Node generation in complex 3D domains for heat conduction problems solved by RBF-FD meshless method

Abstract

A novel algorithm is presented and employed for the fast generation of meshless node distributions over arbitrary 3D domains defined by using the stereolithography (STL) file format. The algorithm is based on the node-repel approach where nodes move according to the mutual repulsion of the neighboring nodes. The iterative node-repel approach is coupled with an octree-based technique for the efficient projection of the nodes on the external surface in order to constrain the node distribution inside the domain. Several tests are carried out on three different mechanical components of practical engineering interest and characterized by complexity of their geometry. The generated node distributions are then employed to solve a steady-state heat conduction test problem by using the Radial Basis Function-generated Finite Differences (RBF-FD) meshless method. Excellent results are obtained in terms of both quality of the generated node distributions and accuracy of the numerical solutions.