These oscillations do not indicate instabilities of the numerical scheme, but reflect the oscillatory time scale resulting from template mass and coupling constant . In 3D simulations, probably due to the larger number of control points, seems to suffice. Our empirical experiences concerning the admissible maximum number of tracers are not conclusive. Since the strongest gradients of the stress occur on the particle surface, computational efficiency suggests to reduce the tracer density in the particle interior. Moreover, in the viscous regime, the inertial effects due to the fluid in the interior of each particle domain are negligible.
Interior tracers are only necessary to resolve changes in the angular velocity accurately.
These will be important if significant changes in the angular velocity occur on time scales shorter than those for the diffusion of vorticity across the particle diameter, i.e., when we leave the regime of validity of the quasistatic approximation. For particle Reynolds numbers of about and sufficiently small concentrations , where it follows from the work of Goldman et al.