Lattice Boltzmann model for Navier-Stokes equations with fractional Laplacian for turbulent Couette flow and parameters identification

主讲人：杜睿

摘要：Turbulence is a very complex flow phenomenal in nature, which can be described by the incompressible Navier-Stokes equations with hyper-singular integral fractional Laplacian 〖(-∆)〗^(α/2) (fLNSEs). In this paper, a lattice Boltzmann model with BGK operator (LBGK) is constructed based on the fractional centered difference scheme for solving this problem. Through Chapman-Enskog analysis, the macroscopic equations can be recovered from the LBGK model. On the other hand, it is very important to determine the differential orders of the fractional derivatives (fractional orders) in fractional system by using experimental data. We modify the physics-informed neural networks to solve the partial differential equations with fractional Laplacian based on the fractional central difference scheme (called fLPINNs). It can be used to identify the fractional order of the incompressible fLNSEs. Finally, numerical examples are provided to verify the effectiveness of LBGK model as well as fLPINNs. And fLPINNs can be applied to estimate model parameters in turbulent Couette flow.

主讲人简介： 2007年在华中科技大学获得博士学位后，加入东南大学数学学院，副教授。2020年入选江苏省高校“青蓝工程”优秀青年骨干教师培养对象. 先后访问美国佛罗里达大学、伍斯特理工学院进行学术研究与交流合作. 主要研究方向为格子Boltzmann方法的理论和应用以及微分方程数值解, 包括分数阶微分方程的高效数值方法等. 已在国内外主流学术期刊JCP、JSC等杂志发表学术论文近三十篇。主持国家自然科学基金项目2项、江苏省自然科学基金1项，参与若干项。

邀请人：柴振华

时间：2022年10月29日（星期六）14:30-16:30