1932

Abstract

Numerical simulations are extensively used to investigate the motion of suspended particles in a fluid and their influence on the dynamics of the overall flow. Contexts range from the rheology of concentrated suspensions in a viscous fluid to the dynamics of particle-laden turbulent flows. This review summarizes several current approaches to the numerical simulation of rigid particles suspended in a flow, pointing out both common features and differences, along with their primary range of application. The focus is on non-Brownian systems for which thermal fluctuations do not play a role, whereas interparticle forces may result in particle self-assembly. Applications may include the motion of a few isolated particles with complex shape or the collective dynamics of many suspended particles.

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2017-01-03
2024-03-28
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Literature Cited

  1. Abbas M, Magaud P, Gao Y, Geoffroy S. 2014. Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers. Phys. Fluids 26:123301 [Google Scholar]
  2. Adami S, Hu X, Adams N. 2013. A transport-velocity formulation for smoothed particle hydrodynamics. J. Comput. Phys. 241:292–307 [Google Scholar]
  3. Aidun C, Clausen J. 2010. Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42:439–72 [Google Scholar]
  4. Apte SV, Martin M, Patankar NA. 2009. A numerical method for fully resolved simulation (FRS) of rigid particle-flow interactions in complex flows. J. Comput. Phys. 228:2712–38 [Google Scholar]
  5. Ardekani AM, Dabiri S, Rangel RH. 2008. Collision of multi-particle and general shape objects in a viscous fluid. J. Comput. Phys. 227:10094–107 [Google Scholar]
  6. Ardekani AM, Rangel RH. 2008. Numerical investigation of particle-particle and particle-wall collisions in a viscous fluid. J. Fluid Mech. 596:437–66 [Google Scholar]
  7. Asmolov ES. 1999. The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J. Fluid Mech. 381:63–87 [Google Scholar]
  8. Baek H, Karniadakis GE. 2012. A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping. J. Comput. Phys. 231:629–52 [Google Scholar]
  9. Balachandar S. 2009. Structured grid methods for solid particles. See Prosperetti & Tryggvason 78–112
  10. Balachandar S, Eaton JK. 2010. Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42:111–33 [Google Scholar]
  11. Batchelor G, Green J. 1972. The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56:375–400 [Google Scholar]
  12. Bhattacharya S, Bławzdziewicz J, Wajnryb E. 2005. Hydrodynamic interactions of spherical particles in suspensions confined between two planar walls. J. Fluid Mech. 541:263–92 [Google Scholar]
  13. Bian X, Ellero M. 2014. A splitting integration scheme for the SPH simulation of concentrated particle suspensions. Comput. Phys. Commun. 185:53–62 [Google Scholar]
  14. Bian X, Litvinov S, Ellero M, Wagner N. 2014. Hydrodynamic shear thickening of particulate suspension under confinement. J. Non-Newton. Fluid Mech. 213:39–49 [Google Scholar]
  15. Blanc F, Peters F, Lemaire E. 2011. Experimental signature of the pair trajectories of rough spheres in the shear-induced microstructure in noncolloidal suspensions. Phys. Rev. Lett. 107:208302 [Google Scholar]
  16. Bossis G, Brady J. 1984. Dynamic simulation of sheared suspensions. I. General method. J. Chem. Phys. 80:5141–54 [Google Scholar]
  17. Botto L, Prosperetti A. 2012. A fully resolved numerical simulation of turbulent flow past one or several spherical particles. Phys. Fluids 24:013303 [Google Scholar]
  18. Brady J. 2001. Computer simulation of viscous suspensions. Chem. Eng. Sci. 56:2921–26 [Google Scholar]
  19. Brady J, Bossis G. 1988. Stokesian dynamics. Annu. Rev. Fluid Mech. 20:111–57 [Google Scholar]
  20. Breugem WP. 2012. A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows. J. Comput. Phys. 231:4469–98 [Google Scholar]
  21. Burton T, Eaton J. 2005. Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545:67–111 [Google Scholar]
  22. Cortez R. 2001. The method of regularized Stokeslets. SIAM J. Sci. Comput. 23:1204–25 [Google Scholar]
  23. Cortez R, Fauci L, Medovikov A. 2005. The method of regularized Stokeslets in three dimensions: analysis, validation, and application to helical swimming. Phys. Fluids 17:031504 [Google Scholar]
  24. Cortez R, Varela D. 2015. A general system of images for regularized Stokeslets and other elements near a plane wall. J. Comput. Phys. 285:41–54 [Google Scholar]
  25. Dance S, Maxey M. 2003. Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow. J. Comput. Phys. 189:212–38 [Google Scholar]
  26. d'Humières D, Ginzburg I, Krafczyk M, Lallemand L, Luo LS. 2002. Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos. Trans. R. Soc. Lond. A 360:437–51 [Google Scholar]
  27. Di Carlo D. 2009. Inertial microfluidics. Lab Chip 9:3038–46 [Google Scholar]
  28. Dong S, Liu D, Maxey MR, Karniadakis GE. 2004. Spectral distributed Lagrange multiplier method: algorithm and benchmark tests. J. Comput. Phys. 195:695–717 [Google Scholar]
  29. Durlofsky L, Brady JF, Bossis G. 1987. Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180:21–49 [Google Scholar]
  30. Ekiel-Jeżewska ML, Wajnryb E, Bławzdziewicz J, Feuillebois F. 2008. Lubrication approximation for microparticles moving along parallel walls. J. Chem. Phys. 129:181102 [Google Scholar]
  31. Elghobashi S, Prosperetti A. 2009. Preface. Int. J. Multiphase Flow 35:791 [Google Scholar]
  32. Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J. 2000. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161:35–60 [Google Scholar]
  33. Feng ZG, Michaelides E. 2005. Proteus: a direct forcing method in the simulations of particulate flows. J. Comput. Phys. 202:20–51 [Google Scholar]
  34. Feuillebois F, Ekiel-Jeżewska ML, Wajnryb E, Sellier A, Bławzdziewiez J. 2015. High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls. J. Fluid Mech. 764:133–47 [Google Scholar]
  35. Gallier S, Lemaire E, Lobry L, Peters F. 2014a. A fictitious domain approach for the simulation of dense suspensions. J. Comput. Phys. 256:367–87 [Google Scholar]
  36. Gallier S, Lemaire E, Peters F, Lobry L. 2014b. Rheology of sheared suspensions of rough frictional particles. J. Fluid Mech. 757:514–49 [Google Scholar]
  37. Gao C, Xu B, Gilchrist JF. 2009. Mixing and segregation of microspheres in microchannel flows of mono- and bidispersed suspensions. Phys. Rev. E 79:036311 [Google Scholar]
  38. Gatignol R. 1983. The Faxén formulas for a rigid particle in an unsteady non-uniform Stokes flow. J. Méc. Théor. Appl. 2:143–60 [Google Scholar]
  39. Glowinski R, Pan TW, Hesla TI, Joseph DD. 1999. A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow 25:755–94 [Google Scholar]
  40. Gonzalez O. 2009. On stable, complete, and singularity-free boundary integral formulations of exterior Stokes flow. SIAM J. Appl. Math. 69:933–58 [Google Scholar]
  41. Grabowski WW, Wang LP. 2013. Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45:293–324 [Google Scholar]
  42. Guasto JS, Ross AS, Gollub JP. 2010. Hydrodynamic irreversibility in particle suspensions with nonuniform strain. Phys. Rev. E 81:061401 [Google Scholar]
  43. Guazzelli E, Morris J. 2012. A Physical Introduction to Suspension Dynamics Cambridge, UK: Cambridge Univ. Press
  44. Gundmundsson K, Prosperetti A. 2013. Improved procedure for the computation of Lamb's coefficients in the Physalis method for particle simulation. J. Comput. Phys. 234:44–59 [Google Scholar]
  45. Guy RD, Hartenstine DA. 2010. On the accuracy of direct forcing immersed boundary methods with projection methods. J. Comput. Phys. 229:2479–96 [Google Scholar]
  46. Hashemi M, Fatehi R, Manzari M. 2012. A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows. Int. J. Non-Linear Mech. 47:626–38 [Google Scholar]
  47. Hdadadi H, Morris J. 2014. Microstructure and rheology of finite inertia neutrally buoyant suspensions. J. Fluid Mech. 749:431–59 [Google Scholar]
  48. Hernández-Ortiz JP, de Pablo JJ, Graham MD. 2007. Fast computation of many-particle hydrodynamic and electrostatic interactions in a confined geometry. Phys. Rev. Lett. 98:140602 [Google Scholar]
  49. Hobson E. 2012. The Theory of Spherical and Ellipsoidal Harmonics New York: Cambridge Univ. Press
  50. Homann H, Bec J. 2010. Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J. Fluid Mech. 651:81–91 [Google Scholar]
  51. Homann H, Bec J, Grauer R. 2013. Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer. J. Fluid Mech. 721:155–79 [Google Scholar]
  52. Hu H. 2009. Finite element methods for particulate flows. See Prosperetti & Tryggvason 2009 113–56
  53. Hu HH. 1996. Direct simulation of flows of solid-liquid mixtures. Int. J. Multiphase Flow 22:335–52 [Google Scholar]
  54. Hu HH, Patankar N, Zhu M. 2001. Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J. Comput. Phys. 169:427–62 [Google Scholar]
  55. Huang H, Yang X, Lu X. 2014. Sedimentation of an ellipsoidal particle in narrow tubes. Phys. Fluids 26:053302 [Google Scholar]
  56. Hughes T, Liu WK, Zimmermann TK. 1981. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Eng. 29:329–49 [Google Scholar]
  57. Ichiki K. 2002. Improvement of the Stokesian dynamics method for systems with a finite number of particles. J. Fluid Mech. 452:231–62 [Google Scholar]
  58. Ingber MS, Feng S, Graham AL, Brenner H. 2008. The analysis of self-diffusion and migration of rough spheres in nonlinear shear flow using a traction-corrected boundary element method. J. Fluid Mech. 598:267–92 [Google Scholar]
  59. Ingber MS, Mondy LA. 1993. Direct second kind boundary integral formulation for Stokes flow problems. Comput. Mech. 11:11–27 [Google Scholar]
  60. Jeffrey D, Onishi Y. 1984. Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J. Fluid Mech. 139:261–90 [Google Scholar]
  61. Johnson AA, Tezduyar T. 1996. Simulation of multiple spheres falling in a liquid-filled tube. Comput. Methods Appl. Mech. Eng. 134:351–73 [Google Scholar]
  62. Johnson AA, Tezduyar TE. 1999. Advanced mesh generation and update methods for 3D flow simulations. Comput. Mech. 23:130–43 [Google Scholar]
  63. Kajishima T. 2004. Influence of particle rotation on the interaction between particle clusters and particle-induced turbulence. Int. J. Heat Fluid Flow 25:721–28 [Google Scholar]
  64. Kang S, Suh YK. 2011. Direct simulation of flows with suspended paramagnetic particles using one-stage smoothed profile method. J. Fluids Struct. 27:266–82 [Google Scholar]
  65. Keaveny EE, Shelley MJ. 2011. Applying a second-kind boundary integral equation for surface tractions in Stokes flow. J. Comput. Phys. 230:2141–59 [Google Scholar]
  66. Kidanemariam AG, Chan-Braun C, Doychev T, Uhlmann M. 2013. Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys. 15:025031 [Google Scholar]
  67. Kim S, Karrila S. 1991. Microhydrodynamics: Principles and Selected Applications Boston: Butterworth-Heinemann
  68. Kumar A, Higdon JJL. 2011. Particle mesh Ewald Stokesian dynamics simulations for suspensions of non-spherical particles. J. Fluid Mech. 675:297–335 [Google Scholar]
  69. Ladd A, Verberg R. 2001. Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104:1191–251 [Google Scholar]
  70. Lallemand L, Luo LS. 2003. Lattice Boltzmann method for moving boundaries. J. Comput. Phys. 184:406–21 [Google Scholar]
  71. Lauga E, Powers TR. 2009. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72:096601 [Google Scholar]
  72. Lee H, Balachandar S. 2010. Drag and lift forces on a spherical particle moving on a wall in a shear flow at finite Re. J. Fluid Mech. 657:89–125 [Google Scholar]
  73. Leiderman K, Bouzarth EL, Cortez R, Layton AT. 2013. A regularization method for the numerical solution of periodic Stokes flow. J. Comput. Phys. 236:187–202 [Google Scholar]
  74. Lindbo D, Tornberg AK. 2010. Spectrally accurate fast summation for periodic Stokes potentials. J. Comput. Phys. 229:8994–9010 [Google Scholar]
  75. Ling Y, Parmar M, Balachandar S. 2013. A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows. Int. J. Multiphase Flow 57:102–14 [Google Scholar]
  76. Liu D, Keaveny E, Maxey M, Karniadakis G. 2009. Force-coupling method for flows with ellipsoidal particles. J. Comput. Phys 228:3559–81 [Google Scholar]
  77. Liu D, Maxey M, Karniadakis G. 2002. A fast method for particulate microflows. J. Microelectromech. Syst. 11:691–702 [Google Scholar]
  78. Loisel V, Abbas M, Masbernat O, Climent E. 2013. The effect of neutrally buoyant finite-size particles on channel flows in the laminar-turbulent transition regime. Phys. Fluids 25:123304 [Google Scholar]
  79. Lomholt S, Maxey M. 2003. Force-coupling method for particles sedimenting in a channel: Stokes flow. J. Comput. Phys. 184:381–405 [Google Scholar]
  80. Loth E, Dorgan AJ. 2009. An equation of motion for particles of finite Reynolds number and size. Environ. Fluid Mech. 9:187–206 [Google Scholar]
  81. Lovalenti PM, Brady JF. 1993. The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256:561–605 [Google Scholar]
  82. Lucci F, Ferrante A, Elghobashi S. 2010. Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650:5–55 [Google Scholar]
  83. Luo X, Beskok A, Karniadakis GE. 2010. Modeling electrokinetic flows by the smoothed profile method. J. Comput. Phys. 229:3828–47 [Google Scholar]
  84. Luo X, Maxey MR, Karniadakis GE. 2009. Smoothed profile method for particulate flows: error analysis and simulations. J. Comput. Phys. 228:1750–69 [Google Scholar]
  85. Mao W, Alexeev A. 2014. Motion of spheriod particles in shear flow with inertia. J. Fluid Mech. 749:145–66 [Google Scholar]
  86. Marrone S, Colagrossi A, Colicchio G, Graziani G. 2013. An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers. J. Comput. Phys. 245:456–75 [Google Scholar]
  87. Matas JP, Morris JF, Guazzelli E. 2009. Lateral force on a rigid sphere in large-inertia laminar pipe flow. J. Fluid Mech. 621:59–67 [Google Scholar]
  88. Maxey M. 1999. Examples of fluid-particle interactions in dispersed two-phase flow Presented at AIAA Fluid Dyn. Conf., 30th, Norfolk, VA, AIAA Pap. 1999-3691
  89. Maxey M, Patel B. 2001. Localized force representations for particles sedimenting in Stokes flow. Int. J. Multiphase Flow 27:1603–26 [Google Scholar]
  90. Maxey MR, Riley JJ. 1983. Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26:883–89 [Google Scholar]
  91. Metzger B, Butler JE. 2012. Clouds of particles in a periodic shear flow. Phys. Fluids 24:021703 [Google Scholar]
  92. Mittal R, Iaccarino G. 2005. Immersed boundary methods. Annu. Rev. Fluid Mech. 37:239–61 [Google Scholar]
  93. Monaghan J. 2005. Smoothed particle hydrodynamics. Rep. Prog. Phys. 68:1703–59 [Google Scholar]
  94. Monaghan J. 2012. Smoothed particle hydrodynamics and its diverse applications. Annu. Rev. Fluid Mech. 44:323–46 [Google Scholar]
  95. Morris JF. 2009. A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta 48:909–23 [Google Scholar]
  96. Muldowney GP, Higdon JJL. 1995. A spectral boundary element approach to three-dimensional Stokes flow. J. Fluid Mech. 298:167–92 [Google Scholar]
  97. Nakayama Y, Yamamoto R. 2005. Simulation method to resolve hydrodynamic interactions in colloidal dispersions. Phys. Rev. E 71:036707 [Google Scholar]
  98. Nguyen N, Ladd A. 2002. Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys. Rev. E 66:046708 [Google Scholar]
  99. Olivieri S, Picano F, Sardina G, Iudicone D, Brandt L. 2014. The effect of the Basset history force on particle clustering in homogeneous and isotropic turbulence. Phys. Fluids 26:041704 [Google Scholar]
  100. Ozarkar SS, Sangani AS. 2008. A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface. Phys. Fluids 20:063301 [Google Scholar]
  101. Pan TW, Glowinski R, Galdi GP. 2002a. Direct simulation of the motion of a settling ellipsoid in Newtonian fluid. J. Comput. Appl. Math. 149:71–82 [Google Scholar]
  102. Pan TW, Joseph DD, Bai R, Glowinski R, Sarin V. 2002b. Fluidization of 1204 spheres: simulation and experiment. J. Fluid Mech. 451:169–91 [Google Scholar]
  103. Pasquetti R, Bwemba R, Cousin L. 2008. A pseudo-penalization method for high Reynolds number unsteady flows. Appl. Numer. Math. 58:946–54 [Google Scholar]
  104. Patankar NA, Singh P, Joseph DD, Glowinski R, Pan TW. 2000. A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow 26:1509–24 [Google Scholar]
  105. Peng C, Teng Y, Hwang B, Guo Z, Wang LP. 2016. Implementation issues and benchmarking of lattice Boltzmann method for moving rigid particle simulations in a viscous flow. Comput. Math. Appl. 72:349–74 [Google Scholar]
  106. Peskin CS. 2002. The immersed boundary method. Acta Numer. 11:479–517 [Google Scholar]
  107. Picano F, Breugem WP, Brandt L. 2015. Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764:463–87 [Google Scholar]
  108. Pivkin I, Richardson PD, Karniadakis G. 2006. Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi. PNAS 103:17164–69 [Google Scholar]
  109. Power H, Miranda G. 1987. Second kind integral equation formulation of Stokes' flows past a particle of arbitrary shape. SIAM J. Appl. Math. 47:689–98 [Google Scholar]
  110. Pozrikidis C. 1992. Boundary Integral and Singularity Methods for Linearized Viscous Flow Cambridge, UK: Cambridge Univ. Press
  111. Prosperetti A, Tryggvason T. 2009. Computational Methods for Multiphase Flow Cambridge, UK: Cambridge Univ. Press
  112. Rahmani M, Wachs A. 2014. Free falling and rising of spherical and angular particles. Phys. Fluids 26:083301 [Google Scholar]
  113. Rampall I, Smart J, Leighton D. 1997. The influence of surface roughness on the particle-pair distribution function of dilute suspensions of non-colloidal spheres in simple shear flow. J. Fluid Mech. 339:1–24 [Google Scholar]
  114. Saffman PG. 1965. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22:385–400 [Google Scholar]
  115. Sangani AS, Acrivos A, Peyla P. 2011. Roles of particle-wall and particle-particle interactions in highly confined suspensions of spherical particles being sheared at low Reynolds numbers. Phys. Fluids 23:083302 [Google Scholar]
  116. Sharma N, Patankar NA. 2005. A fast computation technique for the direct numerical simulation of rigid particulate flows. J. Comput. Phys. 205:439–57 [Google Scholar]
  117. Sierakowski A, Prosperetti A. 2016. Resolved-particle simulation by the Physalis method: enhancements and new capabilities. J. Comput. Phys. 309:164–84 [Google Scholar]
  118. Sierou A, Brady J. 2001. Accelerated Stokesian dynamics simulations. J. Fluid Mech. 448:115–46 [Google Scholar]
  119. Sierou A, Brady JF. 2002. Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46:1031–56 [Google Scholar]
  120. Sierou A, Brady JF. 2004. Shear-induced self-diffusion in non-colloidal suspensions. J. Fluid Mech. 506:285–314 [Google Scholar]
  121. Soldati A, Marchioli C. 2009. Physics and modelling of turbulent particle deposition and entrainment: review of a systematic study. Int. J. Multiphase Flow 35:827–39 [Google Scholar]
  122. Squires K. 2009. Point-particle methods for disperse flows. See Prosperetti & Tryggvason 2009 282–319
  123. Sun Q, Klaseboer E, Khoo BC, Chan DYC. 2015. Boundary regularized integral equation formulation of Stokes flow. Phys. Fluids 27:023102 [Google Scholar]
  124. Swaminathan TN, Mukundakrishnan K, Hu HH. 2006. Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers. J. Fluid Mech. 551:357–85 [Google Scholar]
  125. Swan JW, Brady JF. 2010. Particle motion between parallel walls: hydrodynamics and simulation. Phys. Fluids 22:103301 [Google Scholar]
  126. Swan JW, Brady JF. 2011. The hydrodynamics of confined dispersions. J. Fluid Mech. 687:254–99 [Google Scholar]
  127. Tornberg AK, Greengard L. 2008. A fast multipole method for the three-dimensional Stokes equations. J. Comput. Phys. 227:1613–19 [Google Scholar]
  128. Trask N. 2015. Compatible high-order meshless schemes for viscous fluid flows through l2optimization PhD Thesis, Brown Univ., Providence, RI [Google Scholar]
  129. Trask N, Maxey M, Kim K, Perego M, Parks M. et al. 2015. A scalable consistent second-order SPH solver for unsteady low Reynolds number flows. Comput. Methods Appl. Mech. Eng. 289:155–78 [Google Scholar]
  130. Uhlmann M. 2005. An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209:448–76 [Google Scholar]
  131. Uhlmann M. 2008. Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20:053305 [Google Scholar]
  132. van Hinsberg MAT, ten Thije Boonkkamp JHM, Clercx HJH. 2011. An efficient, second order method for the approximation of the Basset history force. J. Comput. Phys. 230:1465–78 [Google Scholar]
  133. Vázquez-Quesada A, Ellero M. 2016. Rheology and microstructure of non-colloidal suspensions under shear studied with smoothed particle hydrodynamics. J. Non-Newton. Fluid Mech. 233:37–47 [Google Scholar]
  134. Vincent S, Brändle de Motta JC, Sarthou A, Estivalezes JL, Simonin O, Climent E. 2014. A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows. J. Comput. Phys. 256:582–614 [Google Scholar]
  135. Wang LP, Peng C, Guo Z, Yu Z. 2016. Lattice Boltzmann simulation of particle-laden turbulent channel flow. Comput. Fluids 124:226–36 [Google Scholar]
  136. Wen B, Zhang C, Tu Y, Wang C, Fang H. 2014. Galilean invariant fluid-solid interfacial dynamics in lattice Boltzmann simulations. J. Comput. Phys. 266:161–70 [Google Scholar]
  137. Yamamoto R, Kim K, Nakayama Y. 2007. Strict simulations of non-equilibrium dynamics of colloids. Colloids Surf. A 311:42–47 [Google Scholar]
  138. Yang X, Mehmani Y, Perkins W, Pasquali A, Schonherr M. et al. 2016. Intercomparison of 3D pore-scale flow and solute transport simulation methods. Adv. Water Res. 95176–89
  139. Yeo K, Dong S, Climent E, Maxey M. 2010. Modulation of homogeneous turbulence seeded with finite size bubbles or particles. Int. J. Multiphase Flow 36:221–33 [Google Scholar]
  140. Yeo K, Maxey MR. 2010a. Dynamics of concentrated suspensions of non-colloidal particles in Couette flow. J. Fluid Mech. 649:205–31 [Google Scholar]
  141. Yeo K, Maxey MR. 2010b. Simulation of concentrated suspensions using the force-coupling method. J. Comput. Phys. 229:2401–21 [Google Scholar]
  142. Yeo K, Maxey MR. 2011. Numerical simulations of concentrated suspensions of monodisperse particles in a Poiseuille flow. J. Fluid Mech. 682:491–518 [Google Scholar]
  143. Yeo K, Maxey MR. 2013. Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow. Phys. Fluids 25:053303 [Google Scholar]
  144. Youngren GK, Acrivos A. 1975. Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69:377–403 [Google Scholar]
  145. Yu Y, Baek H, Karniadakis GE. 2013. Generalized fictitious methods for fluid-structure interactions: analysis and simulations. J. Comput. Phys. 245:317–46 [Google Scholar]
  146. Yu Z, Phan-Thien N, Tanner RI. 2004. Dynamic simulation of sphere motion in a vertical tube. J. Fluid Mech. 518:61–93 [Google Scholar]
  147. Yu Z, Shao X. 2007. A direct-forcing fictitious domain method for particulate flows. J. Comput. Phys. 227:292–314 [Google Scholar]
  148. Zhang Z, Prosperetti A. 2005. A second-order method for three-dimensional particle simulation. J. Comput. Phys. 210:292–324 [Google Scholar]
  149. Zhou Q, Fan LS. 2014. A second-order accurate immersed boundary–lattice Boltzmann method for particle-laden flows. J. Comput. Phys. 268:269–301 [Google Scholar]
  150. Zurita-Gotor M, Błlawzdziewicz J, Wajnryb E. 2007. Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres. J. Fluid Mech. 592:447–69 [Google Scholar]
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