Meshless simulation of a lid-driven cavity problem with a non-Newtonian fluid

The purpose of the present paper is to solve the lid-driven cavity problem for a non-Newtonian power-law shear thinning and shear thickening fluid by a meshless method. Results are presented for Re=100 and Re=1000, where different levels of shear thinning and thickening are considered. Furthermore, the lid-driven cavity case is made geometrically more complex by adding several circular-shaped obstacles in the geometry. The Navier-Stokes equations are solved with the local meshless diffuse approximate method. The weighted least squares approximation is structured by using the second-order polynomial basis vector and the Gaussian weight function. The explicit Euler scheme is used to perform the artificial time stepping. The non-incremental pressure correction scheme is used to couple the pressure and the velocity fields. Results are presented in terms of viscosity contours, stream function, velocity vectors, mid-plane velocity and viscosity profiles for the steady state. The numerical method is verified by a comparison with the results obtained from the literature, which are computed with the least squares finite element formulation. Furthermore, an investigation of the node density and node distribution type is performed. A near perfect match with the reference solution and between the structured and unstructured node distribution is found. © 2021 The Author(s)