Numerical analysis of advection-diffusion problems on 2D general-shaped domains by means of a RBF Collocation Meshless Method

A Collocation Meshless Method based on local Radial Basis Function (RBF) interpolation is employed to solve two-dimensional advection-diffusion problems with particular reference to the incompressible Navier-Stokes equations in their transient form, i.e., unsteady flows, using primitive variables (U,p). A projection scheme is employed to decouple the continuity and momentum equations; particular attention is given to the choice of the required solvers. This approach is applied to the simulation of unsteady flows for two typical test cases, i.e., the lid-driven cavity problem and the flow past a circular cylinder between parallel walls. Numerical results compare very favorably with literature ones, confirming that this approach can be effectively employed in the numerical simulation of unsteady flows on practical geometries where complex node distributions and large number of nodes are required.