Compact Integrated Radial Basis Function (CIRBF) for natural convection flow in a square cavity

This paper presents a numerical scheme to approximate a set of differential equations establishing the behavior of Newtonian fluid motion. The three primary differential equations are the continuity equation, the momentum equation (aka the Navier-Stokes equation) and the energy equation. The paper uses a numerical approach namely Compact Integrated Radial Basis Function (CIRBF) to approximate space variables whereas Crank-Nicolson and Adams-Bashforth methods are adopted to discretize temporal variables. More specifically, the spatial approximation at a point is obtained by collecting the desired information of two adjacent nodes along with their corresponding derivatives. Our scheme is verified by comparison with the benchmark solution of natural convection flow in a square cavity. The solution is in good agreement with the previously published results, thereby showing the robustness and reliability of CIRBF approach. Keywords: radial basis function (RBF), natural convection flow, square cavity, numerical scheme.