Improved lattice Boltzmann method for conjugate magnetohydrodynamic simulations
Abstract
In the simulation of conjugate magnetohydrodynamic (MHD) flows, where a moving conducting fluid dynamically interacts with bounding conducting walls under the influence of an externally imposed magnetic field, resolving the electrical conductivity transition across the fluid-solid interface introduces significant numerical challenges. In problems with high magnetic Reynolds numbers, it is required to solve the full magnetic induction formulation that has a curl-of-curl term for the magnetic diffusion, which is simplified to a divergence term in the original vector-valued lattice Boltzmann method (LBM). The resulting LBM scheme is valid for simulating fluid domains with a constant conductivity where its bounding solid walls are modelled using appropriate boundary conditions. The current study shows that this scheme is also valid for two-dimensional conjugate MHD simulations where the magnetic field component with non-zero gradients is perpendicular to the conductivity gradient. For general conjugate MHD simulations, we improve the LBM scheme by considering the difference between the curl-of-curl term and the simplified divergence form, which is treated as a source term in the LBM evolution algorithm and computed using an efficient LBM discretisation scheme. The improved LBM scheme automatically satisfies the required conjugate constraints at the fluid-solid interface as a volume integral inside two adjacent boundary layers. The accuracy of the improved LBM scheme is verified by piecewise analytical solutions in benchmark problems with an abrupt conductivity jump across the fluid-solid interface.
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BibTeX
@misc{li2026improved,
title = {{Improved lattice Boltzmann method for conjugate magnetohydrodynamic simulations}},
author = {Jun Li and Wai Hong Ronald Chan and Kun Ting Eddie Chua},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18097},
eprint = {2609.18097},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18097},
}
RIS
TY - UNPB
TI - Improved lattice Boltzmann method for conjugate magnetohydrodynamic simulations
AU - Jun Li
AU - Wai Hong Ronald Chan
AU - Kun Ting Eddie Chua
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18097
UR - https://arxiv.org/abs/2609.18097
AB - In the simulation of conjugate magnetohydrodynamic (MHD) flows, where a moving conducting fluid dynamically interacts with bounding conducting walls under the influence of an externally imposed magnetic field, resolving the electrical conductivity transition across the fluid-solid interface introduces significant numerical challenges. In problems with high magnetic Reynolds numbers, it is required to solve the full magnetic induction formulation that has a curl-of-curl term for the magnetic diffusion, which is simplified to a divergence term in the original vector-valued lattice Boltzmann method (LBM). The resulting LBM scheme is valid for simulating fluid domains with a constant conductivity where its bounding solid walls are modelled using appropriate boundary conditions. The current study shows that this scheme is also valid for two-dimensional conjugate MHD simulations where the magnetic field component with non-zero gradients is perpendicular to the conductivity gradient. For general conjugate MHD simulations, we improve the LBM scheme by considering the difference between the curl-of-curl term and the simplified divergence form, which is treated as a source term in the LBM evolution algorithm and computed using an efficient LBM discretisation scheme. The improved LBM scheme automatically satisfies the required conjugate constraints at the fluid-solid interface as a volume integral inside two adjacent boundary layers. The accuracy of the improved LBM scheme is verified by piecewise analytical solutions in benchmark problems with an abrupt conductivity jump across the fluid-solid interface.
ER -