Finite·Element Analysis of Two-Dimensional Peristaltic Flows : 1st Report, Finite-Element Solutions

Abstract

The finite-element method employing a variational technique is used to solve the full Navier-Stokes equations for peristaltic flows in a two-dimensional channel. The formulation for the non-linear convective terms employs the modified upwind scheme proposed by Dennis and Chang, which provides both computational stability and good solution accuracy even at a high Reynolds number. The interpolation function by which we can transform the numerical solutions at a triangular mesh into those at an arbitrary mesh is also obtained. Plots of the streamlines, vorticities, and velocities obtained in the study are presented. The effects of the Reynolds number and the wavenumber on this flow and the computational method for the non-linear convective terms are discussed. The results show that the inertia effects of the fluid and the effects of large wall slope enhance the backward flow from the narrowest region of the channel. It is important that the Dennis and Chang scheme be used in the formulation for non-linear convective terms when the Reynolds number is large.