High-order artificial compressibility algorithm for simulating non-Newtonian fluid flows

A high-order accurate time-marching algorithm is presented with computational efficiency using the Taylor–Galerkin finite element method, which is based on the extension of artificial compressibility equations to effectively simulate the complex behavior of non-Newtonian fluids under stick-slip boundary conditions. The rheology of non-Newtonian fluids is described by the power-law model, which involves shear thinning ([Formula: see text]), shear thickening ([Formula: see text]) and Newtonian flow ([Formula: see text]). This study examines the effects of key factors influencing the behavior of these fluids. It includes an investigation of fluid rheology (pseudoplasticity or dilatancy) on velocity and pressure distribution, as well as the impact of dimensionless Reynolds numbers and the effects of slipping on flow behavior, with a specific focus at the transition to the slipping zone within the singularity. We observe a peak in shear rate here, which significantly changes the stress distribution within the channel. Furthermore, the algorithm demonstrates high accuracy in convergence while requiring significantly less computational time than certain highly accurate algorithms found in the literature, highlighting its computational efficiency. In addition, we examined the impact of the Mach number on the solutions, and the simulation results demonstrated excellent agreement with previous studies, particularly at low Mach numbers. Our study indicates that the proposed algorithm is worthwhile in the limelight.