Here we propose hybrid Lagrangian–Eulerian (HLE) method for kinetic simulations of plasmas. The HLE method solves advection equations of shape functions unlike particle-in-cell (PIC) method. Although the PIC method cannot preserve the conservation laws of momentum and energy simultaneously, the HLE method can resolve this issue while the particle velocity is formulated by the Lagrangian description. The HLE method discretizes the advection equations and Maxwell's equations with the same scheme, so the momentum and energy exchange between charged particles and electromagnetic field exactly balances in discrete level. Numerical experiments show that linear growth rates of two-stream and Weibel instabilities are reproduced well, and global conservation is exactly preserved except for round-off errors although the velocity space is discretized by the Lagrangian description like the PIC method.

在这里，我们提出了用于等离子体动力学模拟的混合拉格朗日-欧拉 (HLE) 方法。HLE 方法求解形状函数的平流方程，这与粒子在单元格 (PIC) 方法不同。虽然 PIC 方法不能同时保持动量和能量守恒定律，但 HLE 方法可以解决这个问题，而粒子速度由拉格朗日描述制定。HLE方法将平流方程和麦克斯韦方程用相同的格式离散化，因此带电粒子和电磁场之间的动量和能量交换在离散水平上完全平衡。数值实验表明，双流和 Weibel 不稳定性的线性增长率得到了很好的再现，