In this talk, we will first present the macroscopic finite-difference scheme of the mesoscopic lattice Boltzmann method, and then show some details on how to develop the high-order lattice Boltzmann schemes for some different kinds of partial differential equations, including the diffusion equations, convection equations, and convection-diffusion equations. In addition, we also conduct the theoretical stability analysis on the consistency and stability of these high-order lattice Boltzmann models. Finally, we perform some tests on the high-order lattice Boltzmann models, and find that the numerical results are consistent with our theoretical analysis.

Speaker's Profile: Chai Zhenhua, Professor, Doctoral Supervisor, Young Changjiang Scholar of the Ministry of Education, and Distinguished Professor of Huazhong Outstanding Scholars. In recent years, I have mainly been engaged in modeling multiphase fluid systems and researching the mesoscopic lattice Boltzmann method. I have led and participated in more than 10 national level projects such as the National Natural Science Foundation and the National Key Research and Development Program SIAM J. Sci. Comput.、Multiscale Model. Simul.、J. Comput. Phys.、Physica D, Phys. Rev. E More than 160 academic papers have been published in authoritative domestic and foreign academic journals, with over 4200 citations in SCI. Served as Vice Chairman of the Hubei Society of Industrial and Applied Mathematics, Director of the Chinese Society of Industrial and Applied Mathematics, and Member of the Mathematical Mechanics Special Committee of the Chinese Society of Industrial and Applied Mathematics. Also served as Editorial Committee Member for journals such as Computational Physics and International Journal of Fluid Engineering.