The numerical method is based on the Green's function for a Stokeslet in a cylindrical tube [1]. We have implemented both the Fourier-Bessel and residue-sum representations and we obtain identical results whenever the particles are more than a few diameters apart; when they are in near contact there are convergence issues with both methods. We assume that since the suspension is dilute, a typical volume fraction is 2%, the short-range interactions are relatively unimportant, but this remains to be verified. We prefer the Fourier-Bessel representation in our simulations since it enables a linear scaling of the computational time with the number of particles.