论文标题
Fokker-Planck-Landau方程建模碰撞等离子体的HERMITE光谱法
Hermite spectral method for Fokker-Planck-Landau equation modeling collisional plasma
论文作者
论文摘要
我们为Fokker-Planck-Landau（FPL）方程提出了一种HERMITE光谱方法。分布函数和碰撞项均通过HERMITE函数的串联扩展近似。为了处理二次FPL碰撞运算符的复杂性，通过采用二级碰撞算子的较低级术语和扩散的fokker-Planck操作员来构建降低的碰撞模型，以在降低碰撞运算符的Hermite扩展中用于高阶术语。数值方案根据Strang分裂分为三个步骤，在该strank分裂中，使用不同的扩展中心用于不同的数值步骤来利用Hermite功能。在对流和碰撞步骤中采用了标准归一化的HERMITE基础[36]，以利用二次碰撞术语的预先计算的系数，而由局部宏观速度和温度构成的术语则用于加速步骤，在此效果可以简化外部力的效果到eDe ode。不同扩展中心之间的预测是通过[29]中提出的算法实现的。研究了几个数值示例以测试和验证我们的新方法
We propose an Hermite spectral method for the Fokker-Planck-Landau (FPL) equation. Both the distribution functions and the collision terms are approximated by series expansions of the Hermite functions. To handle the complexity of the quadratic FPL collision operator, a reduced collision model is built by adopting the quadratic collision operator for the lower-order terms and the diffusive Fokker-Planck operator for the higher-order terms in the Hermite expansion of the reduced collision operator. The numerical scheme is split into three steps according to the Strang splitting, where different expansion centers are employed for different numerical steps to take advantage of the Hermite functions. The standard normalized Hermite basis [36] is adopted during the convection and collision steps to utilize the precalculated coefficients of the quadratic collision terms, while the one constituted by the local macroscopic velocity and temperature is utilized for the acceleration step, by which the effect of the external force can be simplified to an ODE. Projections between different expansion centers are achieved by an algorithm proposed in [29]. Several numerical examples are studied to test and validate our new method
