# Airway Reopening: The propagation of an air finger into a
collapsed elastic tube

### The computational model

The mathematical model of airway reopening comprises the free
surface Navier-Stokes equations which describe the fluid flow, coupled
to the equations of geometrically non-linear elasticity which
describe the large deformations of the airway wall.
The equations were discretised by finite element methods: Displacement
based finite elements were used to discretise the wall equations which
were formulated in Lagrangian coordinates; the discretisation of the
Navier-Stokes equations (formulated in spatially fixed, Eulerian
coordinates) was achieved by utilising a moving mesh which adapted
itself in response to the wall deformation. The method of spines
was used for the automatic mesh update. The figure below shows
the structure of the mesh (the symmetry of the configuration was
exploited by only discretising one half of the domain) -- the actual computations were carried out with a
much finer resolution.

The discretised fluid and solid equations were solved in a fully
coupled manner, using a Newton-Raphson method with adaptive
parameter incrementation.

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Page last modified: September 28, 2000

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