In this paper an LBGK model for thermocapillary flow in microgravity is proposed. In the model two distribution functions are used for the velocity and temperature fields, respectively. Through the Chapman-Enskog expansion, the macroscopic equations for the thermocapillary flow can be recovered from the LBGK model. The boundary conditions for the thermocapillary flow are treated using the non-equilibrium extrapolation scheme. The model is validated by simulating the thermocapillary flow in a two-dimensional (2D) square cavity with a single free surface and differentially heated side walls. © 2007 Elsevier Ltd. All rights reserved.
Du, R., & Shi, B. (2008). The lattice Boltzmann method for the thermocapillary flow in a cavity under microgravity condition. Computers and Mathematics with Applications, 55(7), 1433–1440. https://doi.org/10.1016/j.camwa.2007.08.008