Abstract
Numerical solution of the kinetics equation is crucial to engineering applications, but remains an extremely challenging task. In recent years, the quadrature-based moment methods (QBMM) are shown as effective numerical methods which preserve positivity of the distributions, have the conservation form and are numerically efficient. However, the mathematical theory of QBMM largely incomplete, and it is difficult to extend the existing approaches to tackle multidimensional problems. In this talk, I will present our recent efforts to clarify the well-posedness of QBMM. The hyperbolicity, realizability and dissipative properties of the moment closure systems are investigated. Then, we develop a discrete-velocity-direction model (DVDM) with minimum entropy principle as a novel and convenient multidimensional extension of the QBMM. In the DVDM, the molecular motion is confined to some prescribed directions but the speed is still a continuous variable in each orientation. Numerical tests with a series of 1-D and 2-D flow problems show the efficiency of the DVDM.
Speaker
黄骞，清华大学能源与动力工程系助理研究员，2017年毕业于清华大学获博士学位。主要从事动理学矩方法、清洁低碳燃烧技术等领域研究，承担自然基金等十余项课题，曾获教育部自然科学一等奖（2022）。
Personal Homepage:
https://www.te.tsinghua.edu.cn/info/1101/1695.htm
