Adaptive RBF-FD meshless solution of 3D fluid flow and heat transfer problems

Abstract

This paper describes an adaptive approach for the solution of 3D steady and incompressible flows with the RBF-FD (Radial Basis Function-Finite Difference) meshless method. This method relies on a set of scattered nodes in the domain instead of a traditional mesh data structure. The lack of connectivity information and the absence of the mesh generation make the RBF-FD method particularly advantageous for the accurate numerical solution of many problems of engineering interest. Furthermore, automatic node generation is possible thanks to many algorithms that recently have been proposed. However, as it happens for mesh-based methods, the accurate solution of partial differential equations usually require proper node distributions with higher node density in specific areas. The approach described in this paper allows the re-generation of the entire node distribution in order to minimize some error indicator by automatically adjusting local node density depending on the domain and physical problem. The main contribution of this work is the introduction of some original error indicators which are used for the aforementioned adaptive node generation and the assessment of their effect on accuracy. Results show good convergence properties and highlight some differences in the behaviour of the different adaptive approaches in the spatial error distribution