Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems

Abstract

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.