Nonlinear steady of natural convection through 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 dis-cretization 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 cylinder, 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.