Unsteady Meshfree Framework for Double-diffusive Natural Convection with Boundary and Geometry Effects

In this study, a meshfree framework based on the reproducing kernel collocation method is proposed for incremental-iterative analysis of double-diffusive natural convection in a porous enclosure, in which the forward difference method is adopted for temporal discretization, and the two-step version of Newton-Raphson method is used for iteration. As the double-diffusive convection problem is composed of multi phases and is influenced by both material and geometric parameters, the resulting system is highly nonlinear and complicated. From the numerical investigation, the partially heated boundary with different buoyancy ratios can yield monocellular flow problems with opposite phenomena depending on the contribution of thermal/solute buoyancy force. For the domains with burrowing inside, the key feature is the contour of stream function, which is separated into two vortexes by the hole in the simply connected domain while the two vortexes are not separated completely in the multiply connected domain due to the geometric compression of two holes. It is further shown that the framework is capable of solving various double-diffusive convection problems with satisfactory accuracy and efficiency by uniform discretization as well as few source points in the approximation.