Efficient 10-moment Hall MHD and exact-gyration schemes

Develop computationally efficient schemes for 10-moment Hall magnetohydrodynamics and for 10-moment magnetohydrodynamics that incorporate the exact pressure-tensor gyration effect without requiring prohibitively small timesteps to resolve ion or electron timescales.

Background

The model neglects the Hall effect and represents pressure-tensor gyration through an artificial relaxation model because directly resolving ion or electron timescales would impose a small timestep. A computationally efficient treatment of Hall physics and exact gyration is therefore identified as an unresolved numerical-development task.

References

The fourth is introducing the Hall effect, and the gyration effect without using an artificial model; this requires a small timestep, since the ion or electron timescales must be resolved. Developing computationally efficient schemes for 10-moment Hall MHD or 10-moment MHD with an exact gyration effect is also among the remaining tasks.

— A generalized energy-consistent finite difference scheme for 10-moment magnetohydrodynamics  (2608.25441 - Akutagawa et al., 26 Aug 2026) in Section 6, Conclusion