A numerical simulation of viscous flows in collapsible tubes with stenoses Original Research Article

A finite element method with streamline diffusion for solving a nonlinear mathematical model with free moving boundary is developed to study the viscous flows in collapsible tubes. In this model, governing equations are incompressible Navier–Stokes equations. The moving boundary is determined by a tube law concerning effects of both circumferentia and longitudinal tensions. The free moving boundary problem is numerically solved by a finite element method with boundary iterations. The numerical solutions show that both circumferentia 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 the studies of the blood flow in arteries with stenosis and the air flow in the airways, which are of potential diagnostic significance.