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Numerical simulations of particulate suspensions via a discretized Boltzmann equation. I: Theoretical foundation. II: Numerical results. (English) Zbl 0815.76085
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 for displacements applied directly to the particles. Extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite-Reynolds-number flows, are reported.

76T99 Multiphase and multicomponent flows
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
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