Computational modeling for multiphase flows with spacecraft application

Progress in Aerospace Sciences

Volumn 43, Issue 4-6, 2007, Pages 138-192

  Uzgoren, Eray ^a   Singh, Rajkeshar ^b   Sim, Jaeheon ^a   Shyy, Wei ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

^b GE GLOBAL RESEARCH   (United States)

Author keywords

Adaptive Cartesian grid; Hilbert space filling curve; Immersed boundary method; Interface tracking; Multi level methods; Parallel computation

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; HILBERT SPACES; MATHEMATICAL MODELS; MULTIPHASE FLOW; PARALLEL PROCESSING SYSTEMS; SPACECRAFT;

ADAPTIVE CARTESIAN GRID; IMMERSED BOUNDARY METHOD; INTERFACE TRACKING; PARALLEL COMPUTATION;

COMPUTATIONAL FLUID DYNAMICS;

EID: 34948874792     PISSN: 03760421     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.paerosci.2007.06.003     Document Type: Review

References (123)

1. Francois M., and Shyy W. Micro-scale drop dynamics for heat transfer enhancement. Progr Aerospace Sci 38 4 (2002) 275
2. Shyy W. Multiphase computations using sharp and continuous interface techniques for micro-gravity applications. C R Mec 332 5-6 (2004) 375
3. Udaykumar H.S., Mittal R., and Shyy W. Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids. J Comput Phys 153 2 (1999) 535
4. Uzgoren E, Sim J, Shyy W. Computations of multiphase fluid flows using marker-based adaptive, multilevel Cartesian grid method. In 45th AIAA aerospace sciences meeting and exhibit reno, NV. AIAA 2007-336, 2007.
5. Symons EP. Draining characteristics of hemispherically bottomed cylinders in a low-gravity environment. NASA technical paper no. 1297, 1978.
6. Peskin C.S. Numerical analysis of blood flow in the heart. J Comput Phys 25 3 (1977) 220-252
7. Udaykumar H.S., Kan H.C., and Shyy W. Multiphase dynamics in arbitrary geometries on fixed Cartesian grids. J Comput Phys 137 2 (1997) 366
8. Pan K.L., Shyy W., and Law C.K. An immersed-boundary method for the dynamics of premixed flames. Int J Heat Mass Transf 45 17 (2002) 3503
9. Francois M., Uzgoren E., Jackson J., et al. Multigrid computations with the immersed boundary technique for multiphase flows. Int J Numer Meth Heat Fluid Flow 14 1 (2004) 98
10. Lörstad D., and Fuchs L. High-order surface tension VOF-model for 3D bubble flows with high density ratio. J Comput Phys 200 1 (2004) 153
11. Singh R., and Shyy W. Three-dimensional adaptive Cartesian grid method with conservative interface restructuring and reconstruction. J Comput Phys 224 1 (2007) 150
12. Juric D., and Tryggvason G. A front-tracking method for dendritic solidification. J Comput Phys 123 1 (1996) 127
13. Tryggvason G., Bunner B., Esmaeeli A., et al. A front-tracking method for the computations of multiphase flow. J Comput Phys 169 2 (2001) 708
14. Gilmanov A., and Sotiropoulos F. A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. J Comput Phys 207 2 (2005) 457
15. Shyy W., Smith R.W., Udaykumar H.S., et al. Computational fluid dynamics with moving boundaries (1996), Taylor & Francis Inc., Bristol, PA, USA
16. Al-Rawahi N., and Tryggvason G. Numerical simulation of dendritic solidification with convection: Three-dimensional flow. J Comput Phys 194 2 (2004) 677
17. Antaki JF, Blelloch GE, Ghattas O, et al. A parallel dynamic-mesh Lagrangian method for simulation of flows with dynamic interfaces. Proceedings of the 2000 ACM/IEEE conference on supercomputing, 2000.
18. Aulisa E., Manservisi S., and Scardovelli R. A surface marker algorithm coupled to an area-preserving marker redistribution method for three-dimensional interface tracking. J Comput Phys 197 2 (2004) 555
19. de Sousa F.S., Mangiavacchi N., Nonato L.G., et al. A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces. J Comput Phys 198 2 (2004) 469
20. Esmaeeli A., and Tryggvason G. Computations of film boiling, part I: numerical method. Int J Heat Mass Transf 47 25 (2004) 5451
21. Francois M., and Shyy W. Computations of drop dynamics with the immersed boundary method, part 1: numerical algorithm and buoyancy-induced effect. Numer Heat Transf: Part B: Fund 44 2 (2003) 101
22. Griffith B.E., and Peskin C.S. On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems. J Comput Phys 208 1 (2005) 75
23. Osher S., and Fedkiw R.P. Level set methods- an overview and some recent results. J Comput Phys 169 2 (2001) 463
24. Peskin C.S. The immersed boundary method. Acta Numer 11 (2003) 479
25. Shyy W. Computational modeling for fluid flow and interfacial transport (1994), Elsevier, New York
26. Sussman M. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. J Comput Phys 187 1 (2003) 110
27. Sussman M. A parallelized, adaptive algorithm for multiphase flows in general geometries. Comput Struct 83 6-7 (2005) 435
28. Tornberg A.K., and Engquist B. Numerical approximations of singular source terms in differential equations. J Comput Phys 200 2 (2004) 462
29. Torres D.J., and Brackbill J.U. The point-set method: front-tracking without connectivity. J Comput Phys 165 2 (2000) 620
30. Ye T., Mittal R., Udaykumar H.S., et al. An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J Comput Phys 156 2 (1999) 209
31. Ye T., Shyy W., Tai C.F., et al. Assessment of sharp-and continuous-interface methods for drop in static equilibrium. Comput Fluids 33 7 (2004) 917
32. Johansen H., and Colella P. A Cartesian grid embedded boundary method for Poisson's equation on irregular domains. J Comput Phys 147 1 (1998) 60
33. Wasekar V.M., and Manglik R.M. Short-time-transient surfactant dynamics and Marangoni convection around boiling nuclei. J Heat Transf 125 5 (2003) 858
34. Perot B., and Nallapati R. A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows. J Comput Phys 184 1 (2003) 192
35. Quan S., and Schmidt D.P. A moving mesh interface tracking method for 3D incompressible two-phase flows. J Comput Phys 221 2 (2007) 761
36. Osher S., and Fedkiw R.P. Level set methods and dynamic implicit surfaces (2002), Springer, Berlin
37. Rider W.J., and Kothe D.B. Reconstructing volume tracking. J Comput Phys 141 2 (1998) 112
38. Scardovelli R., and Zaleski S. Direct numerical simulation of free-surface and interfacial flow. Ann Rev Fluid Mech 31 1 (1999) 567
39. Enright D., Fedkiw R., Ferziger J., et al. A hybrid particle level set method for improved interface capturing. J Comput Phys 183 1 (2002) 83
40. Sussman M., and Puckett E. A coupled level set and volume-of-fluid method for improved interface capturing. J Comput Phys 162 (2000) 301-337
41. Glimm J., Graham M.J., Grove J., et al. Front tracking in two and three dimensions. Comput Math Appl 35 1 (1998)
42. Glimm J., Grove J.W., Li X.L., et al. Robust computational algorithms for dynamic interface tracking in three dimensions. SIAM J Sci Comput 21 6 (1999) 2240
43. Shin S., and Juric D. Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J Comput Phys 180 2 (2002) 427
44. Singh R, Shyy W. Three-dimensional adaptive grid computation with conservative, marker-based tracking for interfacial fluid dynamics. In: 44th AIAA Aerospace sciences meeting and exhibit. AIAA 2006-1523, 2006.
45. Ryskin G., and Leal L.G. Numerical solution of free-boundary problems in fluid mechanics, part 3: bubble deformation in an axisymmetric straining flow. J Fluid Mech 148 (1984) 37
46. Leveque R.J., and Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J Numer Anal 31 4 (1994) 1019
47. Li Z., and Lai M.C. The immersed interface method for the Navier-Stokes equations with singular forces. J Comput Phys 171 2 (2001) 822
48. Liu X.D., Fedkiw R.P., and Kang M. A boundary condition capturing method for Poisson's equation on irregular domains. J Comput Phys 160 1 (2000) 151
49. Kang M., Fedkiw R.P., and Liu X.D. A boundary condition capturing method for multiphase incompressible flow. J Sci Comput 15 3 (2000) 323
50. Marella S., Krishnan S., Liu H., et al. Sharp interface Cartesian grid method I: an easily implemented technique for 3D moving boundary computations. J Comput Phys 210 1 (2005) 1
51. Rider WJ, Kothe DB. Stretching and tearing interface tracking methods. In: AIAA computational fluid dynamics conference and open forum. San Diego, CA: AIAA 1995-1717, 1995.
52. Mittal R., and Iaccarino G. Immersed boundary methods. Annu Rev Fluid Mech 37 01 (2005) 239
53. Wiegmann A., and Bube K.P. The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions. SIAM J Numer Anal 37 3 (2000) 827
54. Hao Y., and Prosperetti A. A numerical method for three-dimensional gas-liquid flow computations. J Comput Phys 196 1 (2004) 126
55. Tryggvason G., Esmaeeli A., and Al-Rawahi N. Direct numerical simulations of flows with phase change. Comput Struct 83 6-7 (2005) 445
56. Renardy Y., and Renardy M. PROST-a parabolic reconstruction of surface tension for the volume-of-fluid method. J Comput Phys 183 2 (2002) 400
57. Shin S., Abdel-Khalik S.I., Daru V., et al. Accurate representation of surface tension using the level contour reconstruction method. J Comput Phys 203 2 (2005) 493
58. Esmaeeli A., and Tryggvason G. Direct numerical simulations of bubbly flows, part 1: low Reynolds number arrays. J Fluid Mech 377 (2000) 313
59. Al-Rawahi N., and Tryggvason G. Numerical simulation of dendritic solidification with convection: two-dimensional geometry. J Comput Phys 180 2 (2002) 471
60. Singh R. Three-dimensional marker-based multiphase flow computation using adaptive Cartesian grid techniques. PhD thesis. Mechanical and Aerospace Engineering. Gainesville: University of Florida; 2006.
61. Engquist B., Tornberg A.K., and Tsai R. Discretization of Dirac delta functions in level set methods. J Comput Phys 207 1 (2005) 28
62. Stockie J.M. Analysis and computation of immersed boundaries, with application to pulp fibres (1997), Institute of Applied Mathematics, University of British Columbia
63. Miller T.F., and Schmidt F.W. Use of a pressure-weighted interpolation method for the solution of the incompressible Navier-Stokes equations on a nonstaggered grid system. Numer Heat Transf 14 2 (1988) 213
64. Gu C.Y. Computation of flows with large body forces, Numerical methods in laminar and turbulent flow (1991), Pineridge Press, Swansea, UK
65. Choi S.K., Kim S.O., Lee C.H., et al. Use of the momentum interpolation method for flows with a large body force. Numer Heat Transf: Part B: Fund 43 3 (2003) 267
66. Yang J., and Balaras E. An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries. J Comput Phys 215 1 (2006) 12
67. Uzgoren E. Adaptive, Multi-domain techniques for two-phase flow computations. PhD thesis. Gainesville, FL: Department of Mechanical and Aerospace Engineering, University of Florida; 2006.
68. Sotiropoulos F., and Abdallah S. The discrete continuity equation in primitive variable solutions of incompressible flow. J Comput Phys 95 1 (1991) 212
69. Aftosmis MJ. Solution adaptive Cartesian grid methods for aerodynamic flows with complex geometries. Lecture notes, von Karman Institute for Fluid Dynamics, Series, 2, 1997.
70. Ham F.E., Lien F.S., and Strong A.B. A Cartesian grid method with transient anisotropic adaptation. J Comput Phys 179 2 (2002) 469
71. Singh R, N'Dri N, Uzgoren E, et al. Three-dimensional adaptive, Cartesian grid method for multiphase flow computations. In: 43 rd AIAA aerospace sciences meeting and exhibit. AIAA 2005-1389, 2005.
72. Balsara D. Divergence-free adaptive mesh refinement for magnetohydrodynamics, Arxiv preprint astro-ph/0112150, 2001.
73. Chorin A.J. Numerical solution of the Navier-Stokes equations. Math Comput 22 104 (1968) 745
74. Kim J., and Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J Comput Phys 59 (1985) 308
75. Tafti D. Alternate formulations for the pressure equation Laplacian on a collocated grid for solving the unsteady incompressible Navier-Stokes equations. J Comput Phys 116 1 (1995) 143
76. Ferziger J.H., and Peric M. Computational methods for fluid dynamics (2002), Springer, New York
77. Losasso F., Fedkiw R., and Osher S. Spatially adaptive techniques for level set methods and incompressible flow. Comput Fluids 35 (2006) 995-1010
78. Fox G.C., Williams R.D., and Messina P.C. Parallel computing works! (1994), Morgan Kaufmann, Los Altos, CA
79. Chan T.F., and Mathew T.P. Domain decomposition algorithms (1994), Department of Mathematics, University of California, Los Angeles
80. Smith B., Bjorstad P., and Gropp W. Domain decomposition: parallel multilevel methods for elliptic partial differential equations (2004), Cambridge University Press, Cambridge
81. Bourgat J, Glowinski R, Tallec P, et al. Variational formulations and algorithms for trace operator in domain decomposition calculations. In: Chan T, Glowinski R, Periaux J, Widlund O, editors. 2nd international symposium on domain decomposition methods for PDEs, Philadelphia, PA, 1989, p. 3.
82. De Roeck Y.H., Le Tallec P., and Vidrascu M. A domain-decomposed solver for nonlinear elasticity. Comput Methods Appl Mech Eng 99 2-3 (1992) 187
83. Le Tallec P. Numerical methods for nonlinear three-dimensional elasticity. Handbook of Numerical Analysis 3 (1994)
84. Mandel J. Balancing domain decomposition. Commun Numer Methods Eng 9 3 (1993) 233
85. Dohrmann C.R. A preconditioner for substructuring based on constrained energy minimization. SIAM J Sci Comput 25 1 (2003) 246
86. Farhat C., Lesoinne M., LeTallec P., et al. FETI-DP: a dual-primal united feti method, part I: a faster alternative to the two-level FETI method. Int J Numer Methods Eng 50 7 (2001) 1523
87. Schwarz H.A. Uber einige Abbildungsaufgaben. Ges Math Abh 11 (1869) 65
88. Garbey M. Acceleration of the Schwarz method for elliptic problems. SIAM J Sci Comput 26 6 (2005) 1871
89. Lions PL. On the Schwarz alternating method III: a variant for nonoverlapping subdomains, 3rd international symposium on domain decomposition methods for partial differential equations, Houston, Texas, March 1989. p. 20.
90. Nataf F., and Rogier F. Factorization of the convection-diffusion operator and the Schwarz algorithm. Math. Models Methods Appl Sci 3 (1995) 567
91. Bramble J.H., Pasciak J.E., and Vassilev A.T. Analysis of non-overlapping domain decomposition algorithms with inexact solves. Math Comput 67 221 (1998) 1
92. Dubois O. Optimized Schwarz methods for the advection-diffusion equation. MSc thesis. Quebec, Canada: Department of Mathematics and Statistics, McGill University; 2003.
93. Garbey M., and Tromeur-Dervout D. On some Aitken-like acceleration of the Schwarz method. Int J Numer Methods Fluids 40 12 (2002) 1493
94. Baranger J., Garbey M., and Oudin-Dardun F. Generalized Aitken-like acceleration of the Schwarz method. Lect Notes Comput Sci Eng 40 (2005) 505
95. Barberou N., Garbey M., Hess M., et al. Efficient metacomputing of elliptic linear and non-linear problems. J Parallel Distrib Comput 63 5 (2003) 564
96. Japhet C., Nataf F., and Rogier F. The optimized order 2 method application to convection-diffusion problems. Future Gener Comput Syst 18 1 (2001) 17
97. Dryja M., Sarkis M.V., and Widlund O.B. Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numer Math 72 3 (1996) 313
98. Graham I.G., and Hagger M.J. Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients. SIAM J Sci Comput 20 6 (1999) 2041
99. Liovic P., Lakehal D., and Liow J.L. LES of turbulent bubble formation and break-up based on interface tracking, direct and large-eddy simulation vol. 5 (2004), Kluwer Academic, V Amsterdam p. 261-270
100. McQueen D., and Peskin C. Shared-memory parallel vector implementation of the immersed boundary method for the computation of blood flow in the beating mammalian heart. J Supercomput 11 3 (1997) 213
101. Xiao F. A Computational model for suspended large rigid bodies in 3D unsteady viscous flows. J Comput Phys 155 2 (1999) 348
102. Croce R., Griebel M., and Schweitzer M.A. A parallel level-set approach for two-phase flow problems with surface tension in three space dimensions. Preprint 157 (2004)
103. Hill JC, Walkington N, Ghattas O, Parallel Eulerian methods for flows with elastic membranes, 2004.
104. Rendleman C.A., Beckner V.E., Lijewski M., et al. Parallelization of structured, hierarchical adaptive mesh refinement algorithms. Comput Visual Sci 3 3 (2000) 147
105. Garey M.R., and Johnson D.S. Computers and intractability: a guide to the theory of NP-completeness (1979), WH Freeman & Co, New York, NY, USA
106. Karypis G., and Kumar V. METIS: a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices (1998), University of Minnesota Sept
107. Butz A.R. Alternative algorithm for Hilbert's space-filling curve. IEEE Trans Comput 20 (1971) 424
108. Lawder JK. Calculation of mappings between one and n-dimensional values using the Hilbert space-filling curve, 2000.
109. Barrett R. Templates for the solution of linear systems: building blocks for iterative methods (1994), SIAM, Philadelphia
110. Wesseling P. Introduction to multigrid methods (1992), Wiley, New York
111. Briggs W.L., and McCormick S.F. A multigrid tutorial (2000), Society for Industrial and Applied Mathematics, Philadelphia, PA, USA
112. Qian J., and Law C.K. Regimes of coalescence and separation in droplet collision. J Fluid Mech 331 (1997) 59
113. Estrade J.P., Carentz H., Lavergne G., et al. Experimental investigation of dynamic binary collision of ethanol droplets-a model for droplet coalescence and bouncing. Int J Heat Fluid Flow 20 5 (1999) 486
114. Ashgriz N., and Poo J.Y. Coalescence and separation in binary collisions of liquid drops. J Fluid Mech Digit Arch 221 (2006) 183
115. Jiang Y.J., Umemura A., and Law C.K. An experimental investigation on the collision behaviour of hydrocarbon droplets. J Fluid Mech Digit Arch 234 (2006) 171
116. Brenn G., Valkovska D., and Danov K.D. The formation of satellite droplets by unstable binary drop collisions. Phys Fluids 13 9 (2001) 2463
117. Willis K., and Orme M. Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity. Exper Fluids 34 1 (2003) 28
118. Rieber M, Frohn A. Navier-Stokes simulation of droplet collision dynamics. In: 7th international symposium on computational fluid dynamics, Beijing, China; 1997. p. 520.
119. Pan Y., and Suga K. Numerical simulation of binary liquid droplet collision. Phys Fluids 17 8 (2005)
120. Tanguy S., and Berlemont A. Application of a level set method for simulation of droplet collisions. Int J Multiphase Flow 31 9 (2005) 1015
121. Nobari M., and Tryggvason G. Numerical simulations of three-dimensional drop collisions. AIAA J 34 4 (1996) 750
122. Mashayek F., Ashgriz N., Minkowycz W.J., et al. Coalescence collision of liquid drops. Int J Heat Mass Transf 46 1 (2003) 77
123. Wang Z.J. A quadtree-based adaptive Cartesian/Quad grid flow solver for Navier-Stokes equations. Comput Fluids 27 (1998) 529-549