Refined radial basis function-generated finite difference analysis of non-Newtonian natural convection

In this paper, we present a refined radial basis function-generated finite difference solution for a non-Newtonian fluid in a closed differentially heated cavity. The non-Newtonian behavior is modeled with the Ostwald–de Waele power law and the buoyancy with the Boussinesq approximation. The problem domain is discretized with scattered nodes without any requirement for a topological relation between them. This allows a trivial generalization of the solution procedure to complex irregular three dimensional (3D) domains, which is also demonstrated by solving the problem in a two dimensional (2D) and 3D geometry mimicking a porous filter. The results in 2D are compared with two reference solutions that use the finite volume method in a conjunction with two different stabilization techniques, where we achieved good agreement with the reference data. The refinement is implemented on top of a dedicated meshless node positioning algorithm using piecewise linear node density function that ensures sufficient node density in the center of the domain while maximizing the node density in a boundary layer where the most intense dynamic is expected. The results show that with a refined approach, more than five times fewer nodes are required to obtain the results with the same accuracy compared to the regular discretization. The paper also discusses the convergence with refined discretization for different scenarios for up to 2×105 nodes, the impact of method parameters, the behavior of the flow in the boundary layer, the behavior of the viscosity, and the geometric flexibility of the proposed solution procedure.