论文标题
曲线坐标中vlasov-马克斯韦尔系统的几何粒子模拟
Geometric Particle-in-Cell Simulations of the Vlasov--Maxwell System in Curvilinear Coordinates
论文作者
论文摘要
保持动力学方程结构的数值方案可以在很长一段时间内提供稳定的仿真结果。 Vlasov-Maxwell方程的电磁粒子求解器，该方程在离散级别保留了vlasov-Maxwell方程的非典型哈密顿结构，已在[Kraus等人中介绍。 2017]。尽管已经获得了笛卡尔坐标的原始配方，但我们将公式扩展到本文中的曲线坐标。对于时间上的离散化，我们讨论了基于哈密顿分裂的几种（半）隐式方法，或者是与泊松基质的反对称分裂结合的离散梯度方法，并讨论了它们的保护特性和计算效率。
Numerical schemes that preserve the structure of the kinetic equations can provide stable simulation results over a long time. An electromagnetic particle-in-cell solver for the Vlasov-Maxwell equations that preserves at the discrete level the non-canonical Hamiltonian structure of the Vlasov-Maxwell equations has been presented in [Kraus et al. 2017]. Whereas the original formulation has been obtained for Cartesian coordinates, we extend the formulation to curvilinear coordinates in this paper. For the discretisation in time, we discuss several (semi-)implicit methods either based on a Hamiltonian splitting or a discrete gradient method combined with an antisymmetric splitting of the Poisson matrix and discuss their conservation properties and computational efficiency.
