Contemporary Meshfree Methods for Three Dimensional Heat Conduction Problems

Abstract

This work aims to be a fairly comprehensive study on the respective performance of several meshfree schemes selected for 3D heat conduction problems. A wide array of such methods is implemented in this paper, two of which are employed in 3D for the first time. These methods are compared in a systematic fashion: First, their ability to approximate the Laplacian operator, the key ingredient of the heat equation, is examined. Synthetic benchmarks as well as a real-world engineering problem where experimental data is available follow. In the interest of reproducibility and knowledge dissemination, the complete source code is made public and can be downloaded from: https://github.com/mroethli/thermal_iwf.