  A geometric numerical method for simulating suspensions of spherical and
non-spherical particles with Stokes drag is proposed. The method combines
divergence-free matrix-valued radial basis function interpolation of the fluid
velocity field with a splitting method integrator that preserves the sum of the
Lyapunov spectrum while mimicking the centrifuge effect of the exact solution.
We discuss how breaking the divergence-free condition in the interpolation step
can erroneously affect how the volume of the particulate phase evolves under
numerical methods. The methods are tested on suspensions of $10^4$ particles
evolving in discrete cellular flow field. The results are that the proposed
geometric methods generate more accurate and cost-effective particle
distributions compared to conventional methods.
