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The following paper describes a numerical simulation of a complete bypass of a stenosed human artery. The considered geometry consists of the narrowed host tube and the bypass graft with a 45-degree angle of connection. Different diameters of the narrowing are tested. Blood is the fluid with shear rate–dependent viscosity; therefore, various rheology mathematical models for generalized Newtonian fluids are considered, namely Cross model, modified Cross model, Carreau model, and Carreau-Yasuda model. The fundamental system of equations is based on the system of generalized Navier-Stokes equations. Generalized Newtonian fluids flow in a bypass tube is numerically simulated by using a SIMPLE algorithm included in the open-source CFD tool, OpenFOAM. The aim of this work is to compare the numerical results for the different mathematical models of the viscosity with the changing diameter of the narrowed channel. [ABSTRACT FROM AUTHOR]

This work deals with the numerical solution of laminar incompressible viscous flow for generalized Newtonian fluids in a branching channel. The governing system of equations is the system of generalized Navier-Stokes equations for incompressible viscous fluids flow. Generalized Newtonian fluids can be divided to two parts: shear thickening fluids and shear thinning fluids. Newtonian fluids are the special case with constant viscosity. For a viscosity function a power-law model is used. Numerical solution of the described model is based on cell-centered finite volume method using explicit Runge-Kutta time integration. The time-marching system of equations with steady boundary conditions is solved by finite volume method in conjunction with an artificial compressibility method. For the time integration an explicit multistage Runge-Kutta method of the second order of accuracy is used. In the case of unsteady computation two numerical methods are considered, artificial compressibility method and dual-time stepping method. Numerical results obtained by these methods are presented and compared. [ABSTRACT FROM AUTHOR]