Cavity flow simulation of Carreau–Yasuda non-Newtonian fluids using PIM meshfree method

Lid-driven cavity flow of a purely-viscous non-Newtonian fluid obeying Carreau–Yasuda rheological model is studied numerically using the PIM meshfree method combined with the Characteristic-Based Split-A algorithm. Results are reported for the velocity and pressure profiles at Reynolds numbers as high as 1000 for a non-Newtonian fluid obeying Carreau–Yasuda rheological model. For Newtonian fluids, results obtained from our PIM–CBS-A method show good agreement with benchmark results published in the literature and obtained using finite difference and/or Finite Element Methods. Our numerical results are also consistent with recent published results obtained using another meshfree method called LSM with the advantage that PIM needs less “points” to achieve the same degree of accuracy. Results obtained for the Carreau–Yasuda model reveals the strong effect of the shear-thinning behavior of a fluid on its flow kinematics within the cavity.