Direct Collocation with Reproducing Kernel Approximation for Two-Phase Coupling System in a Porous Enclosure

The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As behavior in fluid-saturated porous media involves phase coupling, resulting system highly nonlinear nature. To this end, local adopted conjunction Newton–Raphson method. Nevertheless, unveil performance of analysis, only single thermal major concern herein. A unit square designated as model investigate parameters related convergence; several benchmark problems are used verify accuracy approximation, which stability demonstrated by considering various initial conditions, disturbance discretization, inclination, aspect ratio, support size. It shown that larger size can be flexible approximating irregular discretized problems. derivation explicit operators two-phase variables solving using carried out detail.