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
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Unified Formulation of Charge-conserving Current Assignment in Electromagnetic Particle-in-Cell Simulation
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Meiyan Fu,Tiao Lu,Xiangjiang Zhu
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表 4 在七个元胞情形下, V方法, E方法和U方法给出的电流密度公式
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| J | V method (×q2Δt) | E method (×q2Δt) | U method (×q2Δt) | | ξ1 | Δx1(1−2yn−ΔyΔx1Δx) | (0.5−xn)(0.5−yn) | (0.5−xn)(0.5−yn) | | ξ2 | Δx1ΔyΔx1/(Δx) | (0.5−xn)(0.5−yn) | (0.5−xn)(0.5−yn) | | ξ3 | [Δy(2−Δx1)Δx1Δx+(2−ΔxΔy2Δy)(0.5−yn−ΔyΔx1Δx)] | (2+xn−xn+1)(0.5−yn) | (1.5+xn)(0.5−yn) | | ξ4 | Δx1(1+2yn+ΔyΔx1Δx) | (0.5−xn)(2+yn−yn+1) | (0.5−xn)(1.5+yn) | | ξ5 | Δx2(0.5−yn−ΔyΔx1Δx) | (xn+1−0.5)(0.5−yn) | 0 | | ξ6 | ΔxΔy2Δy(0.5−yn−ΔyΔx1Δx) | (xn+1−0.5)(0.5−yn) | 0 | | ξ7 | [Δx2(1.5+yn+ΔyΔx1Δx)+(xn+1−0.5−ΔxΔy2Δy)(2.5−yn+1)] | (xn+1−0.5)(2+yn−yn+1) | (xn+1−0.5)(2.5−yn+1) | | ξ8 | (yn+1−0.5)(2.5−ΔxΔy2Δy−xn+1) | (2+xn−xn+1)(yn+1−0.5) | (2.5−xn+1)(yn+1−0.5) | | ξ9 | (yn+1−0.5)(−0.5+ΔxΔy2Δy+xn+1) | (xn+1−0.5)(yn+1−0.5) | (xn+1−0.5)(yn+1−0.5) | | ξ10 | (yn+1−0.5)(−0.5−ΔxΔy2Δy+xn+1) | (xn+1−0.5)(yn+1−0.5) | (xn+1−0.5)(yn+1−0.5) | | ξ11 | 0 | (0.5−xn)(yn+1−0.5) | 0 | | ξ12 | 0 | (0.5−xn)(yn+1−0.5) | 0 | | 其中: Δx=xn+1−xn, Δy=yn+1−yn, Δx1=0.5−xn, Δy1=ΔyΔx1/Δx, | | xM1=0.5, yM1=yn+Δy1, Δy2=0.5−yM1, Δx2=ΔxΔy2/Δy. |
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