A Free Moving Boundary Model and Boundary Iteration Method for Unsteady Viscous Flow in Stenotic Elastic Tubes

A nonlinear mathematical model with a free moving boundary was introduced to study viscous flow in stenotic elastic tubes subject to a prescribed external pressure at the tube wall and pulsatile pressure drop between the tube inlet and outlet. An iterative numerical method using boundary iteration, pseudocompressibility, and the ADI technique was developed to solve the model. Unsteady effects of stenosis severity and the imposed pressure conditions on the tube wall and flow are studied. Special attention was paid to tube contractions because they can be indications of the tube collapsing. It was found that stenosis can cause more severe tube expansion and contraction under unsteady conditions. The complicated unsteady wall motion can be understood as the superposition of the static tube expansion and contraction caused by the stenosis and as the unsteady tube expansion and contraction caused by the imposed, unsteady pressure conditions.