动态电离等离子体的多尺度数值格式研究

In this project, we are going to develop a multi-scale numerical method (UGKS-Plasma) for partially ionized plasma based on the unified gas kinetic scheme. The UGKS-Plasma is a direct modeling method on discrete space and time, based on the multi-component kinetic equations and Maxwell equations. The key is the construction of the multi-scale numerical flux, the modeling of collision term and the coupling between the flow field and the electromagnetic field. The UGKS-Plasma is capable of capturing the flow physics of plasma from the rarefied regime to the continuum regime and can be used to describe the quasi-neutral plasma in the highly magnetized limiting regime. With proper implementation of ionization model, the UGKS-Plasma can describe the partially ionized plasma. In the continuum regime, in order to increase computational efficiency, a high order GKS-Plasma with the Chapman-Enskog expansion for the distribution functions can be constructed based on the high order spacial reconstruction and multi-stage time evolution. In summary, we will develop efficient numerical methods for partially ionized plasma, which is able to capture the multi-scale flow physics and achieve high accuracy and efficiency in the continuum regime.

本项目基于统一气体动理学格式，发展一种适用于动态电离等离子体的高效多尺度数值格式（UGKS-Plasma）。该数值格式基于多组分气体动理学方程和麦克斯韦方程，在离散时空上进行直接数值建模。通过构造多尺度数值通量、设计恰当的碰撞模型以及构建流场与电磁场的恰当耦合，建立一种能够描述从稀薄到连续流域等离子体流场、且能够应用于近中性强磁化流域等离子体的数值格式。通过在模型中加入适当的电离模型，发展一种能够描述动态电离过程的多尺度数值格式。在连续流域内，基于高阶空间重构和多步时间演化，发展一种适用于描述连续流域内等离子体的高阶动理学格式（GKS-Plasma）。通过本项目的研究，发展一套能够描述全流域动态电离等离子体的高效数值方法，且在连续流域内能够高效高精度模拟等离子体流场，为天文、航天、可控核聚变中等离子体的研究提供科学支撑。

多尺度等离子体数值模拟在航天和核武器等工程领域有重要应用。本项目旨在发展多尺度等离子体数值方法。在本项目的研究周期内，项目组成员发展了适用于等离子体输运的多尺度数值方法UGKS-Plasma，方法能够模拟不同Knudsen数和Larmor尺度下的等离子体输运过程；针对等离子体输运的高维度特性，发展了高效的统一气体动理学波粒方法UGKWP-Plasma，有效降低等离子体输运高维度所带来的计算压力；针对连续流域的等离子体模拟，发展了时空耦合的高精度气体动理学格式，并应用于多组分气体动力学方程的模拟。