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

Abstract

A new and very general technique for simulating solid-uid 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 uid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-ow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic uctuations in the uid 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 the companion paper, extensive numerical tests of the method, for stationary ows, time-dependent ows, and nite Reynolds number ows, are reported.

Multiphase lattice Boltzmann simulations for porous media applications

“…At an early stage of the LBM's development, alternative collision schemes were introduced [61,62]. In particular, the multiple relaxation time (MRT) collision operator can be written as [62][63][64],…”

Mesoscopic simulations of systolic flow in the human abdominal aorta

“…Due to its simple implementation, straightforward parallelization and easy grid generation, the capability of the lattice Boltzmann method has been demonstrated in various complex applications including Newtonian blood flow simulations (Krafczyk et al, 1998;Artoli et al, 2002), nonNewtonian and suspension flows (e.g. Ladd, 1994), and complex geometry (e.g. Kandhai et al, 1999).…”

“…Secondly, the pressure is simply a linear function in the speed of sound (p ¼ rc 2 s ) while the NS solvers need to solve the Poisson equation. Finally and most important for the field of hemodynamics, is that the stress tensor can be directly obtained from the non-equilibrium parts of the distribution functions f ð1Þ i through the following relation (Ladd, 1994;Artoli et al, 2002) …”

Particle stress in suspensions of soft objects

“…The size of the simulation boxes, including the bounce-back walls, is 90 × 90 × (D + 2) (table 1), with full periodicity along the x-and y-axes. The shear flow is imposed by moving bottom and top walls at z = 0 and z = D via the bounce-back boundary condition [1]. In order to maintain the same average shear rate, the wall velocity increases linearly with the wall-towall distance and is 0.06 for the largest simulation box (table 1).…”