Suspensions with small, spherical particles

Abstract: Feasibly computable analytic solutions for systems of many particles in fluid dynamics and electrostatics are few and far-between. Simulations and numerical approximations are essential to studying these systems. This is commonly done without directly calculating the interacting field between particles. In this report a method utilizing the spectral accuracy of the Fourier transform is studied to calculate particle velocities via the surrounding fluid velocity field. The method is applied to a periodic cube of a suspension of small, spherical particles sedimenting in a fluid affected by gravity, in an attempt to mimic the behaviour of a similar infinite system. Results for a few particles qualitatively relate the shape of the solution to the choice of interpolation between particles to grid and quantitatively maps some convergence properties of a certain class of interpolating functions, cardinal B-splines. The properties of the method on the periodic system are also examined and compared to a similar study of the infinite system for many, ~1000, particles.