Structure preserving, transport stabilized finite element methods for two-fluid magnetohydrodynamics

Two-fluid magnetohydrodynamics (MHD) extends single-fluid MHD by retaining separate ion and electron thermodynamics together with an extended Ohm’s law. This enables the capture of Hall physics, dispersive waves, and fast magnetic reconnection – phenomena that are inaccessible to single-fluid MHD and are central to applications such as magnetic confinement fusion, the heliosphere, and the Earth’s magnetosphere.

In this presentation, we discuss a novel spatial discretization for the two-fluid MHD equations based on compatible finite element methods. The approach preserves important structural properties including the divergence-free constraint on the magnetic field, energy conservation, and a consistent treatment of both fluid and magnetic helicity. In particular, the ion velocity and magnetic field spaces are chosen to admit a natural discrete definition of the diagnostically determined electron velocity.

The resulting scheme is designed for low-dissipation regimes in which fluid transport dominates, a setting relevant to many scenarios of interest in the aforementioned applications. To ensure a stable field evolution, we incorporate transport stabilization for all fields while preserving the underlying structural properties of the two-fluid MHD system. The stabilization is based on interior penalty methods, extending our previous work on magnetic field transport in single-fluid resistive MHD (Wimmer, Tang, 2024). Numerical experiments demonstrate the structure preserving and stabilization properties of the method through test cases focusing on fluid helicity, magnetic helicity, and the relative decay rates of helicity and energy in the presence of dissipation.

 

References

Golo A. Wimmer and Xian-Zhu Tang (2024), Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics, Journal of Computational Physics, Volume 501, 112777.