Stream-aligned Magnetohydrodynamics for Solar Wind Simulations

We present a reduced magnetohydrodynamic (MHD) mathematical model describing the dynamical behavior of highly conducting plasmas with frozen-in magnetic fields, constrained by assumption that, there exists frame reference, where field vector, $\mathbf{B}$, is aligned plasma velocity $\mathbf{u}$, at each point. call this solution "stream-aligned MHD" (SA-MHD). Within framework model, electric field, $\mathbf{E} = -\mathbf{u} \times \mathbf{B} \equiv 0$, in induction equation vanishes identically and so does electromagnetic energy flux (Poynting flux), $\mathbf{E}\times\mathbf{B}\equiv0$, equation. At same time, force effect from on motion (the Ampere force) fully taken into account momentum Any steady-state proposed legitimate full MHD system equations. However, converse statement not true: an arbitrary have to vanish (its curl has to, though). Specifically, realistic tree-dimensional solutions for ("ambient") solar atmosphere form so-called Parker spirals, can be efficiently generated within stream-aligned (SA-MHD) no loss generality