基于流守恒和傅立叶谱分析的混合型Wigner-Poisson方程组求解

Solution of Wigner-Poisson System with Combining Flux Balance and Fourier Spectrum Methods

提出一种基于流守恒和傅立叶分析的混合型离散欧拉网格法来求解Wigner-Poisson方程组。在坐标和速度空间分别采用不同的时间推进算法。与一般的离散欧拉法相比,可以显著提高非线性模拟结果的可靠性。通过该方法求解一些常见静电动理学不稳定性在量子等离子体中的行为变化;通过线性的本征解验证代码的可靠性,然后进行一些非线性现象的模拟,包含非线性朗道阻尼以及双流不稳定性的非线性饱和等。

The difference between quantum plasma and classical plasma is mainly reflected in the following two aspects:1)the statistical equilibrium state of the system changes from the classical Maxwell distribution to the Fermi-Dirac distribution;2)the single-particle quantum wave effect of electrons cannot be avoided.Corresponding to the Vlasov equation in the classical plasma,the kinetic equation of the quantum plasma is the Wigner equation,but the numerical solution of the Wigner equation is more complicated than the Vlasov equation.In this paper,we propose a new method based on flux balance and Fourier spectrum methods.The hybrid method is used to solve the Wigner-Poisson equations.This method adopts different time advancing algorithms in the coordinate and velocity spaces.Compared with the general discrete Euler method,it can significantly improve the accuracy of nonlinear simulation results.This paper investigates the behavioral changes of some common electrostatic kinetic instabilities in quantum plasmas through this method;verifies the reliability of the code through linear eigensolutions,and then simulates some nonlinear phenomena,including Nonlinear Landau damping and nonlinear saturation for two-stream instability,etc.