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

TL;DR

This paper introduces an explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems, combining particle discretization with differential forms to ensure gauge symmetry and long-term accuracy in large-scale plasma simulations.

Contribution

It develops a novel explicit high-order symplectic scheme using Hamiltonian splitting and Whitney forms for ideal two-fluid plasma systems, enhancing structure preservation and computational efficiency.

Findings

Successfully verified via wave dispersion relation analysis.

Accurately captured the oscillating two-stream instability.

Suitable for large-scale, multi-scale plasma simulations.

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.