# Article

**Keywords:**

incompressible viscous flow; generalized Newtonian fluids; artificial compressibility; finite volume method

**Summary:**

This article presents the numerical solution of laminar incompressible viscous flow in a branching channel for generalized Newtonian fluids. The governing system of equations is based on the system of balance laws for mass and momentum. The generalized Newtonian fluids differ through choice of a viscosity function. A power-law model with different values of power-law index is used. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge--Kutta time integration. The unsteady system of equations with steady boundary conditions is solved by finite volume method. Steady state solution is achieved for $t \rightarrow \infty$. In this case the artificial compressibility method can be applied. For the time integration an explicit multistage Runge--Kutta method of the second order of accuracy in the time is used. In the case of unsteady computation two numerical methods are considered, artificial compressibility method and dual-time stepping method. The flow is modelled in a bounded computational domain. Numerical results obtained by this method are presented and compared.