We present a Euler-Lagrangian simulation method for rigid particles immersed in fluids described by the Navier-Stokes equation. The no-slip condition between particle and fluid phase is realized by a modification of the volume force term of the Navier-Stokes equation. To this end, a set of tracers is couples the fluid at positions corresponding to the "interior" of a particle with "springs" to a rigid "template" carrying supplementary mass and moment of inertia. The coupling is chosen such that the template-liquid system as a whole behaves almost rigidly and constitutes a particle. Exterior to these particles, the regular Navier-Stokes equation remains valid. This method allows to simulate several hundreds to few thousands particles on workstations with particle Reynolds numbers of 10... 20. A parallel version of the algorithm scales to≈10~6 particles on a 512 node CRAY-T3E. We report results of the application of this method to the case of particles sedimenting under the influence of gravity at particle Reynolds numbers of about unity and recover experimental and theoretical findings for the sedimentation velocity of the suspension and the singleparticle drag. We also study the rheology of suspensions of hydrodynamically interacting particles in 2D shear flows, where we assume that the particles aggregate under the influence of an additional short-ranged attractive force. This model shows shear-thinning.
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