A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation.

We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares problem into a sequence of local nonlinear problems and variational linear problems.

Numerical study of two disks settling in an Oldroyd-B fluid: From periodic interaction to chaining.

In this article, we present a numerical study of the dynamics of two disks sedimenting in a narrow vertical channel filled with an Oldroyd-B fluid. Two kinds of particle dynamics are observed: (i) a periodic interaction between the two disks, and (ii) the formation of a two-disk chain. For the periodic interaction of the two disks, two different motions are observed: (a) the two disks stay far apart and interact periodically, and (b) the two disks interact closely and then far apart in a periodic way, like the drafting, kissing, and tumbling of two disks sedimenting in a Newtonian fluid, due to a weak elastic force.

The dynamics of inextensible capsules in shear flow under the effect of the natural state.

The effect of the natural state on the motion of an inextensible capsule in two-dimensional shear flow has been studied numerically. The energy barrier based on such natural state plays a role for having the transition between two well-known motions, tumbling and tank-treading (TT) with the long axis oscillating about a fixed inclination angle (a swinging mode), when varying the shear rate. Between tumbling and TT with a swinging mode, the intermittent region has been obtained for the capsule with a biconcave rest shape.

Circular band formation for incompressible viscous fluid-rigid-particle mixtures in a rotating cylinder.

In this paper we have investigated a circular band formation of fluid-rigid-particle mixtures in a fully filled cylinder horizontally rotating about its cylinder axis by direct numerical simulation. These phenomena are modeled by the Navier-Stokes equations coupled to the Euler-Newton equations describing the rigid solid motion of the non-neutrally particles. The formation of circular bands studied in this paper is mainly caused by the interaction between particles themselves.

Lateral migration and equilibrium shape and position of a single red blood cell in bounded Poiseuille flows.

Lateral migration and equilibrium shape and position of a single red blood cell (RBC) in bounded two-dimensional Poiseuille flows are investigated by using an immersed boundary method. An elastic spring model is applied to simulate the skeleton structure of a RBC membrane. We focus on studying the properties of lateral migration of a single RBC in Poiseuille flows by varying the initial position, the initial angle, the swelling ratio (s), the membrane bending stiffness of RBC (k{b}), the maximum velocity of fluid flow (u{max}), and the degree of confinement.

Deformation of a single red blood cell in bounded Poiseuille flows.

Deformation of a red blood cell (RBC) in bounded two-dimensional Poiseuille flows is studied by using an immersed boundary method (IBM). An elastic spring model is applied to simulate the skeleton structure of a RBC membrane. As a benchmarking test, the dynamical behavior of a single RBC under a simple shear flow has been validated.