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
2024-10-13
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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 [Google Scholar]
  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 [Google Scholar]
  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 [Google Scholar]
  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 [Google Scholar]
  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 [Google Scholar]
  111. Prosperetti A, Tryggvason T. 2009. Computational Methods for Multiphase Flow Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  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 [Google Scholar]
  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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