论文标题
多维Vlasov-Maxwell系统高效的能源持续力矩方法
Highly efficient energy-conserving moment method for the multi-dimensional Vlasov-Maxwell system
论文作者
论文摘要
我们提出了一种基于[Z. Cai，Y。Fan和R. Li。 CPAM，2014年]。在Hermite扩展的框架下，为多维VM系统推导了全球双曲矩系统，该系统分别将扩展中心和缩放系数设置为宏观速度和局部温度。因此，洛伦兹力项的效果可以减少到有关宏观速度和高阶的力矩系数的几种OD中，这可以显着降低整个系统的计算成本。提出了一种能量支持的数值方案来求解力矩方程和麦克斯韦方程，其中只需要求解线性方程式系统。研究了几个数值示例，例如两流不稳定性，微生的不稳定性和二维Orszag Tang Vortex问题，以验证数值方案的效率和出色的能量性能。
We present an energy-conserving numerical scheme to solve the Vlasov-Maxwell (VM) system based on the regularized moment method proposed in [Z. Cai, Y. Fan, and R. Li. CPAM, 2014]. The globally hyperbolic moment system is deduced for the multi-dimensional VM system under the framework of the Hermite expansions, where the expansion center and the scaling factor are set as the macroscopic velocity and local temperature, respectively. Thus, the effect of the Lorentz force term could be reduced into several ODEs about the macroscopic velocity and the moment coefficients of higher order, which could significantly reduce the computational cost of the whole system. An energy-conserving numerical scheme is proposed to solve the moment equations and the Maxwell equations, where only a linear equation system needs to be solved. Several numerical examples such as the two-stream instability, Weibel instability, and the two-dimensional Orszag Tang vortex problem are studied to validate the efficiency and excellent energy-preserving property of the numerical scheme.
