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

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