# Article

**Keywords:**

Oldroyd-B fluids; finite volume method; artificial compressibility; branching channel

**Summary:**

The aim of this paper is to describe the numerical results of numerical modelling of steady flows of laminar incompressible viscous and viscoelastic fluids. The mathematical models are Newtonian and Oldroyd-B models. Both models can be generalized by cross model in shear thinning meaning.
Numerical tests are performed on three dimensional geometry, a branched channel with one entrance and two output parts. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge–Kutta time integration. Steady state solution is achieved for $t \rightarrow \infty$. In this case the artificial compressibility method can be applied.