Numerical simulation of unsteady moving boundary flows in physiological systems using finite volume methods

In this work unsteady moving boundary problems characterising physiological flows are simulated using a finite volume numerical method for solving the integral form of the unsteady incompressible Navier-Stokes equations for both Newtonian and non-Newtonian flows. The method is applied to simulate a channel flow with an indentation on one of its walls which moves in a prescribed cyclic manner. Differences between unsteady Newtonian and non-Newtonian flows are assessed by a power-law model exhibiting shear thinning viscosity. The investigation shows that for a non-Newtonian fluid, there are differences in the velocity profiles and in the structure and size of the reversed flow region as compared with the corresponding Newtonian fluid. The comparison of non- Newtonian and Newtonian wall shear stress reveals a slight decrease of magnitude on the average for the non- Newtonian case. The method is also applied to simulate peristaltic pumping flow through a circular tube by means of an infinite train of sinusoidal waves travelling along the wall of an axi-symmetric tube. The computational modelling presented in this work is extended to moderate Reynolds number, wave amplitude, and wavelength. Some new results of velocity, pressure, wall shear stress distribution for different peristaltic flow conditions ahave been obtained. The effect of the wave amplitude, wavelength and Reynolds number on the trapping phenomena is also investigated.