报告人：雍稳安教授

报告题目：Discrete-velocity-direction models of BGK-type with minimum entropy

报告摘要：

(1) In this talk, I will present discrete-velocity-direction models (DVDMs) with collisions of BGK-type for simulating rarefied flows. Unlike the conventional kinetic models, the new models restrict the transport to finite fixed directions but leaves the transport speed to be a 1-D continuous variable. Analogous to the BGK equation, the discrete equilibriums of the new models are determined by minimizing a discrete entropy. We investigate the existence of the discrete equilibriums and the $H$-theorem. We also show that the discrete equilibriums can be efficiently obtained by solving a convex optimization problem.

(2) The proposed models provide a new way in choosing discrete velocities for the computational practice of the conventional discrete-velocity methodology. It also facilitates a convenient multidimensional extension of the extended quadrature method of moments. We validate the models with numerical experiments for a number of flows, including 2 D Riemann problems.

报告时间：2022.12.25   上午11:00-14:00

报告形式：腾讯会议；  会议号：349-804-159 

获取会议密码请发邮件至：yangchang@hit.edu.cn

报告人简介：雍稳安，清华大学长聘教授，博士生导师。1992年于德国海德堡大学取得博士学位，2005年取得德国教授资格（habilitation），其主要研究领域是偏微分方程、数值方法和非平衡态热力学。系统地建立了双曲偏微分方程松弛问题的数学理论，找到了这类问题的内在共性（Yong's stability condition）。创立了非平衡态热力学的守恒耗散理论（CDF），并成功地应用于生物、地学等领域，提出了已被实验验证的描述可压缩粘弹性流体流动的数学模型（Yong's model）。在计算流体力学方面，证明了工程上广泛使用的格子 Boltzmann 方法的稳定收敛性，并针对这种数值方法率先提出了单点边界格式（ZY method），已被广泛使用。主要结果发表在 Arch. Rational Mech. Anal.,  Automatica，J. Comput. Phys.，Philos. Trans. Royal Soc. A,  Siam 系列等相关领域的知名国际刊物上，有些结果已被若干权威专著和教材所采纳。