# High-order two-fluid plasma solver for direct numerical simulations of plasma flows with full transport phenomena

## TL;DR

This paper introduces a high-order two-fluid plasma solver capable of simulating plasma flows with full transport phenomena, validated against canonical problems and applicable across multiple regimes.

## Contribution

The paper develops and validates a comprehensive two-fluid plasma solver with full transport effects, capable of resolving all relevant scales in plasma simulations.

## Key findings

- Solver accurately reproduces Alfven and whistler dispersion relations.
- Successfully simulates electromagnetic plasma shocks and magnetic reconnection.
- Converged DNS-like solutions achieved with ion Reynolds number below 2.3.

## Abstract

The two-fluid plasma equations for a single ion species, with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating term have been implemented in the CFDNS code and solved by using sixth-order non-dissipative compact finite differences for plasma flows in several different regimes. In order to be able to fully resolve all the dynamically relevant time and length scales, while maintaining computational feasibility, the assumptions of infinite speed of light and negligible electron inertia have been made. Non-dimensional analysis of the two-fluid plasma equations shows that, by varying the characteristic/background number density, length scale, temperature, and magnetic strength, the corresponding Hall, resistive, and ideal magnetohydrodynamics (MHD) equations can be recovered as limiting cases. The accuracy and robustness of this two-fluid plasma solver in handling plasma flows in different regimes have been validated against four canonical problems: Alfven and whistler dispersion relations, electromagnetic plasma shock, and magnetic reconnection. For all test cases, by using physical dissipation and diffusion, with negligible numerical dissipation/diffusion, fully converged Direct Numerical Simulations (DNS)-like solutions are obtained when the ion Reynolds number based on grid size is smaller than a threshold value which is about 2.3 in this study. For the magnetic reconnection problem, the results show that the magnetic flux saturation time and value converge when the ion and magnetic Reynolds numbers are large enough. Thus, the DNS-like results become relevant to practical problems with much larger Reynolds numbers.