A Fractional Step Immersed Boundary Method for Stokes Flow with an Inextensible Interface Enclosing a Solid Particle

In this paper, we develop a fractional step method based on the immersed boundary (IB) formulation for Stokes flow with an inextensible (incompressible) interface enclosing a solid particle. In addition to solving for the fluid variables such as the velocity and pressure, the present problem involves finding an extra unknown elastic tension such that the surface divergence of the velocity is zero along the interface, and an extra unknown particle surface force such that the velocity satisfies the no-slip boundary condition along the particle surface. While the interface moves with local fluid velocity, the enclosed particle hereby undergoes a rigid body motion, and the system is closed by the force-free and torque-free conditions along the particle surface. The equations are then discretized by standard centered difference schemes on a staggered grid, and the interactions between the interface and particle with the fluid are discretized using a discrete delta function as in the IB method. The resultant li...