  We study the settling of solid particles within a viscous incompressible
fluid contained in a two-dimensional channel, where the mass density of the
particles is slightly greater than that of the fluid. The fluid-structure
interaction problem is simulated numerically using the immersed boundary
method, with an added mass term that is incorporated using a Boussinesq
approximation. Simulations are performed with a single circular particle, and
also with two particles in various initial configurations. The terminal
settling velocities for the particles correspond closely with both theoretical
and experimental results, and the single-particle dynamics reproduce expected
behavior qualitatively. The two-particle simulations exhibit
drafting-kissing-tumbling dynamics that is similar to what is observed in other
experimental and numerical studies.
