Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45366220200401Numerical Simulation of Non-Newtonian Inelastic Flows in Channel based on Artificial Compressibility Method2712831469910.22055/jacm.2019.29948.1650ENReisan Y.YasirDepartment of Mathematics, College of Science, University of Basrah, Basrah, Iraq0000-0002-5553-0389Alaa H.Al-MuslimawiDepartment of Mathematics, College of Science, University of Basrah, Basrah, Iraq0000-0002-1427-5094Bashaeer K.JassimDepartment of Mathematics, College of Science, University of Basrah, Basrah, Iraq0000-0002-0274-9598Journal Article20190616In this study, inelastic constitutive modelling is considered for the simulation of shear-thinning fluids through a circular channel. Numerical solutions are presented for power-law inelastic model, considering axisymmetric Poiseuille flow through a channel. The numerical simulation of such fluid is performed by using the Galerkin finite element approach based on artificial compression method (<em>AC</em>-method). Usually, the Naiver-Stoke partial differential equations are used to describe fluid activity. These models consist of two partial differential equations; a continuity equation (mass conservation) and time-dependent conservation of momentum, which are maintained in the cylindrical coordinate system (axisymmetric) flow in current study. The effects of many factors such as Reynolds number (<em>Re</em>) and artificial compressibility parameter (ß<sub>ac</sub>) are discussed in this study. In particular, this study confirms the effect of these parameters on the convergence level. To meet the method analysis, Poiseuille flow along a circular channel under an isothermal state is used as a simple test problem. This test is conducted by taking a circular section of the pipe. The Findings reveal that, there is a significant effect from the inelastic parameters upon the the velocity temporal convergence-rates of velocity, while for pressue, the change in convergence is modest. In addition, the rate of convergence is increased as the values of artificial compressibility parameter (ß<sub>ac</sub>) are decreased.http://jacm.scu.ac.ir/article_14699_fe042cf6c8c12d9b83d37e24cc9df375.pdf