Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation
- 25 July 1994
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 271, 285-309
- https://doi.org/10.1017/s0022112094001771
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.Keywords
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This publication has 25 references indexed in Scilit:
- Observation of Brownian motion on the time scale of hydrodynamic interactionsPhysical Review Letters, 1993
- Lattice Boltzmann computational fluid dynamics in three dimensionsJournal of Statistical Physics, 1992
- Scaling of transient hydrodynamic interactions in concentrated suspensionsPhysical Review Letters, 1992
- Self-diffusion of colloidal particles in a two-dimensional suspension: Are deviations from Fick’s law experimentally observable?Physical Review Letters, 1991
- Parallel Computational Strategies for Hydrodynamic Interactions Between Rigid Particles of Arbitrary Shape in a Viscous FluidJournal of Rheology, 1989
- Stokes problems of multiparticle systems: A numerical method for arbitrary flowsPhysics of Fluids A: Fluid Dynamics, 1989
- Hydrodynamic interactions in a suspension of spherical particlesThe Journal of Chemical Physics, 1988
- Application of lattice-gas cellular automata to the Brownian motion of solids in suspensionPhysical Review Letters, 1988
- Stokesian DynamicsAnnual Review of Fluid Mechanics, 1988
- Numerical Solution of the Nonlinear Boltzmann Equation for Nonequilibrium Gas Flow ProblemsAnnual Review of Fluid Mechanics, 1984