Local Time-Step TLM Unstructured Block Meshing for Electromagnetic and Bio-Thermal Applications
Résumé
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.
Mots clés
computational electromagnetics
heat transfer
time-domain analysis
transmission line matrix methods
CFL limit
Courant-Friedrichs-Lewy limit
bio-thermal applications
cell aspect ratio
computational domain
cubic cells
electromagnetic applications
fine discretization
heat transfer TLM models
interfacing block regions
irregular structured grids
local time-step TLM unstructured block meshing
memory cost reduction
quasihomogenous regions
substantial coarseness error reduction
time-domain transmission-line matrix
uniform fine grid
Biological system modeling
Computational modeling
Finite difference methods
Mathematical model
Media
Time-varying systems
Bio-heat equation
block meshing
local time step
long-term stability
multiphysics
multiscale problems
time-domain methods
transmission-line matrix method (TLM)