I.; Komori, S., Drag and lift forces acting on a spherical water droplet in homogeneous linear shear air flow, J. Fluid Mech., 570, 155-175 (2007) · Zbl 1111.76012
[82] Tarjan, R. E., Depth first search and linear graph algorithms, SIAM J. Comput., 1, 2, 146-160 (1972) · Zbl 0251.05107
[83] Thorpe, S. A., Dynamical processes of transfer at the sea surface, Prog. Oceanogr., 35, 4, 315-352 (1995)
[84] Thulasiraman, K.; Swamy, M. N.S., Graphs: Theory and Algorithms (1992), John Wiley & Sons · Zbl 0766.05001
[85] Vatti, B. R., A generic solution to polygon clipping, Commun. ACM, 35, 7, 56-63 (1992)
[86] Villermaux, E., Fragmentation, Annu. Rev. Fluid Mech., 39, 419-446 (2007) · Zbl 1296.76164
[87] Watanabe, Y.; Saruwatari, A.; Ingram, D. M., Free-surface flows under impacting droplets, J. Comput. Phys., 227, 2344-2365 (2008) · Zbl 1261.76039
[88] Welch, S. W.J., Local simulation of two-phase flows including interface tracking with mass-transfer, J. Comput. Phys., 121, 1, 142-154 (1995) · Zbl 0839.76069
[89] Willert, C. E.; Gharib, M., The interaction of spatially modulated vortex pairs with free surfaces, J. Fluid Mech., 345, 227-250 (1997)
[90] Williams, S. A.; Bell, J. B.; Garcia, A. L., Algorithm refinement for fluctuating hydrodynamics, Multiscale Model. Simul., 6, 1256-1280 (2008) · Zbl 1247.76065
[91] Xie, X.; Musson, L. C.; Pasquali, M., An isochoric domain deformation method for computing steady free surface flows with conserved volumes, J. Comput. Phys., 226, 398-413 (2007) · Zbl 1310.76102
[92] Xu, S.; Wang, Z. J., Systematic derivation of jump conditions for the immersed interface method in three-dimensional flow simulation, SIAM J. Sci. Comput., 27, 6, 1948-1980 (2006) · Zbl 1136.76346
[93] Yabe, T.; Xiao, F.; Utsumi, T., The constrained interpolation profile method for multiphase analysis, J. Comput. Phys., 169, 556-593 (2001) · Zbl 1047.76104
[94] Yang, B.; Prosperetti, A., A second-order boundary-fitted projection method for free-surface flow computations, J. Comput. Phys., 213, 574-590 (2006) · Zbl 1136.76415
[95] Zhang, C.; Shen, L.; Yue, D. K.P., The mechanism of vortex connection at a free surface, J. Fluid Mech., 384, 207-241 (1999) · Zbl 0936.76016
[96] Zhang, Q.; Liu, P. L.-F., A new interface tracking method: The polygonal area mapping method, J. Comput. Phys., 227, 8, 4063-4088 (2008) · Zbl 1135.76041
[97] Q. Zhang, P.L.-F. Liu, A numerical study of swash flows generated by bores, Coastal Eng., 2009, in press, doi:10.1016/j.coastaleng.2008.04.010.; Q. Zhang, P.L.-F. Liu, A numerical study of swash flows generated by bores, Coastal Eng., 2009, in press, doi:10.1016/j.coastaleng.2008.04.010.
[98] Zinchenko, A. Z.; Rother, M. A.; Davis, R. H., A novel boundary-integral algorithm for viscous interaction of deformable drops, Phys. Fluids A - Fluid Dynam., 9, 6, 1493-1511 (1997)
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