A Fully Meshless Approach to the Numerical Simulation of Heat Conduction Problems over Arbitrary 3D Geometries

One of the goals of new CAE (Computer Aided Engineering) software is to reduce both time and costs of the design process without compromising accuracy. This result can be achieved, for instance, by promoting a “plug and play” philosophy, based on the adoption of automatic mesh generation algorithms. This in turn brings about some drawbacks, among others an unavoidable loss of accuracy due to the lack of specificity of the produced discretization. Alternatively it is possible to rely on the so called “meshless” methods, which skip the mesh generation process altogether. The purpose of this paper is to present a fully meshless approach, based on Radial Basis Function generated Finite Differences (RBF-FD), for the numerical solution of generic elliptic PDEs, with particular reference to time-dependent and steady 3D heat conduction problems. The absence of connectivity information, which is a peculiar feature of this meshless approach, is leveraged in order to develop an efficient procedure that accepts as input any given geometry defined by a stereolithography surface (.stl file format). In order to assess its performance, the aforementioned strategy is tested over multiple geometries, selected for their complexity and engineering relevance, highlighting excellent results both in terms of accuracy and computational efficiency. In order to account for future extensibility and performance, both node generation and domain discretization routines are entirely developed using Julia, an emerging programming language that is rapidly establishing itself as the new standard for scientific computing.