Computational investigation of non-Newtonian inelastic flows in a 4:1 contraction based on artificial compressibility method

An efficient numerical scheme is proposed in this study through a combination of the artificial compressibility (AC) and Taylor–Galerkin pressure–correction (TG–PC) methods. This strategy is realized by rewriting the continuity equation with the artificial compressibility formulation and then incorporating it into the TG–PC numerical framework. The performance of the proposed method is illustrated by solving the Navier–Stokes equations which describe incompressible inelastic non-Newtonian flow through a 4:1 contraction channel. The power-law-type constitutive relation is included to take the viscosity of the fluid into consideration. Convergence behavior of the numerical solution for velocity and pressure fields is systematically studied with changes to the artificial compressibility parameter ( β ac ) , power-law index ( n ) , and Reynolds number ( R e ) . Moreover, a comparison between the artificial compressibility and its incompressible counterpart is made to reveal any influence on the computed velocity and pressure fields. Further, the influences of power-law index on shear rate as well as normal stress at the bottom wall of the contraction are studied. The formation and evolution of the recirculation region is also discussed and a measure for the vortex length is proposed to describe stretching properties under different rheology conditions.