电磁粒子模拟中电荷守恒的电流分配方案满足的统一公式

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付梅艳,卢朓,朱湘疆

Unified Formulation of Charge-conserving Current Assignment in Electromagnetic Particle-in-Cell Simulation

Meiyan Fu,Tiao Lu,Xiangjiang Zhu

表 3 在六个元胞情形下, V方法、E方法和U方法给出的电流密度公式

$J$	V method $(\times \frac{q}{2\Delta t})$	E method $(\times \frac{q}{2\Delta t})$	U method $(\times \frac{q}{2\Delta t})$
$\xi_1$	$\Delta x_1 (1 - 2y^{n} - \Delta y\frac{\Delta x_1}{\Delta x})$	$\Delta x_1 (1 - 2y^{n} - \Delta y)$	$\Delta x_1 (1 - 2y^{n} - \frac{1}{2}\Delta y)$
$\xi_2$	$\Delta x_1 \Delta y \frac{\Delta x_1}{\Delta x}$	$\Delta x_1 \Delta y$	$\Delta x_1 \frac{1}{2}\Delta y$
$\xi_3$	$\Delta y[\frac{\Delta x_1}{\Delta x}(2-\Delta x_1) + \frac{\Delta x_2}{\Delta x}(2-\Delta x_2)]$	$\Delta y (2-\Delta x_1-\Delta x_2)$	$\Delta y (2 - \frac{1}{2}\Delta x_1 - \frac{1}{2}\Delta x_2)$
$\xi_4$	$\Delta x_1 (1 + 2y^{n} + \Delta y\frac{\Delta x_1}{\Delta x})$	$\Delta x_1 (1 + 2y^{n} + \Delta y)$	$\Delta x_1 (1 + 2y^{n} + \frac{1}{2}\Delta y)$
$\xi_5$	$\Delta x_2 (1 - 2y^{n} - \Delta y - \Delta y\frac{\Delta x_1}{\Delta x})$	$\Delta x_2 (1 - 2y^{n} - \Delta y)$	$\Delta x_2 (1 - 2y^{n} - \frac{3}{2}\Delta y)$
$\xi_6$	$\Delta x_2 \frac{\Delta x_2}{\Delta x} \Delta y$	$\Delta x_2 \Delta y$	$\Delta x_2 \frac{1}{2} \Delta y$
$\xi_7$	$\Delta x_2 (1 + 2y^{n} + \Delta y + \Delta y\frac{\Delta x_1}{\Delta x})$	$\Delta x_2 (1 + 2y^{n} + \Delta y)$	$\Delta x_2 (1 + 2y^{n} + \frac{3}{2}\Delta y)$
其中: $\Delta x = x^{n+1}-x^{n}, \ \Delta y = y^{n+1}-y^{n}, \ \Delta x_1 = 0.5-x^{n}, \ \Delta x_2 = x^{n+1}-0.5.$