Correction to: Scientific Reports https://doi.org/10.1038/s41598-025-20747-7, published online 21 October 2025

The original version of this Article contained errors in the title of the paper. As a result, in the subsection Lattice Boltzmann formulation for fluid flow and heat transfer, the first sentence Reference 25 was replaced with Reference 23. As a result:

“Based on the simplified double distribution function model (DDF) in reference [25], this paper adopts the single relaxation time format and introduces the external force term to construct the lattice Boltzmann equations (LBEs) for flow and heat transfer respectively and solves the momentum and energy distribution functions fi(x, t) and gi(x, t) at the mesoscale.”

now reads:

“Based on the simplified double distribution function model (DDF) in reference [23], this paper adopts the single relaxation time format and introduces the external force term to construct the lattice Boltzmann equations (LBEs) for flow and heat transfer respectively and solves the momentum and energy distribution functions fi(x, t) and gi(x, t) at the mesoscale.”

Additionally, the Reference List was revised. In the original Article Reference 23 was erroneously listed as: Peng, Y., Shu, C. & Chew, Y. T. Simplified thermal lattice Boltzmann model for incompressible thermal flows [J]. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 68(2 Pt 2), 026701 (2003).

Reference 23 was revised to: Yu Wenxu, Guan Xiangyu, Zhao Junyi, et al. Transient Temperature Rise Simulation and Load Capacity Evaluation of Oil-immersed Transformer Based on Lattice Boltzmann Method [J]. Transactions of the Chinese Society for Electrical Engineering, 2025, 40(10): 3315–3325. https://doi.org/10.19595/j.cnki.1000-6753.tces.240772.

The original Article has been corrected.