  A numerical method for the quasi-neutral two-fluid (QNTF) plasma model is
described. The basic equations are ion and electron fluid equations and the
Maxwell equations without displacement current. The neglect of displacement
current is consistent with the assumption of charge neutrality. It thus reduces
to the ideal magnetohydrodynamic (MHD) equations in the long wavelength limit,
but the two-fluid effect appearing at ion and electron inertial scales is fully
taken into account. It is shown that the basic equations may be rewritten in a
form that has formally the same structure as the MHD equations. The total mass,
momentum, and energy are all written in the conservative form. A new
three-dimensional numerical simulation code has been developed for the QNTF
equations. The HLL (Harten-Lax-van Leer) approximate Riemann solver combined
with the upwind constrained transport (UCT) scheme is applied. The method was
originally developed for MHD (Londrillo & Del Zanna, 2004), but works quite
well for the present model as well. The simulation code is able to capture
sharp multidimensional discontinuities as well as dispersive waves arising from
the two-fluid effect at small scales without producing $\nabla \cdot
\mathbf{B}$ errors. It is well known that conventional Hall-MHD codes often
suffer a numerical stability issue associated with short wavelength whistler
waves. On the other hand, since finite electron inertia introduces an upper
bound to the phase speed of whistler waves in the present model, our code is
free from the issue even without explicit dissipation terms or implicit time
integration. Numerical experiments have confirmed that there is no need to
resolve characteristic time scales such as plasma frequency or cyclotron
frequency for numerical stability. Consequently, the QNTF model offers a better
alternative to the Hall-MHD or fully electromagnetic two-fluid models.
