Numerical investigation of inelastic Fluid Flows based on Artificial Compressibility Method

Department of Mathematics, Faculty of Computer Sciences & Mathematics, University of Kufa, Kufa, Iraq.

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 13 May 2026

Abstract

This article presents a numerical investigation of two distinct incompressible non-Newtonian flow configurations. The first one deals with flow through a straight channel, the second one concerns flow in a square cavity subjected to the uniform translation of the upper lid at a given velocity both in two-dimensional space. For both geometries, analytical solutions are derived and subsequently employed to define appropriate boundary conditions. Numerically, the governing equations is solved by an artificial compressibility approach in combination with the Galerkin finite element method. Fluid system is governed by the Navier-Stokes equations (N-S), and non-Newtonian characteristics are captured using the power-law constitutive relation. The work systematically investigates the influence of changes in power-law index (n) on velocity and pressure fields for both flows. Moreover, convergence characteristics of the numerical scheme being considered are discussed and for all tested n-values an efficient and reliable convergence within a velocity field is observed. The presented data is validated against the state-of-art data available in the literature leading to concurrence with existing results thus ensuring strength and robustness of the methodology.