Two-Dimensional Thermal Diffusion Equation Solver Based on Unstructured Transmission-Line Modelling and Optimal Delaunay Triangular Meshes

The transmission-line modelling (TLM) method has been widely applied to many areas including electromagnetic and heat conduction problems. Its unstructured version, unstructured TLM (UTLM), however, has not hitherto been fully exploited in thermal diffusion problems. This paper derives in detail a thermal UTLM scheme to solve the two-dimensional diffusion equation numerically based on the optimal Delaunay triangular (ODT) mesh.