Advertisement

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

  • Marcela Cruchaga
  • Laura Battaglia
  • Mario Storti
  • Jorge D’Elía
Original Paper

Abstract

In this paper we present a summary of numerical methods for solving free surface and two fluid flow problems. We will focus the attention on level set formulations extensively used in the context of the finite element method. In particular, numerical developments to achieve accurate solutions are described. Specific topics of the algorithms, like mass preservation and interface redefinition, are evaluated. To illustrate these aspects, numerical strategies previously developed are applied to the solution of a sloshing and a water column collapse problems. To assess the capabilities of these techniques, the numerical results are compared against each other and with experimental data. Considering these aspects, the present work is aimed to outline some well reported aspects of level set-like formulations.

Notes

Acknowledgments

The authors thank the support given by research projects: Chilean Council for Scientific and Technological Research (CONICYT-FONDECYT 1130278); the Scientific Research Projects Management Department of the Vice Presidency of Research, Development and Innovation (DICYT-VRID) at Universidad de Santiago de Chile; Association of Universities: Montevideo Group (AUGM); Argentinean Council for Scientific Research (CONICET project PIP 112-20111-00978); Argentinean National Agency for Technological and Scientific Promotion (ANPCyT, PICT 2492/2010) and Universidad Nacional del Litoral, Argentina (Projects CAI+D 501-201101-00134, CAI+D 501-201101-00233, CAI+D 501-201101-00495).

References

  1. 1.
    Adalsteinsson D, Sethian JA (1995) A fast level set method for propagating interfaces. J Comput Phys 118(2):269–277. doi: 10.1006/jcph.1995.1098 zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Akin JE, Tezduyar TE, Ungor M (2007) Computation of flow problems with the mixed interface-tracking/interface-capturing technique (MITICT). Comput Fluids 36(1):2–11. doi: 10.1016/j.compfluid.2005.07.008 zbMATHCrossRefGoogle Scholar
  3. 3.
    Akkerman I, Bazilevs Y, Kees C, Farthing M (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230(11):4137–4152. doi: 10.1016/j.jcp.2010.11.044 zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Aliabadi S, Tezduyar TE (2000) Stabilized-finite-element/interface-capturing technique for parallel computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 190(34):243–261. doi: 10.1016/S0045-7825(00)00200-0 zbMATHCrossRefGoogle Scholar
  5. 5.
    Aliabadi S, Johnson A, Zellars B, Abatan A, Berger C (2002) Parallel simulation of flows in open channels. Future Gener Comput Syst 18(5):627–637. doi: 10.1016/S0167-739X(01)00062-0 zbMATHCrossRefGoogle Scholar
  6. 6.
    Aliabadi S, Abedi J, Zellars B (2003) Parallel finite element simulation of mooring forces on floating objects. Int J Numer Methods Fluids 41(8):809–822. doi: 10.1002/fld.459 zbMATHCrossRefGoogle Scholar
  7. 7.
    Amsden AA, Harlow FH (1970) The SMAC method: a numerical technique for calculating incompressible fluid flows. Technical report, Los Alamos National LaboratoryGoogle Scholar
  8. 8.
    Anderson DM, McFadden GB, Wheeler AA (1998) Diffuse-interface methods in fluid mechanics. Ann Rev Fluid Mech 30:139–165. doi: 10.1146/annurev.fluid.30.1.139 MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ashgriz N, Barbat T, Wang G (2004) A computational Lagrangian–Eulerian advection remap for free surface flows. Int J Numer Methods Fluids 44(1):1–32. doi: 10.1002/fld.620 zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Aulisa E, Manservisi S, Scardovelli R (2003) A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows. J Comput Phys 188(2):611–639. doi: 10.1016/S0021-9991(03)00196-7 zbMATHCrossRefGoogle Scholar
  11. 11.
    Aulisa E, Manservisi S, Scardovelli R (2004) A surface marker algorithm coupled to an area-preserving marker redistribution method for three-dimensional interface tracking. J Comput Phys 197(2):555–584. doi: 10.1016/j.jcp.2003.12.009 zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Aulisa E, Manservisi S, Scardovelli R, Zaleski S (2007) Interface reconstruction with least-squares fit and split advection in three-dimensional cartesian geometry. J Comput Phys 225(2):2301–2319. doi: 10.1016/j.jcp.2007.03.015 zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Ausas RF, Sousa FS, Buscaglia GC (2010) An improved finite element space for discontinuous pressures. Comput Methods Appl Mech Eng 199(1720):1019–1031. doi: 10.1016/j.cma.2009.11.011 zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Ausas RF, Dari EA, Buscaglia GC (2011) A geometric mass-preserving redistancing scheme for the level set function. Int J Numer Methods Fluids 65(8):989–1010. doi: 10.1002/fld.2227 zbMATHCrossRefGoogle Scholar
  15. 15.
    Ausas RF, Buscaglia GC, Idelsohn SR (2012) A new enrichment space for the treatment of discontinuous pressures in multi-fluid flows. Int J Numer Methods Fluids 70(7):829–850. doi: 10.1002/fld.2713 MathSciNetCrossRefGoogle Scholar
  16. 16.
    Baer TA, Cairncross RA, Schunk PR, Rao RR, Sackinger PA (2000) A finite element method for free surface flows of incompressible fluids in three dimensions. Part II. Dynamic wetting lines. Int J Numer Methods Fluids 33(3):405–427. doi: 10.1002/1097-0363(20000615)33:3<405:AID-FLD14>3.0.CO;2-4
  17. 17.
    Baiges J, Codina R, Coppola-Owen H (2011) The fixed-mesh ALE approach for the numerical simulation of floating solids. Int J Numer Methods Fluids 67(8):1004–1023. doi: 10.1002/fld.2403 zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Battaglia L, D’Elía J, Storti M, Nigro N (2006) Numerical simulation of transient free surface flows using a moving mesh technique. J Appl Mech 73(6):1017–1025. doi: 10.1115/1.2198246 zbMATHCrossRefGoogle Scholar
  19. 19.
    Battaglia L, Storti MA, D’Elía J (2010) Bounded renormalization with continuous penalization for level set interface-capturing methods. Int J Numer Methods Eng 84(7):830–848. doi: 10.1002/nme.2925 zbMATHCrossRefGoogle Scholar
  20. 20.
    Battaglia L, Storti MA, D’Elía J (2010) Simulation of free-surface flows by a finite element interface capturing technique. Int J Comput Fluid Dyn 24(3–4):121–133. doi: 10.1080/10618562.2010.495695 zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Battaglia L, D’Elía J, Storti M (2012) Simulación numérica de la agitación en tanques de almacenamiento de líquidos mediante una estrategia lagrangiana euleriana arbitraria. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 28(2):124–134. doi: 10.1016/j.rimni.2012.02.001 CrossRefGoogle Scholar
  22. 22.
    Battaglia L, Cruchaga MA, Storti MA, D’Elía J (2014) Simulación de flujos con superficie libre mediante una metodología de captura de interfase. In: Bertolino G, Cantero M, Storti M, Teruel F (eds) Mecánica computacional, vol XXXIII, pp 2161–2174Google Scholar
  23. 23.
    Battaglia L, D’Ela J, Storti MA (2011) Computational fluid dynamics: theory, analysis and applications, chap. Numerical approaches for solving free surface fluid flows. Nova Science Publishers, pp 351–384. ISBN: 978-1-61209-276-8Google Scholar
  24. 24.
    Behr M, Abraham F (2002) Free-surface flow simulations in the presence of inclined walls. Comput Methods Appl Mech Eng 191(47–48):5467–5483. doi: 10.1016/S0045-7825(02)00444-9 zbMATHCrossRefGoogle Scholar
  25. 25.
    Behr M (2004) On the application of slip boundary condition on curved boundaries. Int J Numer Methods Fluids 45(1):43–51. doi: 10.1002/fld.663 zbMATHCrossRefGoogle Scholar
  26. 26.
    Biausser B, Fraunié P, Grilli S, Marcer R (2004) Numerical analysis of the internal kinematics and dynamics of 3-D breaking waves on slopes. Int J Offshore Polar Eng 14(4):247–256Google Scholar
  27. 27.
    Biausser B, Guignard S, Marcer R, Frauni P (2004) 3D two phase flows numerical simulations by SL-VOF method. Int J Numer Methods Fluids 45(6):581–604. doi: 10.1002/fld.708 zbMATHCrossRefGoogle Scholar
  28. 28.
    Bonet J, Lok TS (1999) Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comput Methods Appl Mech Eng 180(1–2):97–115. doi: 10.1016/S0045-7825(99)00051-1 zbMATHMathSciNetCrossRefGoogle Scholar
  29. 29.
    Bonet J, Kulasegaram S, Rodriguez-Paz M, Profit M (2004) Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems. Comput Methods Appl Mech Eng 193(1214):1245–1256. doi: 10.1016/j.cma.2003.12.018 zbMATHCrossRefGoogle Scholar
  30. 30.
    Braess H, Wriggers P (2000) Arbitrary Lagrangian Eulerian finite element analysis of free surface flow. Comput Methods Appl Mech Eng 190(12):95–109. doi: 10.1016/S0045-7825(99)00416-8 zbMATHCrossRefGoogle Scholar
  31. 31.
    Brooks AN, Hughes TJ (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32(13):199–259. doi: 10.1016/0045-7825(82)90071-8 zbMATHMathSciNetCrossRefGoogle Scholar
  32. 32.
    Caboussat A (2005) Numerical simulation of two-phase free surface flows. Arch Comput Methods Eng 12(2):165–224. doi: 10.1007/BF03044518 zbMATHMathSciNetCrossRefGoogle Scholar
  33. 33.
    Caboussat A, Picasso M, Rappaz J (2005) Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J Comput Phys 203(2):626–649. doi: 10.1016/j.jcp.2004.09.009 zbMATHMathSciNetCrossRefGoogle Scholar
  34. 34.
    Caboussat A, Clausen P, Rappaz J (2012) Numerical simulation of two-phase flow with interface tracking by adaptive Eulerian grid subdivision. Math Comput Model 55(3–4):490–504. doi: 10.1016/j.mcm.2011.08.027 zbMATHMathSciNetCrossRefGoogle Scholar
  35. 35.
    Cairncross RA, Schunk PR, Baer TA, Rao RR, Sackinger PA (2000) A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion. Int J Numer Methods Fluids 33(3):375–403. doi: 10.1002/1097-0363(20000615)33:3<375:AID-FLD13>3.0.CO;2-O
  36. 36.
    Carrica PM, Wilson RV, Stern F (2006) Unsteady RANS simulation of the ship forward speed diffraction problem. Comput Fluids 35(6):545–570. doi: 10.1016/j.compfluid.2005.08.001 zbMATHCrossRefGoogle Scholar
  37. 37.
    Carrica PM, Wilson RV, Noack RW, Stern F (2007) Ship motions using single-phase level set with dynamic overset grids. Comput Fluids 36(9):1415–1433. doi: 10.1016/j.compfluid.2007.01.007 zbMATHCrossRefGoogle Scholar
  38. 38.
    Carrica PM, Wilson RV, Stern F (2007) An unsteady single-phase level set method for viscous free surface flows. Int J Numer Methods Fluids 53(2):229–256. doi: 10.1002/fld.1279 zbMATHMathSciNetCrossRefGoogle Scholar
  39. 39.
    Carrica PM, Sadat-Hosseini H, Stern F (2012) CFD analysis of broaching for a model surface combatant with explicit simulation of moving rudders and rotating propellers. Comput Fluids 53:117–132. doi: 10.1016/j.compfluid.2011.10.002 zbMATHCrossRefGoogle Scholar
  40. 40.
    Castiglione T, Stern F, Bova S, Kandasamy M (2011) Numerical investigation of the seakeeping behavior of a catamaran advancing in regular head waves. Ocean Eng 38(16):1806–1822. doi: 10.1016/j.oceaneng.2011.09.003 CrossRefGoogle Scholar
  41. 41.
    Cervone A, Manservisi S, Scardovelli R (2010) Simulation of axisymmetric jets with a finite element Navier–Stokes solver and a multilevel VOF approach. J Comput Phys 229(19):6853–6873. doi: 10.1016/j.jcp.2010.05.025 zbMATHMathSciNetCrossRefGoogle Scholar
  42. 42.
    Cervone A, Manservisi S, Scardovelli R (2011) An optimal constrained approach for divergence-free velocity interpolation and multilevel VOF method. Comput Fluids 47(1):101–114Google Scholar
  43. 43.
    Chessa J, Belytschko T (2003) An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension. Int J Numer Methods Eng 58(13):2041–2064. doi: 10.1002/nme.946 zbMATHMathSciNetCrossRefGoogle Scholar
  44. 44.
    Chessa J, Belytschko T (2003) An extended finite element method for two-phase fluids. J Appl Mech 70(1):10–17. doi: 10.1115/1.1526599 zbMATHMathSciNetCrossRefGoogle Scholar
  45. 45.
    Chippada S, Jue TC, Joo SW, Wheeler MF, Ramaswamy B (1996) Numerical simulation of free-boundary problems. Int J Comput Fluid Dyn 7(1–2):91–118. doi: 10.1080/10618569608940754 zbMATHCrossRefGoogle Scholar
  46. 46.
    Codina R, Soto O (2002) A numerical model to track two-fluid interfaces based on a stabilized finite element method and the level set technique. Int J Numer Methods Fluids 40(1–2):293–301. doi: 10.1002/fld.277 zbMATHCrossRefGoogle Scholar
  47. 47.
    Codina R, Houzeaux G, Coppola-Owen H, Baiges J (2009) The fixed-mesh ALE approach for the numerical approximation of flows in moving domains. J Comput Phys 228(5):1591–1611. doi: 10.1016/j.jcp.2008.11.004 zbMATHMathSciNetCrossRefGoogle Scholar
  48. 48.
    Compère G, Marchandise E, Remacle JF (2008) Transient adaptivity applied to two-phase incompressible flows. J Comput Phys 227(3):1923–1942. doi: 10.1016/j.jcp.2007.10.002 zbMATHMathSciNetCrossRefGoogle Scholar
  49. 49.
    Coppola-Owen AH, Codina R (2005) Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions. Int J Numer Methods Fluids 49(12):1287–1304. doi: 10.1002/fld.963 zbMATHMathSciNetCrossRefGoogle Scholar
  50. 50.
    Coppola-Owen AH, Codina R (2007) A finite element model for free surface flows on fixed meshes. Int J Numer Methods Fluids 54(10):1151–1171. doi: 10.1002/fld.1412 zbMATHMathSciNetCrossRefGoogle Scholar
  51. 51.
    Coppola-Owen H, Codina R (2011) A free surface finite element model for low Froude number mould filling problems on fixed meshes. Int J Numer Methods Fluids 66(7):833–851. doi: 10.1002/fld.2286 zbMATHMathSciNetCrossRefGoogle Scholar
  52. 52.
    Corsini A, Rispoli F, Santoriello A, Tezduyar T (2006) Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. Comput Mech 38(4–5):356–364. doi: 10.1007/s00466-006-0045-x zbMATHMathSciNetCrossRefGoogle Scholar
  53. 53.
    Corsini A, Rispoli F, Sheard A, Tezduyar T (2012) Computational analysis of noise reduction devices in axial fans with stabilized finite element formulations. Comput Mech 50(6):695–705. doi: 10.1007/s00466-012-0789-4 zbMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    Cruchaga M, Oñate E, Idelsohn S (1995) On the pseudomaterial approach for the analysis of transient forming processes. Commun Numer Methods Eng 11(2):137–148. doi: 10.1002/cnm.1640110207 zbMATHCrossRefGoogle Scholar
  55. 55.
    Cruchaga MA, Oñate E (1997) A finite element formulation for incompressible flow problems using a generalized streamline operator. Comput Methods Appl Mech Eng 143(12):49–67. doi: 10.1016/S0045-7825(97)84579-3 zbMATHCrossRefGoogle Scholar
  56. 56.
    Cruchaga MA, Oñate E (1999) A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces. Comput Methods Appl Mech Eng 173(12):241–255. doi: 10.1016/S0045-7825(98)00272-2 zbMATHCrossRefGoogle Scholar
  57. 57.
    Cruchaga M, Celentano D, Tezduyar T (2001) A moving Lagrangian interface technique for flow computations over fixed meshes. Comput Methods Appl Mech Eng 191(67):525–543. doi: 10.1016/S0045-7825(01)00300-0 zbMATHCrossRefGoogle Scholar
  58. 58.
    Cruchaga M, Celentano D, Tezduyar T (2002) Computation of mould filling processes with a moving lagrangian interface technique. Commun Numer Methods Eng 18(7):483–493. doi: 10.1002/cnm.506 zbMATHCrossRefGoogle Scholar
  59. 59.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2005) Moving-interface computations with the edge-tracked interface locator technique (ETILT). Int J Numer Methods Fluids 47(6–7):451–469. doi: 10.1002/fld.825 zbMATHCrossRefGoogle Scholar
  60. 60.
    Cruchaga M, Celentano D, Breitkopf P, Villon P, Rassineux A (2006) A front remeshing technique for a Lagrangian description of moving interfaces in two-fluid flows. Int J Numer Methods Eng 66(13):2035–2063. doi: 10.1002/nme.1616 zbMATHCrossRefGoogle Scholar
  61. 61.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2007) Collapse of a liquid column: numerical simulation and experimental validation. Comput Mech 39(4):453–476. doi: 10.1007/s00466-006-0043-z zbMATHCrossRefGoogle Scholar
  62. 62.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2007) A numerical model based on the mixed interface-tracking/interface-capturing technique (MITICT) for flows with fluidsolid and fluidfluid interfaces. Int J Numer Methods Fluids 54(6–8):1021–1030. doi: 10.1002/fld.1498 zbMATHCrossRefGoogle Scholar
  63. 63.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2009) Computational modeling of the collapse of a liquid column over an obstacle and experimental validation. J Appl Mech Trans ASME 76(2):021202–021206. doi: 10.1115/1.3057439 CrossRefGoogle Scholar
  64. 64.
    Cruchaga M, Celentano D, Breitkopf P, Villon P, Rassineux A (2010) A surface remeshing technique for a Lagrangian description of 3D two-fluid flow problems. Int J Numer Methods Fluids 63(4):415–430. doi: 10.1002/fld.2073 zbMATHGoogle Scholar
  65. 65.
    Cruchaga MA, Reinoso RS, Storti MA, Celentano DJ, Tezduyar TE (2013) Finite element computation and experimental validation of sloshing in rectangular tanks. Comput Mech 52(6):1301–1312. doi: 10.1007/s00466-013-0877-0 zbMATHCrossRefGoogle Scholar
  66. 66.
    Desjardins O, Moureau V, Pitsch H (2008) An accurate conservative level set/ghost fluid method for simulating turbulent atomization. J Comput Phys 227(18):8395–8416. doi: 10.1016/j.jcp.2008.05.027 zbMATHMathSciNetCrossRefGoogle Scholar
  67. 67.
    de Sousa F, Mangiavacchi N, Nonato L, Castelo A, Tomé M, Ferreira V, Cuminato J, McKee S (2004) A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces. J Comput Phys 198(2):469–499. doi: 10.1016/j.jcp.2004.01.032 zbMATHMathSciNetCrossRefGoogle Scholar
  68. 68.
    Dettmer W, Perić D (2006) A computational framework for free surface fluid flows accounting for surface tension. Comput Methods Appl Mech Eng 195(23–24):3038–3071. doi: 10.1016/j.cma.2004.07.057 zbMATHCrossRefGoogle Scholar
  69. 69.
    Di Mascio A, Broglia R, Muscari R (2007) On the application of the single-phase level set method to naval hydrodynamic flows. Comput Fluids 36(5):868–886. doi: 10.1016/j.compfluid.2006.08.001 zbMATHCrossRefGoogle Scholar
  70. 70.
    Di Pietro DA, Lo Forte S, Parolini N (2006) Mass preserving finite element implementations of the level set method. Appl Numer Math 56(9):1179–1195. doi: 10.1016/j.apnum.2006.03.003 zbMATHMathSciNetCrossRefGoogle Scholar
  71. 71.
    Dumbser M (2011) A simple two-phase method for the simulation of complex free surface flows. Comput Methods Appl Mech Eng 200(9–12):1204–1219. doi: 10.1016/j.cma.2010.10.011 zbMATHMathSciNetCrossRefGoogle Scholar
  72. 72.
    Dumbser M (2013) A diffuse interface method for complex three-dimensional free surface flows. Comput Methods Appl Mech Eng 257:47–64. doi: 10.1016/j.cma.2013.01.006 zbMATHMathSciNetCrossRefGoogle Scholar
  73. 73.
    Elgeti S, Sauerland H, Pauli L, Behr M (2012) On the usage of NURBS as interface representation in free-surface flows. Int J Numer Methods Fluids 69(1):73–87. doi: 10.1002/fld.2537 zbMATHMathSciNetCrossRefGoogle Scholar
  74. 74.
    Elias RN, Coutinho ALGA (2007) Stabilized edge-based finite element simulation of free-surface flows. Int J Numer Methods Fluids 54(6–8):965–993. doi: 10.1002/fld.1475 zbMATHMathSciNetCrossRefGoogle Scholar
  75. 75.
    Elias RN, Martins MAD, Coutinho ALGA (2007) Simple finite element-based computation of distance functions in unstructured grids. Int J Numer Methods Eng 72(9):1095–1110. doi: 10.1002/nme.2079 zbMATHMathSciNetCrossRefGoogle Scholar
  76. 76.
    Enright D, Fedkiw R, Ferziger J, Mitchell I (2002) A hybrid particle level set method for improved interface capturing. J Comput Phys 183(1):83–116. doi: 10.1006/jcph.2002.7166 zbMATHMathSciNetCrossRefGoogle Scholar
  77. 77.
    Enright D, Losasso F, Fedkiw R (2005) A fast and accurate semi-Lagrangian particle level set method. Comput Struct 83(67):479–490. doi: 10.1016/j.compstruc.2004.04.024 MathSciNetCrossRefGoogle Scholar
  78. 78.
    Faltinsen OM, Timokha AN (2010) A multimodal method for liquid sloshing in a two-dimensional circular tank. J Fluid Mech 665:457–479. doi: 10.1017/S002211201000412X zbMATHMathSciNetCrossRefGoogle Scholar
  79. 79.
    Farhat C, Geuzaine P (2004) Design and analysis of robust ALE time-integrators for the solution of unsteady flow problems on moving grids. Comput Methods Appl Mech Eng 193(3941):4073–4095. doi: 10.1016/j.cma.2003.09.027 zbMATHMathSciNetCrossRefGoogle Scholar
  80. 80.
    Fedkiw RP, Aslam T, Merriman B, Osher S (1999) A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J Comput Phys 152(2):457–492. doi: 10.1006/jcph.1999.6236 zbMATHMathSciNetCrossRefGoogle Scholar
  81. 81.
    Feldman J, Bonet J (2007) Dynamic refinement and boundary contact forces in sph with applications in fluid flow problems. Int J Numer Methods Eng 72(3):295–324. doi: 10.1002/nme.2010 zbMATHMathSciNetCrossRefGoogle Scholar
  82. 82.
    Feng Y, Perić D (2000) A time-adaptive space-time finite element method for incompressible Lagrangian flows with free surfaces: computational issues. Comput Methods Appl Mech Eng 190(57):499–518. doi: 10.1016/S0045-7825(99)00425-9 zbMATHCrossRefGoogle Scholar
  83. 83.
    Feng YT, Perić D (2003) A spatially adaptive linear space-time finite element solution procedure for incompressible flows with moving domains. Int J Numer Methods Fluids 43(9):1099–1106. doi: 10.1002/fld.546 zbMATHCrossRefGoogle Scholar
  84. 84.
    Fries TP (2009) The intrinsic XFEM for two-fluid flows. Int J Numer Methods Fluids 60(4):437–471. doi: 10.1002/fld.1901 zbMATHMathSciNetCrossRefGoogle Scholar
  85. 85.
    Fuster D, Agbaglah G, Josserand C, Popinet S, Zaleski S (2009) Numerical simulation of droplets, bubbles and waves: state of the art. Fluid Dyn Res 41(6):065,001. doi: 10.1088/0169-5983/41/6/065001 CrossRefGoogle Scholar
  86. 86.
    Galaktionov OS, Anderson PD, Peters GWM, Van de Vosse FN (2000) An adaptive front tracking technique for three-dimensional transient flows. Int J Numer Methods Fluids 32(2):201–217. doi: 10.1002/(SICI)1097-0363(20000130)32:2<201:AID-FLD934>3.0.CO;2-D
  87. 87.
    Ganesan S, Matthies G, Tobiska L (2007) On spurious velocities in incompressible flow problems with interfaces. Comput Methods Appl Mech Eng 196(7):1193–1202. doi: 10.1016/j.cma.2006.08.018 zbMATHMathSciNetCrossRefGoogle Scholar
  88. 88.
    Garcia-Espinosa J, Valls A, Oñate E (2008) ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problems. Int J Numer Methods Eng 76(9):1297–1327. doi: 10.1002/nme.2348 zbMATHCrossRefGoogle Scholar
  89. 89.
    Geuzaine P, Grandmont C, Farhat C (2003) Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations. J Comput Phys 191(1):206–227. doi: 10.1016/S0021-9991(03)00311-5 zbMATHCrossRefGoogle Scholar
  90. 90.
    Gois JP, Nakano A, Nonato LG, Buscaglia GC (2008) Front tracking with moving-least-squares surfaces. J Comput Phys 227(22):9643–9669. doi: 10.1016/j.jcp.2008.07.013 zbMATHMathSciNetCrossRefGoogle Scholar
  91. 91.
    González D, Cueto E, Chinesta F, Doblaré M (2007) A natural element updated Lagrangian strategy for free-surface fluid dynamics. J Comput Phys 223(1):127–150. doi: 10.1016/j.jcp.2006.09.002 zbMATHMathSciNetCrossRefGoogle Scholar
  92. 92.
    Greaves D (2004) Simulation of interface and free surface flows in a viscous fluid using adapting quadtree grids. Int J Numer Methods Fluids 44(10):1093–1117. doi: 10.1002/fld.687 zbMATHCrossRefGoogle Scholar
  93. 93.
    Greaves DM (2006) Simulation of viscous water column collapse using adapting hierarchical grids. Int J Numer Methods Fluids 50(6):693–711. doi: 10.1002/fld.1073 zbMATHMathSciNetCrossRefGoogle Scholar
  94. 94.
    Groß S, Reusken A (2007) An extended pressure finite element space for two-phase incompressible flows with surface tension. J Comput Phys 224(1):40–58. doi: 10.1016/j.jcp.2006.12.021 zbMATHMathSciNetCrossRefGoogle Scholar
  95. 95.
    Gueyffier D, Li J, Nadim A, Scardovelli R, Zaleski S (1999) Volume-of-Fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J Comput Phys 152(2):423–456. doi: 10.1006/jcph.1998.6168 zbMATHCrossRefGoogle Scholar
  96. 96.
    Guignard S, Marcer R, Rey V, Kharif C, Frauni P (2001) Solitary wave breaking on sloping beaches: 2-D two phase flow numerical simulation by SL-VOF method. Eur J Mech B Fluids 20(1):57–74. doi: 10.1016/S0997-7546(00)01104-3 zbMATHMathSciNetCrossRefGoogle Scholar
  97. 97.
    Güler I, Behr M, Tezduyar T (1999) Parallel finite element computation of free-surface flows. Comput Mech 23(2):117–123. doi: 10.1007/s004660050391 zbMATHCrossRefGoogle Scholar
  98. 98.
    Haagh GAAV, Van De Vosse FN (1998) Simulation of three-dimensional polymer mould filling processes using a pseudo-concentration method. Int J Numer Methods Fluids 28(9):1355–1369. doi: 10.1002/(SICI)1097-0363(19981215)28:9<1355:AID-FLD770>3.0.CO;2-C
  99. 99.
    Harlow FH, Welch JE (1965) Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids 8(12):2182–2189. doi: 10.1063/1.1761178 zbMATHCrossRefGoogle Scholar
  100. 100.
    Hartmann D, Meinke M, Schrder W (2010) The constrained reinitialization equation for level set methods. J Comput Phys 229(5):1514–1535. doi: 10.1016/j.jcp.2009.10.042 zbMATHMathSciNetCrossRefGoogle Scholar
  101. 101.
    Hernández J, López J, Gómez P, Zanzi C, Faura F (2008) A new volume of fluid method in three dimensions—Part I: multidimensional advection method with face-matched flux polyhedra. Int J Numer Methods Fluids 58(8):897–921. doi: 10.1002/fld.1776 zbMATHCrossRefGoogle Scholar
  102. 102.
    Herrmann M (2008) A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids. J Comput Phys 227(4):2674–2706. doi: 10.1016/j.jcp.2007.11.002 zbMATHMathSciNetCrossRefGoogle Scholar
  103. 103.
    Hieber SE, Koumoutsakos P (2005) A Lagrangian particle level set method. J Comput Phys 210(1):342–367. doi: 10.1016/j.jcp.2005.04.013 zbMATHMathSciNetCrossRefGoogle Scholar
  104. 104.
    Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225. doi: 10.1016/0021-9991(81)90145-5 zbMATHCrossRefGoogle Scholar
  105. 105.
    Huang J, Carrica PM, Stern F (2007) Coupled ghost fluid/two-phase level set method for curvilinear body-fitted grids. Int J Numer Methods Fluids 55(9):867–897. doi: 10.1002/fld.1499 zbMATHMathSciNetCrossRefGoogle Scholar
  106. 106.
    Huang J, Carrica PM, Stern F (2008) Semi-coupled air/water immersed boundary approach for curvilinear dynamic overset grids with application to ship hydrodynamics. Int J Numer Methods Fluids 58(6):591–624. doi: 10.1002/fld.1758 zbMATHCrossRefGoogle Scholar
  107. 107.
    Huerta A, Liu WK (1988) Viscous flow with large free surface motion. Comput Methods Appl Mech Eng 69(3):277–324. doi: 10.1016/0045-7825(88)90044-8 zbMATHCrossRefGoogle Scholar
  108. 108.
    Hughes TJ, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29(3):329–349. doi: 10.1016/0045-7825(81)90049-9 zbMATHMathSciNetCrossRefGoogle Scholar
  109. 109.
    Hughes T, Tezduyar T (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45(1–3):217–284. doi: 10.1016/0045-7825(84)90157-9 zbMATHMathSciNetCrossRefGoogle Scholar
  110. 110.
    Ianniello S, Mascio AD (2010) A self-adaptive oriented particles level-set method for tracking interfaces. J Comput Phys 229(4):1353–1380. doi: 10.1016/j.jcp.2009.10.034 zbMATHMathSciNetCrossRefGoogle Scholar
  111. 111.
    Idelsohn SR, Storti MA, Oñate E (2001) Lagrangian formulations to solve free surface incompressible inviscid fluid flows. Comput Methods Appl Mech Eng 191(67):583–593. doi: 10.1016/S0045-7825(01)00303-6 zbMATHCrossRefGoogle Scholar
  112. 112.
    Idelsohn S, Oñate E, Del Pin F (2004) The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods Eng 61(7):964–989. doi: 10.1002/nme.1096 zbMATHCrossRefGoogle Scholar
  113. 113.
    Jacobsen NG, Fuhrman DR, Fredse J (2012) A wave generation toolbox for the open-source CFD library: openfoam. Int J Numer Methods Fluids 70(9):1073–1088. doi: 10.1002/fld.2726 CrossRefGoogle Scholar
  114. 114.
    Jahanbakhsh E, Panahi R, Seif M (2007) Numerical simulation of three-dimensional interfacial flows. Int J Numer Methods Heat Fluid Flow 17(4):384–404. doi: 10.1108/09615530710739167 zbMATHMathSciNetCrossRefGoogle Scholar
  115. 115.
    Jeong JH, Yang DY (2004) Finite element analysis of filling stage in die-casting process using marker surface method and adaptive grid refinement technique. Int J Numer Methods Fluids 44(2):209–230. doi: 10.1002/fld.637 zbMATHCrossRefGoogle Scholar
  116. 116.
    Jiang G, Peng D (2000) Weighted ENO schemes for Hamilton–Jacobi equations. SIAM J Sci Comput 21(6):2126–2143. doi: 10.1137/S106482759732455X zbMATHMathSciNetCrossRefGoogle Scholar
  117. 117.
    Johnson A, Tezduyar T (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119(12):73–94. doi: 10.1016/0045-7825(94)00077-8 zbMATHCrossRefGoogle Scholar
  118. 118.
    Kees C, Akkerman I, Farthing M, Bazilevs Y (2011) A conservative level set method suitable for variable-order approximations and unstructured meshes. J Comput Phys 230(12):4536–4558. doi: 10.1016/j.jcp.2011.02.030 zbMATHMathSciNetCrossRefGoogle Scholar
  119. 119.
    Kim MS, Lee WI (2003) A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part I: new free surface-tracking algorithm and its verification. Int J Numer Methods Fluids 42(7):765–790. doi: 10.1002/fld.553 zbMATHCrossRefGoogle Scholar
  120. 120.
    Kim MS, Park JS, Lee WI (2003) A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems. Int J Numer Methods Fluids 42(7):791–812. doi: 10.1002/fld.554 zbMATHMathSciNetCrossRefGoogle Scholar
  121. 121.
    Kleefsman K, Fekken G, Veldman A, Iwanowski B, Buchner B (2005) A volume-of-fluid based simulation method for wave impact problems. J Comput Phys 206(1):363–393. doi: 10.1016/j.jcp.2004.12.007 zbMATHMathSciNetCrossRefGoogle Scholar
  122. 122.
    Kohno H, Tanahashi T (2004) Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement. Int J Numer Methods Fluids 45(9):921–944. doi: 10.1002/fld.715 zbMATHMathSciNetCrossRefGoogle Scholar
  123. 123.
    Koshizuka S, Oka Y (1996) Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng 123:421–434Google Scholar
  124. 124.
    Kurioka S, Dowling DR (2009) Numerical simulation of free surface flows with the level set method using an extremely high-order accuracy WENO advection scheme. Int J Comput Fluid Dyn 23(3):233–243. doi: 10.1080/10618560902776786 zbMATHCrossRefGoogle Scholar
  125. 125.
    Kuzmin D (2014) An optimization-based approach to enforcing mass conservation in level set methods. J Comput Appl Math 258:78–86. doi: 10.1016/j.cam.2013.09.009 zbMATHMathSciNetCrossRefGoogle Scholar
  126. 126.
    Labeur RJ, Wells GN (2009) Interface stabilised finite element method for moving domains and free surface flows. Comput Methods Appl Mech Eng 198(58):615–630. doi: 10.1016/j.cma.2008.09.014 zbMATHCrossRefGoogle Scholar
  127. 127.
    Le Chenadec V, Pitsch H (2013) A 3D unsplit forward/backward volume-of-fluid approach and coupling to the level set method. J Comput Phys 233(1):10–33. doi: 10.1016/j.jcp.2012.07.019 zbMATHMathSciNetCrossRefGoogle Scholar
  128. 128.
    LeVeque R (1996) High-resolution conservative algorithms for advection in incompressible flow. SIAM J Numer Anal 33(2):627–665. doi: 10.1137/0733033 zbMATHMathSciNetCrossRefGoogle Scholar
  129. 129.
    Lewis RW, Usmani AS, Cross J (1995) Efficient mould filling simulation in castings by an explicit finite element method. Int J Numer Methods Fluids 20(6):493–506. doi: 10.1002/fld.1650200606 zbMATHCrossRefGoogle Scholar
  130. 130.
    Lewis RW, Postek EW, Han Z, Gethin DT (2006) A finite element model of the squeeze casting process. Int J Numer Methods Heat Fluid Flow 16(5):539–572. doi: 10.1108/09615530610669102 zbMATHCrossRefGoogle Scholar
  131. 131.
    Lewis R, Ravindran K (2000) Finite element simulation of metal casting. Int J Numer Methods Eng 47(1–3):29–59. doi: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<29:AID-NME760>3.0.CO;2-X
  132. 132.
    Li Z, Jaberi FA, Shih TIP (2008) A hybrid Lagrangian–Eulerian particle-level set method for numerical simulations of two-fluid turbulent flows. Int J Numer Methods Fluids 56(12):2271–2300. doi: 10.1002/fld.1621 zbMATHMathSciNetCrossRefGoogle Scholar
  133. 133.
    Liu M, Liu G (2010) Smoothed particle hydrodynamics (SPH): an overview and recent developments. Arch Comput Methods Eng 17(1):25–76. doi: 10.1007/s11831-010-9040-7 MathSciNetCrossRefGoogle Scholar
  134. 134.
    Löhner R, Yang C, Oñate E (2006) On the simulation of flows with violent free surface motion. Comput Methods Appl Mech Eng 195(41–43):5597–5620. doi: 10.1016/j.cma.2005.11.010 zbMATHCrossRefGoogle Scholar
  135. 135.
    Löhner R, Appanaboyina S, Cebral JR (2008) Comparison of body-fitted, embedded and immersed solutions of low Reynolds-number 3-D incompressible flows. Int J Numer Methods Fluids 57(1):13–30. doi: 10.1002/fld.1604 zbMATHCrossRefGoogle Scholar
  136. 136.
    Löhner R, Baum J, Charman C, Pelessone D (2003) Fluid-structure interaction simulations using parallel computers. In: Palma J, Sousa A, Dongarra J, Hernndez V (eds) High performance computing for computational science VECPAR 2002, Lecture notes in computer science, vol 2565. Springer, Berlin, pp 3–23. doi: 10.1007/3-540-36569-9_1
  137. 137.
    Löhner R, Camelli F, Baum J, Togashi F, Soto O (2001) Advances in FEFLO. In: 51st AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition. American Institute of Aeronautics and Astronautics. doi: 10.2514/6.2013-373
  138. 138.
    López J, Hernández J, Gómez P, Faura F (2004) A volume of fluid method based on multidimensional advection and spline interface reconstruction. J Comput Phys 195(2):718–742. doi: 10.1016/j.jcp.2003.10.030 zbMATHCrossRefGoogle Scholar
  139. 139.
    López J, Hernández J, Gómez P, Faura F (2005) An improved PLIC-VOF method for tracking thin fluid structures in incompressible two-phase flows. J Comput Phys 208(1):51–74. doi: 10.1016/j.jcp.2005.01.031 zbMATHCrossRefGoogle Scholar
  140. 140.
    López EJ, Nigro NM, Storti MA, Toth JA (2007) A minimal element distortion strategy for computational mesh dynamics. Int J Numer Methods Eng 69(9):1898–1929. doi: 10.1002/nme.1838 zbMATHCrossRefGoogle Scholar
  141. 141.
    López EJ, Nigro NM, Storti MA (2008) Simultaneous untangling and smoothing of moving grids. Int J Numer Methods Eng 76(7):994–1019. doi: 10.1002/nme.2347 zbMATHCrossRefGoogle Scholar
  142. 142.
    López J, Zanzi C, Gómez P, Faura F, Hernández J (2008) A new volume of fluid method in three dimensions—Part II: piecewise-planar interface reconstruction with cubic-Bézier fit. Int J Numer Methods Fluids 58(8):923–944. doi: 10.1002/fld.1775 zbMATHCrossRefGoogle Scholar
  143. 143.
    Losasso F, Gibou F, Fedkiw R (2004) Simulating water and smoke with an octree data structure. ACM Trans Graph 23(3):457–462. doi: 10.1145/1015706.1015745 CrossRefGoogle Scholar
  144. 144.
    Losasso F, Fedkiw R, Osher S (2006) Spatially adaptive techniques for level set methods and incompressible flow. Comput Fluids 35(10):995–1010. doi: 10.1016/j.compfluid.2005.01.006
  145. 145.
    Marchandise E, Remacle JF (2006) A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows. J Comput Phys 219(2):780–800. doi: 10.1016/j.jcp.2006.04.015 zbMATHMathSciNetCrossRefGoogle Scholar
  146. 146.
    Marchandise E, Remacle JF, Chevaugeon N (2006) A quadrature-free discontinuous Galerkin method for the level set equation. J Comput Phys 212(1):338–357. doi: 10.1016/j.jcp.2005.07.006 zbMATHMathSciNetCrossRefGoogle Scholar
  147. 147.
    Maronnier V, Picasso M, Rappaz J (1999) Numerical simulation of free surface flows. J Comput Phys 155(2):439–455. doi: 10.1006/jcph.1999.6346 zbMATHMathSciNetCrossRefGoogle Scholar
  148. 148.
    Maronnier V, Picasso M, Rappaz J (2003) Numerical simulation of three-dimensional free surface flows. Int J Numer Methods Fluids 42(7):697–716. doi: 10.1002/fld.532 zbMATHMathSciNetCrossRefGoogle Scholar
  149. 149.
    Martin JC, Moyce WJ (1952) Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos Trans R Soc Lond Ser A Math Phys Sci 244(882):312–324. doi: 10.1098/rsta.1952.0006 MathSciNetCrossRefGoogle Scholar
  150. 150.
    Mashayek F, Ashgriz N (1995) A hybrid finite-element—volume-of-fluid method for simulating free surface flows and interfaces. Int J Numer Methods Fluids 20(12):1363–1380. doi: 10.1002/fld.1650201205 zbMATHMathSciNetCrossRefGoogle Scholar
  151. 151.
    Mashayek F, Ashgriz N (1995) A spine-flux method for simulating free surface flows. J Comput Phys 122(2):367–379. doi: 10.1006/jcph.1995.1222 zbMATHCrossRefGoogle Scholar
  152. 152.
    Masud A, Hughes TJ (1997) A space-time Galerkin/least-squares finite element formulation of the Navier–Stokes equations for moving domain problems. Comput Methods Appl Mech Eng 146(12):91–126. doi: 10.1016/S0045-7825(96)01222-4 zbMATHMathSciNetCrossRefGoogle Scholar
  153. 153.
    McKee S, Tomé M, Ferreira V, Cuminato J, Castelo A, Sousa F, Mangiavacchi N (2008) The MAC method. Comput Fluids 37(8):907–930. doi: 10.1016/j.compfluid.2007.10.006 zbMATHMathSciNetCrossRefGoogle Scholar
  154. 154.
    Minev P, Chen T, Nandakumar K (2003) A finite element technique for multifluid incompressible flow using Eulerian grids. J Comput Phys 187(1):255–273. doi: 10.1016/S0021-9991(03)00098-6 zbMATHMathSciNetCrossRefGoogle Scholar
  155. 155.
    Mompean G, Thais L, Tomé M, Castelo A (2011) Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models. Comput Fluids 44(1):68–78. doi: 10.1016/j.compfluid.2010.12.010 zbMATHMathSciNetCrossRefGoogle Scholar
  156. 156.
    Mut F, Buscaglia GC, Dari EA (2006) New mass-conserving algorithm for level set redistancing on unstructured meshes. ASME J Appl Mech 73(6):1011–1016. doi: 10.1115/1.2198244 zbMATHMathSciNetCrossRefGoogle Scholar
  157. 157.
    Navti S, Lewis R, Taylor C (1998) Numerical simulation of viscous free surface flow. Int J Numer Methods Heat Fluid Flow 8(4):445–464. doi: 10.1108/09615539810213223 zbMATHCrossRefGoogle Scholar
  158. 158.
    Nithiarasu P (2005) An arbitrary Lagrangian Eulerian (ALE) formulation for free surface flows using the characteristic-based split (CBS) scheme. Int J Numer Methods Fluids 48(12):1415–1428. doi: 10.1002/fld.987 zbMATHMathSciNetCrossRefGoogle Scholar
  159. 159.
    Olsson E, Kreiss G (2005) A conservative level set method for two phase flow. J Comput Phys 210(1):225–246. doi: 10.1016/j.jcp.2005.04.007 zbMATHMathSciNetCrossRefGoogle Scholar
  160. 160.
    Olsson E, Kreiss G, Zahedi S (2007) A conservative level set method for two phase flow II. J Comput Phys 225(1):785–807. doi: 10.1016/j.jcp.2006.12.027 zbMATHMathSciNetCrossRefGoogle Scholar
  161. 161.
    Oñate E, García J (2001) A finite element method for fluidstructure interaction with surface waves using a finite calculus formulation. Comput Methods Appl Mech Eng 191(67):635–660. doi: 10.1016/S0045-7825(01)00306-1 zbMATHCrossRefGoogle Scholar
  162. 162.
    Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys 79(1):12–49. doi: 10.1016/0021-9991(88)90002-2 zbMATHMathSciNetCrossRefGoogle Scholar
  163. 163.
    Osher S, Fedkiw RP (2001) Level set methods: an overview and some recent results. J Comput Phys 169(2):463–502. doi: 10.1006/jcph.2000.6636 zbMATHMathSciNetCrossRefGoogle Scholar
  164. 164.
    Owkes M, Desjardins O (2013) A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows. J Comput Phys 249:275–302. doi: 10.1016/j.jcp.2013.04.036 zbMATHMathSciNetCrossRefGoogle Scholar
  165. 165.
    Park IR, Kim KS, Kim J, Van SH (2009) A volume-of-fluid method for incompressible free surface flows. Int J Numer Meth Fluids 61(12):1331–1362. doi: 10.1002/fld.2000 zbMATHMathSciNetCrossRefGoogle Scholar
  166. 166.
    Parolini N, Quarteroni A (2005) Mathematical models and numerical simulations for the Americas Cup. Comput Methods Appl Mech Eng 194(9–11):1001–1026. doi: 10.1016/j.cma.2004.06.020 zbMATHMathSciNetCrossRefGoogle Scholar
  167. 167.
    Pilliod JEJ, Puckett EG (2004) Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J Comput Phys 199(2):465–502. doi: 10.1016/j.jcp.2003.12.023 zbMATHMathSciNetCrossRefGoogle Scholar
  168. 168.
    Quecedo M, Pastor M, Herreros M, Merodo JF, Zhang Q (2005) Comparison of two mathematical models for solving the dam break problem using the FEM method. Comput Methods Appl Mech Eng 194(3638):3984–4005. doi: 10.1016/j.cma.2004.09.011 zbMATHCrossRefGoogle Scholar
  169. 169.
    Quecedo M, Pastor M (2001) Application of the level set method to the finite element solution of two-phase flows. Int J Numer Methods Eng 50(3):645–663. doi: 10.1002/1097-0207(20010130)50:3<645:AID-NME42>3.0.CO;2-2
  170. 170.
    Raad PE, Bidoae R (2005) The three-dimensional Eulerian–Lagrangian marker and micro cell method for the simulation of free surface flows. J Comput Phys 203(2):668–699. doi: 10.1016/j.jcp.2004.09.013 zbMATHCrossRefGoogle Scholar
  171. 171.
    Rabier S, Medale M (2003) Computation of free surface flows with a projection FEM in a moving mesh framework. Comput Methods Appl Mech Eng 192(4142):4703–4721. doi: 10.1016/S0045-7825(03)00456-0 zbMATHMathSciNetCrossRefGoogle Scholar
  172. 172.
    Radovitzky R, Ortiz M (1998) Lagrangian finite element analysis of Newtonian fluid flows. Int J Numer Methods Eng 43(4):607–619. doi: 10.1002/(SICI)1097-0207(19981030)43:4<607:AID-NME399>3.0.CO;2-N
  173. 173.
    Raessi M, Pitsch H (2012) Consistent mass and momentum transport for simulating incompressible interfacial flows with large density ratios using the level set method. Comput Fluids 63:70–81. doi: 10.1016/j.compfluid.2012.04.002 MathSciNetCrossRefGoogle Scholar
  174. 174.
    Rafiee A, Pistani F, Thiagarajan K (2011) Study of liquid sloshing: numerical and experimental approach. Comput Mech 47(1):65–75. doi: 10.1007/s00466-010-0529-6 zbMATHMathSciNetCrossRefGoogle Scholar
  175. 175.
    Ramaswamy B, Kawahara M (1987) Lagrangian finite element analysis applied to viscous free surface fluid flow. Int J Numer Methods Fluids 7(9):953–984. doi: 10.1002/fld.1650070906 zbMATHCrossRefGoogle Scholar
  176. 176.
    Ramshaw JD, Trapp JA (1976) A numerical technique for low-speed homogeneous two-phase flow with sharp interfaces. J Comput Phys 21(4):438–453. doi: 10.1016/0021-9991(76)90039-5 zbMATHMathSciNetCrossRefGoogle Scholar
  177. 177.
    Ravindran K, Lewis R (1998) Finite element modelling of solidification effects in mould filling. Finite Elem Anal Des 31(2):99–116. doi: 10.1016/S0168-874X(98)00053-5 zbMATHCrossRefGoogle Scholar
  178. 178.
    Ray B, Biswas G, Sharma A, Welch SW (2013) Clsvof method to study consecutive drop impact on liquid pool. Int J Numer Methods Heat Fluid Flow 23(1):143–158. doi: 10.1108/09615531311289150 MathSciNetCrossRefGoogle Scholar
  179. 179.
    Rider WJ, Kothe DB (1998) Reconstructing volume tracking. J Comput Phys 141(2):112–152. doi: 10.1006/jcph.1998.5906 zbMATHMathSciNetCrossRefGoogle Scholar
  180. 180.
    Rispoli F, Corsini A, Tezduyar TE (2007) Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD). Comput Fluids 36(1):121–126. doi: 10.1016/j.compfluid.2005.07.004 zbMATHCrossRefGoogle Scholar
  181. 181.
    Rouy E, Tourin A (1992) A viscosity solutions approach to shape-from-shading. SIAM J Numer Anal 29(3):867–884. doi: 10.1137/0729053 zbMATHMathSciNetCrossRefGoogle Scholar
  182. 182.
    Saito H, Scriven L (1981) Study of coating flow by the finite element method. J Comput Phys 42(1):53–76. doi: 10.1016/0021-9991(81)90232-1 zbMATHCrossRefGoogle Scholar
  183. 183.
    Sauerland H, Fries TP (2011) The extended finite element method for two-phase and free-surface flows: a systematic study. J Comput Phys 230(9):3369–3390. doi: 10.1016/j.jcp.2011.01.033 zbMATHMathSciNetCrossRefGoogle Scholar
  184. 184.
    Sauerland H, Fries TP (2012) The stable XFEM for two-phase flows. Comput Fluids 87:41–49. doi: 10.1016/j.compfluid.2012.10.017 MathSciNetCrossRefGoogle Scholar
  185. 185.
    Scardovelli R, Zaleski S (1999) Direct numerical simulation of free-surface and interfacial flow. Annu Rev Fluid Mech 31(1):567–603. doi: 10.1146/annurev.fluid.31.1.567 MathSciNetCrossRefGoogle Scholar
  186. 186.
    Scardovelli R, Zaleski S (2003) Interface reconstruction with least-square fit and split Eulerian–Lagrangian advection. Int J Numer Methods Fluids 41(3):251–274. doi: 10.1002/fld.431 zbMATHCrossRefGoogle Scholar
  187. 187.
    Sethian JA (1996) A fast marching level set method for monotonically advancing fronts. Proc Natl Acad Sci USA 93:1591–1595Google Scholar
  188. 188.
    Sethian J (2001) Evolution, implementation, and application of level set and fast marching methods for advancing fronts. J Comput Phys 169(2):503–555. doi: 10.1006/jcph.2000.6657 zbMATHMathSciNetCrossRefGoogle Scholar
  189. 189.
    Sethian JA, Smereka P (2003) Level set methods for fluid interfaces. Annu Rev Fluid Mech 35:341–372. doi: 10.1146/annurev.fluid.35.101101.161105 MathSciNetCrossRefGoogle Scholar
  190. 190.
    Sheu TW, Yu C, Chiu P (2009) Development of a dispersively accurate conservative level set scheme for capturing interface in two-phase flows. J Comput Phys 228(3):661–686. doi: 10.1016/j.jcp.2008.09.032 zbMATHMathSciNetCrossRefGoogle Scholar
  191. 191.
    Shin S, Juric D (2009) A hybrid interface method for three-dimensional multiphase flows based on front tracking and level set techniques. Int J Numer Methods Fluids 60(7):753–778. doi: 10.1002/fld.1912 zbMATHCrossRefGoogle Scholar
  192. 192.
    Shu CW, Osher S (1988) Efficient implementation of essentially non-oscillatory shock-capturing schemes. J Comput Phys 77(2):439–471. doi: 10.1016/0021-9991(88)90177-5 zbMATHMathSciNetCrossRefGoogle Scholar
  193. 193.
    Shu CW, Osher S (1989) Efficient implementation of essentially non-oscillatory shock-capturing schemes. II. J Comput Phys 83(1):32–78. doi: 10.1016/0021-9991(89)90222-2 zbMATHMathSciNetCrossRefGoogle Scholar
  194. 194.
    Soulaïmani A, Fortin M, Dhatt G, Ouellet Y (1991) Finite element simulation of two- and three-dimensional free surface flows. Comput Methods Appl Mech Eng 86(3):265–296. doi: 10.1016/0045-7825(91)90224-T zbMATHCrossRefGoogle Scholar
  195. 195.
    Soulaïmani A, Saad Y (1998) An arbitrary Lagrangian–Eulerian finite element method for solving three-dimensional free surface flows. Comput Methods Appl Mech Eng 162(14):79–106. doi: 10.1016/S0045-7825(97)00330-7 zbMATHCrossRefGoogle Scholar
  196. 196.
    Souli M, Zolesio J (2001) Arbitrary Lagrangian–Eulerian and free surface methods in fluid mechanics. Comput Methods Appl Mech Eng 191(35):451–466. doi: 10.1016/S0045-7825(01)00313-9 zbMATHCrossRefGoogle Scholar
  197. 197.
    Strain J (1999) Fast tree-based redistancing for level set computations. J Comput Phys 152(2):664–686. doi: 10.1006/jcph.1999.6259 zbMATHMathSciNetCrossRefGoogle Scholar
  198. 198.
    Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114(1):146–159. doi: 10.1006/jcph.1994.1155 zbMATHCrossRefGoogle Scholar
  199. 199.
    Sussman M, Smereka P (1997) Axisymmetric free boundary problems. J Fluid Mech 341:269–294. doi: 10.1017/S0022112097005570 zbMATHMathSciNetCrossRefGoogle Scholar
  200. 200.
    Sussman M, Fatemi E, Smereka P, Osher S (1998) An improved level set method for incompressible two-phase flows. Comput Fluids 27(56):663–680. doi: 10.1016/S0045-7930(97)00053-4 zbMATHCrossRefGoogle Scholar
  201. 201.
    Sussman M, Almgren AS, Bell JB, Colella P, Howell LH, Welcome ML (1999) An adaptive level set approach for incompressible two-phase flows. J Comput Phys 148(1):81–124. doi: 10.1006/jcph.1998.6106 zbMATHMathSciNetCrossRefGoogle Scholar
  202. 202.
    Sussman M, Fatemi E (1999) An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J Sci Comput 20(4):1165–1191. doi: 10.1137/S1064827596298245 zbMATHMathSciNetCrossRefGoogle Scholar
  203. 203.
    Sussman M, Puckett EG (2000) A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J Comput Phys 162(2):301–337. doi: 10.1006/jcph.2000.6537 zbMATHMathSciNetCrossRefGoogle Scholar
  204. 204.
    Sussman M (2003) A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. J Comput Phys 187(1):110–136. doi: 10.1016/S0021-9991(03)00087-1 zbMATHMathSciNetCrossRefGoogle Scholar
  205. 205.
    Sussman M (2005) A parallelized, adaptive algorithm for multiphase flows in general geometries. Comput Struct 83(6–7):435–444. doi: 10.1016/j.compstruc.2004.06.006 CrossRefGoogle Scholar
  206. 206.
    Sussman M, Smith K, Hussaini M, Ohta M, Zhi-Wei R (2007) A sharp interface method for incompressible two-phase flows. J Comput Phys 221(2):469–505. doi: 10.1016/j.jcp.2006.06.020 zbMATHMathSciNetCrossRefGoogle Scholar
  207. 207.
    Tezduyar T, Park Y (1986) Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59(3):307–325. doi: 10.1016/0045-7825(86)90003-4 zbMATHCrossRefGoogle Scholar
  208. 208.
    Tezduyar T (1991) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44. doi: 10.1016/S0065-2156(08)70153-4
  209. 209.
    Tezduyar T, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94(3):339–351. doi: 10.1016/0045-7825(92)90059-S
  210. 210.
    Tezduyar T, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94(3):353–371. doi: 10.1016/0045-7825(92)90060-W zbMATHMathSciNetCrossRefGoogle Scholar
  211. 211.
    Tezduyar T, Mittal S, Ray S, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95(2):221–242. doi: 10.1016/0045-7825(92)90141-6
  212. 212.
    Tezduyar T, Aliabadi S, Behr M (1998) Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 155(3–4):235–248. doi: 10.1016/S0045-7825(97)00194-1 zbMATHCrossRefGoogle Scholar
  213. 213.
    Tezduyar TE, Aliabadi S (2000) EDICT for 3D computation of two-fluid interfaces. Comput Methods Appl Mech Eng 190(34):403–410. doi: 10.1016/S0045-7825(00)00210-3 zbMATHCrossRefGoogle Scholar
  214. 214.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8(2):83–130. doi: 10.1007/BF02897870 zbMATHMathSciNetCrossRefGoogle Scholar
  215. 215.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43(5):555–575. doi: 10.1002/fld.505 zbMATHMathSciNetCrossRefGoogle Scholar
  216. 216.
    Tezduyar TE (2006) Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces. Comput Methods Appl Mech Eng 195(23–24):2983–3000. doi: 10.1016/j.cma.2004.09.018 zbMATHMathSciNetCrossRefGoogle Scholar
  217. 217.
    Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36(2):191–206. doi: 10.1016/j.compfluid.2005.02.011 zbMATHMathSciNetCrossRefGoogle Scholar
  218. 218.
    Thompson E (1986) Use of pseudo-concentrations to follow creeping viscous flows during transient analysis. Int J Numer Methods Fluids 6(10):749–761. doi: 10.1002/fld.1650061005 CrossRefGoogle Scholar
  219. 219.
    Tomé M, Filho A, Cuminato J, Mangiavacchi N, Mckee S (2001) GENSMAC3D: a numerical method for solving unsteady three-dimensional free surface flows. Int J Numer Methods Fluids 37(7):747–796. doi: 10.1002/fld.148 zbMATHCrossRefGoogle Scholar
  220. 220.
    Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys 100(1):25–37. doi: 10.1016/0021-9991(92)90307-K zbMATHCrossRefGoogle Scholar
  221. 221.
    van der Pijl SP, Segal A, Vuik C, Wesseling P (2005) A mass-conserving level-set method for modelling of multi-phase flows. Int J Numer Methods Fluids 47(4):339–361. doi: 10.1002/fld.817 zbMATHCrossRefGoogle Scholar
  222. 222.
    Vartdal M, Bøckmann A (2013) An oriented particle level set method based on surface coordinates. J Comput Phys 251:237–250. doi: 10.1016/j.jcp.2013.05.044 MathSciNetCrossRefGoogle Scholar
  223. 223.
    Wackers J, Koren B, Raven H, Ploeg A, Starke A, Deng G, Queutey P, Visonneau M, Hino T, Ohashi K (2011) Free-surface viscous flow solution methods for ship hydrodynamics. Arch Comput Methods Eng 18(1):1–41. doi: 10.1007/s11831-011-9059-4 zbMATHMathSciNetCrossRefGoogle Scholar
  224. 224.
    Wall WA, Genkinger S, Ramm E (2007) A strong coupling partitioned approach for fluid-structure interaction with free surfaces. Comput Fluids 36(1):169–183. doi: 10.1016/j.compfluid.2005.08.007 zbMATHCrossRefGoogle Scholar
  225. 225.
    Wan T, Aliabadi S, Bigler C (2009) A hybrid scheme based on finite element/volume methods for two immiscible fluid flows. Int J Numer Methods Fluids 61(8):930–944. doi: 10.1002/fld.1997 zbMATHMathSciNetCrossRefGoogle Scholar
  226. 226.
    Wang CY, Teng Jt, Huang GP (2011) Numerical simulation of sloshing motion inside a two dimensional rectangular tank by level set method. Int J Numer Methods Heat Fluid Flow 21(1):5–31. doi: 10.1108/09615531111095049 zbMATHCrossRefGoogle Scholar
  227. 227.
    Wilson RV, Carrica PM, Stern F (2007) Simulation of ship breaking bow waves and induced vortices and scars. Int J Numer Methods Fluids 54(4):419–451. doi: 10.1002/fld.1406
  228. 228.
    Wörner M (2012) Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications. Microfluid Nanofluid 12(6):841–886. doi: 10.1007/s10404-012-0940-8
  229. 229.
    Xu Z, Accorsi M (2004) Finite element mesh update methods for fluid-structure interaction simulations. Finite Elem Anal Des 40(9–10):1259–1269. doi: 10.1016/j.finel.2003.05.001 CrossRefGoogle Scholar
  230. 230.
    Yang X, James AJ (2006) Analytic relations for reconstructing piecewise linear interfaces in triangular and tetrahedral grids. J Comput Phys 214(1):41–54. doi: 10.1016/j.jcp.2005.09.002 zbMATHMathSciNetCrossRefGoogle Scholar
  231. 231.
    Yang X, James AJ, Lowengrub J, Zheng X, Cristini V (2006) An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. J Comput Phys 217(2):364–394. doi: 10.1016/j.jcp.2006.01.007 zbMATHMathSciNetCrossRefGoogle Scholar
  232. 232.
    Yang J, Stern F (2009) Sharp interface immersed-boundary/level-set method for wave-body interactions. J Comput Phys 228(17):6590–6616. doi: 10.1016/j.jcp.2009.05.047 zbMATHMathSciNetCrossRefGoogle Scholar
  233. 233.
    Zahedi S, Kronbichler M, Kreiss G (2012) Spurious currents in finite element based level set methods for two-phase flow. Int J Numer Methods Fluids 69(9):1433–1456. doi: 10.1002/fld.2643 zbMATHMathSciNetCrossRefGoogle Scholar
  234. 234.
    Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31(3):335–362. doi: 10.1016/0021-9991(79)90051-2 zbMATHMathSciNetCrossRefGoogle Scholar
  235. 235.
    Zhang Y, Zou Q, Greaves D (2010) Numerical simulation of free-surface flow using the level-set method with global mass correction. Int J Numer Methods Fluids 63(6):651–680. doi: 10.1002/fld.2090 zbMATHMathSciNetGoogle Scholar
  236. 236.
    Zhao L, Mao J, Bai X, Liu X, Li T, Williams J (2014) Finite element implementation of an improved conservative level set method for two-phase flow. Comput Fluids 100:138–154. doi: 10.1016/j.compfluid.2014.04.027 MathSciNetCrossRefGoogle Scholar
  237. 237.
    Zhou H, Li JF, Wang TS (2008) Simulation of liquid sloshing in curved-wall containers with arbitrary Lagrangian–Eulerian method. Int J Numer Methods Fluids 57(4):437–452. doi: 10.1002/fld.1602 zbMATHMathSciNetCrossRefGoogle Scholar
  238. 238.
    Zienkiewicz OC, Codina R (1995) A general algorithm for compressible and incompressible flow—Part I. The split, characteristic-based scheme. Int J Numer Methods Fluids 20(8–9):869–885. doi: 10.1002/fld.1650200812 zbMATHMathSciNetCrossRefGoogle Scholar
  239. 239.
    Zienkiewicz O, Nithiarasu P, Codina R, Vázquez M, Ortiz P (1999) The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problems. Int J Numer Methods Fluids 31(1):359–392. doi: 10.1002/(SICI)1097-0363(19990915)31:1<359:AID-FLD984>3.0.CO;2-7

Copyright information

© CIMNE, Barcelona, Spain 2014

Authors and Affiliations

  • Marcela Cruchaga
    • 1
  • Laura Battaglia
    • 2
    • 3
  • Mario Storti
    • 2
    • 4
  • Jorge D’Elía
    • 2
    • 4
  1. 1.Universidad de Santiago de Chile (USACH)SantiagoChile
  2. 2.Centro de Investigación de Métodos Computacionales CIMEC CONICET and UN LitoralSanta FeArgentina
  3. 3.Facultad Regional Santa Fe (FRSF) U Tecnológica NacionalSanta FeArgentina
  4. 4.Facultad de Ingeniería y Ciencias Hídricas FICH UN LitoralSanta FeArgentina

Personalised recommendations