# Article

**Keywords:**

generalized Newtonian fluid; Oldroyd-B fluid; finite volume method; Runge-Kutta scheme

**Summary:**

This work deals with the numerical solution of generalized Newtonian and Oldroyd-B fluids flow. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible laminar viscous and viscoelastic fluids. Two different definition of the stress tensor are considered. For viscous case Newtonian
model is used. For the viscoelastic case Oldroyd-B model is tested. Both presented models can be generalized. In this case the viscosity is defined as a shear rate dependent viscosity function $\mu (\dot{\gamma})$. One of the most frequently used shear-thinning models is a cross model. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge Kutta time integration. The numerical results of generalized
Newtonian and generalized Oldroyd-B fluids flow obtained by this method are
presented and compared.