Local Time-Step TLM Unstructured Block Meshing for Electromagnetic and Bio-Thermal Applications

Many practical problems are of multiscale nature. This issue appears when relatively small regions inside the computational domain have a large impact on the overall behavior of the structure. This requires using small mesh size in these regions of interest for adequately representing their geometrical details. Using uniform fine grid everywhere is computationally very exhaustive. The use of irregular structured grids may lead to some memory cost reduction as compared to uniform fine mesh. However, it imposes a smaller time step and yields higher dispersion as cell aspect ratio deviates from unity. The alternate approach is to use block meshing which allows fine discretization in regions with fine details and larger mesh size in quasi homogenous regions. The main disadvantage of this technique is that a global time step corresponding to the Courant-Friedrichs-Lewy (CFL) limit in the smallest cells should be used to avoid long-term instability. In this paper, we present a time-domain transmission-line matrix (TLM) algorithm for interfacing block regions that allows the use of local time steps. Hence, cubic cells can be optimally used in all regions with substantial coarseness error reduction. Applied to both electromagnetic and heat transfer TLM models, simulation experiments are presented to show the behavior and performances of the algorithm.