Numerical and Asymptotic Solutions for Peristaltic Motion of Nonlinear Viscous Flows with Elastic Free Boundaries

A mathematical model for peristaltic motion of nonlinear viscous flows with elastic free boundaries is introduced. An iterative numerical method is used to solve the free boundary problem. Long wave asymptotic expansion is developed and the zeroth order approximation is used as the numerical initial condition. The existence and uniqueness of the solution for the free boundary equation derived from the long wave expansion are proved. Computations were conducted to study the long wave approximation, the numerical solutions for the exact equations, and the influences of the parameters on the solutions. Key words, peristaltic, Navier-Stokes, long wave, free boundary, elasticity AMS subject classifications. 76, 39, 41, 34