The worm-LBM: enabling accurate ballistic-diffusive phonon transport

Direct discretization schemes for the Boltzmann transport equation (BTE) are plagued by numerical smearing, angular false scattering, and ray effect. The lattice Boltzmann method (LBM) has the advantage that it does not suffer from the first two problems. But, the limited angular resolution responsible for the ray effect hinders the application of conventional LBM in the ballistic regime.
We propose the worm-LBM algorithm, which allows for a high number of propagation directions by alternating in time the basic directions described within the next neighbor LBM schemes [1]. Here we will present the algorithm's structure and its accuracy for describing various ballistic-diffusive phonon transport cases.

[1] R. Hammer, V. Fritz, and N. Bedoya-Martínez, "The worm-LBM, an algorithm for a high number of propagation directions on a lattice Boltzmann grid: the case of phonon transport" arXiv preprint arXiv:1911.00180v2 (2020).