Numerical simulation of pulsatile flow in constricted axi-symmetric tubes

Abstract

A finite element algorithm is presented to solve the Navier—Stokes equations in an axi-symmetric tube of variable cross-section. The stream function and the vorticity are used as the unknown variables and under this formulation the relevant set of equations is solved in an explicit form using linear interpolating functions and the Galerkin approach. The element integrals corresponding to this type of equations are computed through explicit multiplication and term-by-term integration. The algorithm presented consists of an iterative procedure which ensures periodic solutions in both time and space. The accuracy of the model was satisfactorily tested against analytical solutions for straight tubes. The laminar oscillating flow of a Newtonian fluid through a tube with periodically varying cross-section is adopted as an approximation to the pulsatile flow in blood vessels. The effect of varying the basic parameters in this complicated flow can be evaluated by the means of solutions obtained from the finite element model. Using a representative set of cases it is shown that important properties, such as velocities and shear stresses, are strongly influenced by changes in the flow characteristics.