This is exactly how our worm-LBM emulates "ballistic" heat carriers (e.g. phonons), on the computational grid. By staying on the grid, in contrast to other algorithms, the worm-LBM avoids numerical smearing and enables an accurate description of heat transport at the nano- and microscale, where ballistic transport prevails and the conventional Fourier heat equation fails. We are happy to announce that we have recently validated the worm-LBM algorithm and that it is ready for challenging “phonon resolved” thermal transport problems for future devices and applications.
Link: https://doi.org/10.1016/j.ijheatmasstransfer.2021.121030