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

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 ze...

Uniform Error Estimates for Navier-stokes Flow with a Moving Boundary Using the Immersed Interface Method

We prove that uniform accuracy of almost second order can be achieved with a finite difference method applied to Navier-Stokes flow at low Reynolds number with a moving boundary, or interface, creating jumps in the velocity gradient and pressure. Difference operators are corrected to O(h) near the interface using the immersed interface method, adding terms related to the jumps, on a regular gri...

An Unconditionally Energy Stable Penalty Immersed Boundary Method for Simulating the Dynamics of an Inextensible Interface Interacting with a Solid Particle

In this paper, a novel penaltymethod based on the immersed boundary formulation is proposed for simulating the transient Stokes flow with an inextensible interface enclosing a suspended solid particle. The main idea of this approach relies on the penalty techniques by modifying the constitutive equation of Stokes flow toweaken the incompressibility condition, relating the surface divergence to ...

A Simple Immersed Interface Method for the Stokes Flow with Singular Forces

In this paper, we introduce a simple version of immersed interface method (IIM) for the Stokes flow with singular forces along an interface. The numerical method is based on applying the Taylor’s expansions along the normal direction and incorporating the solution and its normal derivative jumps into the finite difference approximations. The numerical results show that the scheme is second-orde...

An Immersed Interface Method for Incompressible Navier-Stokes Equations