理想二流体系统的显式高阶非正则辛算法
Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
摘要：
提出了理想二流体系统的一种显式高阶非正则辛算法。在拉格朗日描述中，流体被离散为粒子，而电磁场和内能被处理为固定网格上的离散微分形式场。在Whitney插值形式的帮助下，该格式保持了电磁场的规范对称性，而压力场则自然地由离散的内能导出。整个系统使用由He等人发现的Hamilton分裂方法求解，该方法已被成功地应用于辛粒子网格格式的构造。由于其结构保持性和显式性，该算法特别适合于大规模模拟的物理问题，是多尺度的，需要长期的保真度和精度。该算法通过两个测试进行了验证：研究波的色散关系在两个流体等离子体系统和振荡双流不稳定性。
英文摘要：
An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as discrete differential form fields on a fixed mesh. With the assistance of Whitney interpolating forms, this scheme preserves the gauge symmetry of the electromagnetic field, and the pressure field is naturally derived from the discrete internal energy. The whole system is solved using the Hamiltonian splitting method discovered by He et al., which was been successfully adopted in constructing symplectic particle-in-cell schemes. Because of its structure preserving and explicit nature, this algorithm is especially suitable for large-scale simulations for physics problems that are multi-scale and require long-term fidelity and accuracy. The algorithm is verified via two tests: studies of the dispersion relation of waves in a two-fluid plasma system and the oscillating two-stream instability.
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