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.

报告人简介：柴振华，教授，博士生导师，教育部青年长江学者，华中卓越学者特聘教授。近年来，主要从事多相流体系统的建模与介观格子Boltzmann方法研究，主持和参与国家自然科学基金、国家重点研发计划等国家级项目10余项，在SIAM J. Sci. Comput.、Multiscale Model. Simul.、J. Comput. Phys.、Physica D, Phys. Rev. E等国内外权威学术期刊共发表学术论文160余篇，SCI他引4200余次。担任湖北省工业与应用数学学会副理事长、中国工业与应用数学学会理事、中国工业与应用数学学会数学力学专委会委员等学术兼职，《计算物理》《International Journal of Fluid Engineering》等杂志编委。