A 3D DLM/FD method for simulating the motion of spheres in a bounded shear flow of Oldroyd-B fluids

We present a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in Oldroyd-B fluids under creeping conditions. The results concerning two ball interaction in a three dimensional (3D) bounded shear flow are obtained for Weissenberg numbers up to 1. The pass and return trajectories of the two ball mass centers are similar to those in a Newtonian fluid; but they lose the symmetry due to the effect of elastic force arising from viscoelastic fluids. A tumbling chain of two balls (a dipole) may occur, depending on the value of the Weissenberg number and the initial vertical displacement of the ball mass center to the middle plane between two walls.