Numerical solution of unsteady generalized Newtonian and Oldroyd-B fluids flow by dual time-stepping method

This work deals with the numerical solution of viscous and viscoelastic fluids flow. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible laminar fluids. Different models for the stress tensor are considered. For viscous fluids flow Newtonian model is used. For the describing of the behaviour of the mixture of viscous and viscoelastic fluids Oldroyd-B model is used. Numerical solution of the described models is based on cell-centered finite volume method in conjunction with artificial compressibility method. For time integration an explicit multistage Runge-Kutta scheme is used. In the case of unsteady computation dual-time stepping method is considered. The principle of dual-time stepping method is following. The artificial time is introduced and the artificial compressibility method in the artificial time is applied.