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Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation

  • Anthony J. C. Ladd (a1)
Abstract

A new and very general technique for simulating solid–fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in a companion paper (Part 2), extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite-Reynolds-number flows, are reported.

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Bossis, G. & Brady, J. F.1987Self-diffusion of Brownian particles in concentrated suspensions under shear. J. Chem. Phys.87, 5437.

Brady, J. F. & Bossis, G.1988Stokesian dynamics. Ann. Rev. Fluid. Mech.20, 111.

Chen, S., Wang, Z., Shan, X. & Doolen, G. D.1992Lattice Boltzmann computational fluid dynamics in three dimension. J. Statist Phys68, 379.

Durlofsky, L., Brady, J. F. & Bossis, G. 1987 Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21.

Ermak, D. L. & McCammon, J. A.1978Brownian dynamics with hydrodynamic interactions. J. Chem. Phys.69, 1352.

Fogelson, A. L. & Peskin, C. S.1988A fast numerical method for solving the three-dimensional Stokes equations in the presence of suspended particles. J. Comput. Phys.79, 50.

Frisch, U., Hasslacher, B. & Pomeau, Y.1986Lattice gas automata for the Navier–Stokes equation. Phys. Rev. Lett.56, 1505.

Higuera, F., Succi, S. & Benzi, R.1989Lattice gas dynamics with enhanced collisions. Europhys. Lett.9, 345.

Hoef, M. A. van der, Frenkel, D. & Ladd, A. J. C.1991Self-diffusion of colloidal particles in a two-dimensional suspension: are deviations from Fick's law experimentally observable? Phys. Rev. Lett.67, 3459.

Hoogerbrugge, P. J. & Koelman, J. M. V. A.1992Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett.19, 155.

Kao, M. H., Yodh, A. G. & Pine, D. J.1993Observation of Brownian motion on the time scale of the hydrodynamic interaction. Phys. Rev. Lett.70, 242.

Karrila, S. J., Fuentes, Y. O. & Kim, S.1989Parallel computational strategies for hydrodynamic interactions between rigid particles of arbitrary shape in a viscous fluid. J. Rheol.33, 913.

Koelman, J. M. V. A. & Hoogerbrugge, P. J.1993Dynamic simulations of hard-sphere suspensions under steady shear. Europhys. Lett.21, 363.

Ladd, A. J. C.1988Hydrodynamic interactions in a suspension of spherical particles. J. Chem. Phys.88, 5051.

Ladd, A. J. C.1993Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation. Phys. Rev. Lett.70, 1339.

Ladd, A. J. C.1994Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech.271, 311.

Ladd, A. J. C., Colvin, M. E. & Frenkel, D.1988Application of lattice-gas cellular automata to the Brownian motion of solids in suspension. Phys. Rev. Lett.60, 975.

Ladd, A. J. C. & Frenkel, D.1990Dissipative hydrodynamic interactions via lattice-gas cellular automata. Phys. Fluids A 2, 1921.

McNamara, G. R. & Alder, B. J.1993Analysis of the lattice Boltzmann treatment of hydrodynamics. Physica A 194, 218.

McNamara, G. R. & Zanetti, G.1988Use of the Boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett.61, 2332.

Sulsky, D. & Brackbill, J. U.1991A numerical method for suspension flow. J. Comput. Phys.96, 339.

Tran-Cong, T. & Phan-Thien, N.1989Stokes problems of multiparticle systems: A numerical method for arbitrary flows. Phys. Fluids A 1, 453.

Yen, S. M.1984Numerical solution of the nonlinear Boltzmann equation for nonequilibrium gas flow problems. Ann. Rev. Fluid Mech.16, 67.

Zanetti, G.1989The hydrodynamics of lattice gas automata. Phys. Rev. A 40, 1539.

Zhu, J. X., Durian, D. J., Müller, J., Weitz, D. A. & Pine, D. J.1992Scaling of transient hydrodynamic interactions in concentrated suspensions. Phys. Rev. Lett.68, 2559.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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