Numerical modelling of incompressible flows for Newtonian and non-Newtonian fluids

This paper deals with numerical solution of two-dimensional and three-dimensional steady and unsteady laminar incompressible flows for Newtonian and non-Newtonian shear thickening fluids flow through a branching channel. The mathematical model used in this work is the generalized system of Navier–Stokes equations. The right hand side of this system is defined by the power-law model. The finite volume method combined with artificial compressibility method is used for numerical simulations of generalized Newtonian fluids flow. Numerical solution is divided into two parts, steady state and unsteady. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behaviour. For unsteady solution high artificial compressibility coefficient β2 is considered. An artificial compressibility method with a pulsation of the pressure in the outlet boundary is used.