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Simulations of over $10^3$ hydrodynamically coupled solid spheres areperformed to investigate collective motion of linear trains and regular squarearrays of particles suspended in a fluid bounded by two parallel walls. Ournovel accelerated Stokesian-dynamics algorithm relies on simplificationsassociated with the Hele--Shaw asymptotic far-field form of the flow scatteredby the particles. The simulations reveal propagation of particle-displacementwaves, deformation and rearrangements of a particle lattice, propagation ofdislocation defects in ordered arrays, and long-lasting coexistence of orderedand disordered regions.

Hydrodynamic crystals: collective dynamics of regular arrays of spherical particles in a parallel-wall channel