Nonlinear steady-state analysis of natural convection using a high-order continuation approach

Abstract

In this investigation, we present a novel Meshfree method for addressing nonlinear steady natural convection equations, leveraging the Radial Point Interpolation Method (RPIM) for discretization and a high-order continuation procedure for solution computation. The proposed approach is validated through examples involving two-dimensional air-filled cavities with diverse geometries and different boundary conditions, considering constant fluid properties except density. The numerical simulations demonstrate good agreement with Finite Element Method (FEM) and literature data. Various parameters, such as Rayleigh number, angular position of the inner elliptic and hexagonal cylinders, and radius of the inner circular cylinder, are systematically analyzed. Results, including streamlines, isotherms, and average equivalent conductivity, are presented graphically, establishing the effectiveness and accuracy of the proposed method.