A numerical study of partially ionised plasma using a 2D two-fluid magnetohydrodynamic code

In a magnetised, partially ionised plasma, such as the lower solar atmosphere, the co-existence of both charged and neutral particles and their interaction lead to effects that do not occur in fully ionised plasma. Multi-fluid magnetohydrodynamic (MHD) models of a plasma account for the degree of ionisation and the resulting effects more accurately than common single-fluid MHD models. A 2D two-fluid MHD code has been developed (writ-ten in C++) to study partially ionised plasma, based on the Kurganov-Tadmor scheme. The advantage of this scheme is that it is Riemann-solver free, which makes computation faster, and it exhibits a small, time step independent numerical viscosity, which makes the code stable and accurate for much smaller time steps than usual schemes allow for. The explicit Euler and fourth-order Runge-Kutta scheme are implemented to integrate the solution in time. Furthermore, the implementation of a spatial domain decomposition scheme, which is based on Message Passing Interface (MPI) standard, allows for parallel computing. The code has been verified successfully and a number of tests were per-formed, such as the Sod-shock tube test and the Brio-Wu shock test. Moreover, the effect of ionisation and recombination on a magnetised, partially ionised plasma was investi-gated by studying a 1.5D slow-mode shock simulation and the 2D Orszag-Tang vortex simulation. The effect on the properties of both fluids, the ionised and the neutral fluid, are compared to simulations where collisions are the only coupling mechanism between the fluids. In the initialisation, the two simulations are fundamentally different; whereas the driver of the slow-mode shock formation is the discontinuity in the magnetic field, it is the velocity field that predominantly drives the vortex formation in the Orszag-Tang vortex simulation. However, for both, it was found that the movement of the ionised fluid decreases as well as the shock speeds when ionisation and recombination are included. The partial ionisation state of the plasma adds complexity to the numerical modelling of the solar atmosphere and so multi-fluid codes have long been ignored. Therefore, the code developed here provides a tool to unlock new investigations into the lower solar atmosphere and will allow new physics on the Sun to be explored