A three-dimensional computer model for fluid flow through a collapsible tube

A three-dimensional computer model has been developed and implemented to simulate fluid flow though a collapsible tube. The program uses the immersed boundary method of Peskin, in which a flexible boundary layer is immersed in a fluid. The boundary is both affected by and has an effect on the motion of the fluid. The setup includes an upstream pressure, a downstream pressure, and an external pressure. By adjusting the relative sizes and signs of these pressures the tube can exhibit various phenomena. The interesting case is when the upstream pressure is greater than the externally applied pressure, which is in turn greater than the downstream pressure. Under such conditions the tube can display partial collapse and spontaneous oscillations of the collapsed region. This thesis discusses a computer model which can be used to study collapse in such a tube. The program runs on the Cray C-90 computer at the Pittsburgh Supercomputing Center. The code has been vectorized to speed up computation and can be parallelized. The computer code is being used to simulate the experimental setup used by Conrad. It models a long, thin tube attached at both ends to rigid supports. The tube is defined by a series of points arranged into fibers running along and winding around the length of the tube. A pressure source and sink are also modeled. Caps are placed at either end, surrounding the source and sink, to prevent fluid leakage from the tube. The entire structure is immersed in a 256 x 32 x 32 point grid which is used for solving the fluid dynamics equations. The immersed boundary method is modified to improve its volume conservation properties. This modification has previously been implemented only in the two-dimensional case. Volume conservation is checked by integrating the source and sink flows and monitoring the volume enclosed by the tube and caps. Such a program can be used for a broad range of applications to the dynamics or biological fluids, among them, blood flow through a vein and air flow through the pulmonary system in the presence of diseases such as asthma that favor airway collapse.