An Updated Lagrangian Monolithic Formulation for Steady-State Fluid-Structure Interaction Problems

Author(s):  
Stephane Etienne ◽  
Dominique Pelletier ◽  
Andre Garon
Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 94 ◽  
Author(s):  
Cornel Marius Murea

A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.


2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Rouzbeh Amini ◽  
Victor H. Barocas

Corneoscleral indentation changes the iris contour and alters the angle between the iris and cornea. Although this effect has long been observed, the mechanism by which it occurs remains poorly understood. Previous theoretical research has shown that corneoscleral indentation can deform the eye globe and consequently rotate the iris root. In this work, we studied the fluid-structure interaction between the iris and aqueous humor, driven by iris root rotation. The iris root rotation obtained from our previous whole-globe model was used as a boundary condition for a fluid-structure interaction finite element model of the anterior eye. We studied the effect of two parameters-rotation angle and indentation speed-on the iris contour and aqueous humor dynamics. We found that posterior rotation of the iris root caused posterior bowing of the iris. After the iris root was returned to its original orientation, the aqueous humor was trapped in the anterior chamber because the iris tip pinned against the lens (reverse pupillary block). After 0.5–2 min of simulation, aqueous humor secretion into the posterior chamber and outflow from the anterior chamber allowed the system to return to its original steady state flow condition. The faster or farther the iris root rotated, the longer it took to return to steady state. Reverse pupillary block following corneoscleral indentation is a possible explanation for the clinical observation that prevention of blinking causes the iris to drift forward.


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