Numerical analysis of heat conduction problems on 3D general-shaped domains by means of a RBF Collocation Meshless Method

A Collocation Meshless Method based on Radial Basis Function (RBF) interpolation is employed to solve steady state heat conduction problems on 3D domains of arbitrary shape. The set of points required by the numerical method is generated through a novel and simple technique which automatically produces a distribution with variable point density and which adapts to each specific geometry. Numerical results are systematically compared to the corresponding analytical solutions considering several combinations of parameters; convergence tests have also been carried out. The favorable properties that will be outlined suggest that this approach can be an effective and flexible tool in the numerical simulation of heat conduction problems with complex 3D geometries.