Lattice-Boltzmann methods for suspensions of solid particles

In this paper, dedicated to Prof. Jean-Pierre Hansen, I will summarise the development of lattice-Boltzmann methods for simulating the dynamics of colloidal suspensions. I will describe the main ideas and subsequent improvements, and place them in the wider context of particle-based methods for fluid dynamics.

[1]  Graeme A. Bird,et al.  Molecular Gas Dynamics , 1976 .

[2]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  R. Benzi,et al.  Lattice Gas Dynamics with Enhanced Collisions , 1989 .

[4]  R. Glowinski,et al.  A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows , 2000 .

[5]  A. Ladd Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation , 1993, Journal of Fluid Mechanics.

[6]  A. Ladd,et al.  Lattice Boltzmann Simulations of Soft Matter Systems , 2008, 0803.2826.

[7]  S. Succi The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2001 .

[8]  A. Ladd,et al.  Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  David R. Noble,et al.  A consistent hydrodynamic boundary condition for the lattice Boltzmann method , 1995 .

[10]  Konrad Hinsen,et al.  Friction and mobility of many spheres in Stokes flow , 1994 .

[11]  Paul Manneville,et al.  Cellular Automata and Modeling of Complex Physical Systems , 1989 .

[12]  Irina Ginzburg,et al.  Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations , 2005 .

[13]  A. Ladd,et al.  Lattice-Boltzmann Simulations of Particle-Fluid Suspensions , 2001 .

[14]  Antje Sommer,et al.  Theory Of Simple Liquids , 2016 .

[15]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .

[16]  B. Alder,et al.  Decay of the Velocity Autocorrelation Function , 1970 .

[17]  James J. Feng,et al.  Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation , 1994, Journal of Fluid Mechanics.

[18]  Dynamics of colloidal dispersions via lattice-gas models of an incompressible fluid , 1989 .

[19]  Xiaoyi He,et al.  Lattice Boltzmann Method on Curvilinear Coordinates System , 1997 .

[20]  A. Ladd Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results , 1993, Journal of Fluid Mechanics.

[21]  Cyrus K. Aidun,et al.  Lattice Boltzmann simulation of solid particles suspended in fluid , 1995 .

[22]  R. Winkler,et al.  Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids , 2008, 0808.2157.

[23]  Cyrus K. Aidun,et al.  Extension of the Lattice-Boltzmann Method for Direct Simulation of Suspended Particles Near Contact , 2003 .

[24]  A. Wagner,et al.  Fluctuating ideal-gas lattice Boltzmann method with fluctuation dissipation theorem for nonvanishing velocities. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[26]  P. Lallemand,et al.  Lattice Boltzmann method for moving boundaries , 2003 .

[27]  C. Lowe,et al.  Simulating solid colloidal particles using the lattice-Boltzmann method , 2000 .

[28]  P. Coveney,et al.  Entropic lattice Boltzmann methods , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[29]  A. Fogelson,et al.  A fast numerical method for solving the three-dimensional Stokes' equations in the presence of suspended particles , 1988 .

[30]  A. Malevanets,et al.  Mesoscopic model for solvent dynamics , 1999 .

[31]  Junfeng Zhang,et al.  An improved bounce-back scheme for complex boundary conditions in lattice Boltzmann method , 2012, J. Comput. Phys..

[32]  A. Ladd,et al.  Interpolated boundary condition for lattice Boltzmann simulations of flows in narrow gaps. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Jacques Periaux,et al.  A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow , 2000 .

[34]  M. Cates,et al.  Fluctuating lattice Boltzmann , 2004, cond-mat/0402598.

[35]  John F. Brady,et al.  Accelerated Stokesian Dynamics simulations , 2001, Journal of Fluid Mechanics.

[36]  Zanetti,et al.  Use of the Boltzmann equation to simulate lattice gas automata. , 1988, Physical review letters.

[37]  R. Glowinski,et al.  Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow , 2002 .

[38]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  Jean-Pierre Hansen,et al.  Phase Transitions of the Lennard-Jones System , 1969 .

[40]  C. Aidun,et al.  Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation , 1998, Journal of Fluid Mechanics.

[41]  Peng Yuan,et al.  A mass conserving boundary condition for the lattice Boltzmann equation method , 2008, J. Comput. Phys..

[42]  J. Boon The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[43]  Z. Feng,et al.  The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems , 2004 .

[44]  L. Luo,et al.  Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation , 1997 .

[45]  A. Sangani,et al.  An O(N) algorithm for Stokes and Laplace interactions of particles , 1996 .

[46]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[47]  J. Monaghan Smoothed particle hydrodynamics , 2005 .

[48]  Iliya V. Karlin,et al.  Perfect entropy functions of the Lattice Boltzmann method , 1999 .

[49]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[50]  Ladd Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation. , 1993, Physical review letters.

[51]  C. Peskin,et al.  A three-dimensional computational method for blood flow in the heart. 1. Immersed elastic fibers in a viscous incompressible fluid , 1989 .

[52]  Pep Español,et al.  Smoothed dissipative particle dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Wei Shyy,et al.  Force evaluation in the lattice Boltzmann method involving curved geometry. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Daniel D. Joseph,et al.  Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows , 1994, Journal of Fluid Mechanics.

[55]  L. Luo,et al.  A priori derivation of the lattice Boltzmann equation , 1997 .

[56]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[57]  Anthony J. C. Ladd,et al.  Hydrodynamic interactions in a suspension of spherical particles , 1988 .

[58]  P. Mazur,et al.  Many-sphere hydrodynamic interactions and mobilities in a suspension , 1982 .

[59]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[60]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[61]  I. Ginzburg Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation , 2005 .

[62]  Alfonso Caiazzo,et al.  Boundary forces in lattice Boltzmann: Analysis of Momentum Exchange algorithm , 2008, Comput. Math. Appl..

[63]  C. Aidun,et al.  Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force , 2009 .

[64]  Dominique d'Humières,et al.  Multireflection boundary conditions for lattice Boltzmann models. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[65]  Aleksander S Popel,et al.  Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method. , 2008, Journal of biomechanics.

[66]  B. Shi,et al.  Discrete lattice effects on the forcing term in the lattice Boltzmann method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[67]  Wei Shyy,et al.  Regular Article: An Accurate Curved Boundary Treatment in the Lattice Boltzmann Method , 1999 .

[68]  G. Bird Molecular Gas Dynamics and the Direct Simulation of Gas Flows , 1994 .

[69]  Daan Frenkel,et al.  Dissipative hydrodynamic interactions via lattice‐gas cellular automata , 1990 .

[70]  U. Frisch,et al.  Low-viscosity lattice gases , 1990 .

[71]  M. Berger,et al.  An Adaptive Version of the Immersed Boundary Method , 1999 .

[72]  P. Lallemand,et al.  Momentum transfer of a Boltzmann-lattice fluid with boundaries , 2001 .

[73]  W. Steckelmacher Molecular gas dynamics and the direct simulation of gas flows , 1996 .

[74]  P. Español,et al.  Statistical Mechanics of Dissipative Particle Dynamics. , 1995 .

[75]  Alfonso Caiazzo,et al.  Corrected momentum exchange method for lattice Boltzmann simulations of suspension flow. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[76]  W. Shyy,et al.  A multi‐block lattice Boltzmann method for viscous fluid flows , 2002 .

[77]  Solving the Fokker-Planck kinetic equation on a lattice. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[78]  Cyrus K. Aidun,et al.  Lattice-Boltzmann Method for Complex Flows , 2010 .

[79]  C. Peskin Flow patterns around heart valves: A numerical method , 1972 .

[80]  O. Filippova,et al.  Grid Refinement for Lattice-BGK Models , 1998 .

[81]  B. Alder,et al.  Analysis of the lattice Boltzmann treatment of hydrodynamics , 1993 .

[82]  C. Peskin The immersed boundary method , 2002, Acta Numerica.

[83]  P. Adler,et al.  Boundary flow condition analysis for the three-dimensional lattice Boltzmann model , 1994 .

[84]  Ulf D. Schiller,et al.  Statistical mechanics of the fluctuating lattice Boltzmann equation. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[85]  S. Succi,et al.  Three-Dimensional Flows in Complex Geometries with the Lattice Boltzmann Method , 1989 .