Nonlinear Meshfree Collocation Method for Solving Double-Diffusive Natural Convection in a Porous Enclosure

A meshfree collocation method formulated by using reproducing kernel shape functions with Newton-Raphson method is presented with application to analyzing a three-phase coupling system in a porous enclosure. To tackle such a highly nonlinear phenomenon caused by double-diffusive natural convection, direct collocation using local approximation in conjunction with a two-step iteration solver is employed to stably and efficiently solve this problem. It has been shown that a determined and well-conditioned system is established under the collocation framework with reproducing kernel approximation. By conducting the parametric study, the numerical results have demonstrated the robustness of the proposed method in analyzing the porous enclosure by considering various geometry, boundary conditions, and governing parameters.