Numerical simulation of Newtonian and non-Newtonian flows in bypass

This paper deals with the numerical solution of Newtonian and non-Newtonian flows with biomedical applications. The flows are supposed to be laminar, viscous, incompressible and steady or unsteady with prescribed pressure variation at the outlet. The model used for non-Newtonian fluids is a variant of power law. Governing equations in this model are incompressible Navier–Stokes equations. For numerical solution we use artificial compressibility method with three stage Runge–Kutta method and finite volume method in cell centered formulation for discretization of space derivatives. The following cases of flows are solved: steady Newtonian and non-Newtonian flow through a bypass connected to main channel in 2D, steady Newtonian flow in angular bypass in 3D and unsteady non-Newtonian flow through bypass in 2D. Some 2D and 3D results that could have application in the area of biomedicine are presented.