Localized Meshless Modeling of Natural-Convective Viscous Flows

A localized radial-basis function (RBF) collocation meshless method is developed for natural-convection heat transfer problems in fully viscous fluid flows. The expansion method is based on the localized collocation of polynomial-augmented Hardy multiquadrics RBF, and it is efficiently formulated to generate derivative fields through simple inner products of small-order vectors. The solution of the Navier-Stokes equations is formulated using a third-order-accurate explicit fractional time-stepping method and a velocity-correction scheme. Several cases are studied and confirmed to attain accurate results when compared to classical benchmark solutions as well as numerical predictions provided by the commercial computational fluid dynamics code Fluent.