内禀局部高斯定律保持的PIC方法：一种用于等离子体模拟的自洽场-粒子更新格式
Intrinsic local Gauss's law preserving PIC method: A self-consistent field-particle update scheme for plasma simulations
AI总结：
本文提出一种内禀保持高斯定律的局部PIC方法，通过按维度拆分子步实现场-粒子自洽更新并松弛电场自由能，避免求解Poisson/Ampère方程，在经典基准测试中验证了其优势，适用于大规模并行等离子体模拟。
摘要：
为了进行物理上忠实的粒子云网格（PIC）模拟，高斯定律是一项关键要求，因为违反该定律往往会导致长期等离子体模拟中出现灾难性错误。本文提出了一种新方法，该方法在Vlasov-Ampère/Vlasov-Poisson系统中内禀地强制满足高斯定律，无需辅助场修正或专门的电流沉积技术。通过将粒子运动沿计算网格的每个维度拆分为子步，电场得以局部且与粒子运动一致地更新。为了进一步获得无旋电场，发展了一种局部更新格式，在满足高斯定律的约束下松弛电场自由能。所提出的方法避免了求解Poisson方程或Ampère方程，从而得到每个时间步具有线性复杂度的局部算法，可灵活地与PIC模拟中粒子运动的各种时间离散格式相结合。理论分析验证了所提出的方法确实精确保持离散高斯定律。在经典基准测试上的数值实验，包括Landau阻尼、双流不稳定性和Diocotron不稳定性，展示了所提出方法的关键优势。预期所提出方法的局部特性使其成为大规模等离子体并行模拟中一个有前景的工具。
英文摘要：
In order to perform physically faithful particle-in-cell (PIC) simulations, the Gauss's law stands as a critical requirement, since its violation often leads to catastrophic errors in long-term plasma simulations. This work proposes a novel method that intrinsically enforces the Gauss's law for the Vlasov-Ampère/Vlasov-Poisson system without requiring auxiliary field corrections or specialized current deposition techniques. The electric field is managed to get updated locally and consistently with the motion of particles via splitting the motion into sub-steps along each dimension of the computational mesh. To further obtain a curl-free electric field, a local update scheme is developed to relax the electric-field free energy subject to the Gauss's law. The proposed method avoids solving the Poisson's or Ampère's equation, resulting in a local algorithm of linear complexity for each time step which can be flexibly combined with various temporal discretization for particle motion in PIC simulations. Theoretical analysis verifies that the proposed method indeed maintains the discrete Gauss's law exactly. Numerical tests on classical benchmarks, including the Landau damping, two-stream instability and Diocotron instability, demonstrate the key advantages of the proposed method. It is expected that the local nature of the proposed method makes it a promising tool in parallel simulations of large-scale plasmas.
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