Direct simulations of spherical particle suspensions in a sliding tri-perioidic cell

We present a finite-element/fictitious-domain scheme for 3D direct simulations of suspensions of spherical particles in a Newtonian fluid in simple shear flow in a tri-periodic computational domain, which is a 3D extension of the authors' previous 2-D work [J. Comput. Phys. 194 (2004) 742]. The sliding tri-periodic cell, where suspensions in an unbounded domain in simple shear may be treated by a representative particulate problem in a unit cell, has been implemented with the mortar element method. The force-free torque-free rigid body motion of ta spherical particle is described by the rigid-shell description and implemented by Lagrangian multipliers only on the particle boundary. The bulk stress is obtained by simple boundary integrals. Through the several example problems, we discuss the the rheological properties of the bulk shear viscosity and the first/second normal stress coefficients.