Abstract
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.
Highlights
The governing system of equations is the system of balance laws of mass and momentum for incompressible fluids
Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge–Kutta time integration
The homogeneous Dirichlet boundary condition for the velocity vector is used on the wall
Summary
The governing system of equations is the system of balance laws of mass and momentum for incompressible fluids. This system is completed by the equation for a viscoelastic part of stress tensor, [1]: div u = 0. The symbols Ts and Te represent the Newtonian and viscoelastic parts of the stress tensor and. In this case the viscosity μ is defined by viscosity function according to the cross model (for more details see [8]).
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