# Article

**Keywords:**

viscous fluids flow; generalized Newtonian fluids; cross model; finite volume method; Runge-Kutta scheme; artificial compressibility method

**Summary:**

This work presents the numerical solution of laminar incompressible viscous flow in a three dimensional branching channel with circular cross section for generalized Newtonian fluids. This model can be generalized by cross model in shear thinning meaning. The governing system of equations is based on the system of balance laws for mass and momentum. Numerical tests are performed on a three dimensional geometry, the branching channel with one entrance and two outlet parts. Numerical solution of the described model is based on central finite volume method using explicit Runge--Kutta time integration. The steady state solution is achieved for $t \rightarrow \infty$. In this case the artificial compressibility method will be applied. In the case of unsteady computation artificial compressibility method is considered.