A numerical simulation of viscous flows in collapsible tubes with stenoses

A finite element method with streamline diffusion for solving a nonlinear m athematical model with free moving boundary is developed to study the visco us flows in collapsible tubes. In this model, governing equations are incom pressible Navier-Stokes equations. The moving boundary is determined by a t ube law concerning effects of both circumferentia and longitudinal tensions . The free moving boundary problem is numerically solved by a finite elemen t method with boundary iterations. The numerical solutions show that both c ircumferentia and longitudinal tensions affect the motion of the tube wall, therefore affect the contraction and expansion of the tube. Relationships of the stenosis severity and flow data, such as flow rate and flow pressure , are obtained from numerical results. Applications of this model include t he studies of the blood how in arteries with stenosis and the air flow in t he airways, which are of potential diagnostic significance, (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.