The ideal magnetohydrodynamic equations describe a flow of compresible inviscid electrically conducting fluid. In terms of mathematics, this equations are combination of Euler equations for fluid flow together with the Maxwell equations for electromagnetism.
The MHD rotor test case employed MHD validation under ideal non-resistive conditions. This two-dimensional problem consists of a rotating cylinder with density ten times superior to that of the surrounding environment. This problem is solved in a square domain [0,1]x[0,1]. The initial conditions for the magnetic field and thermodynamic pressure are: By = 0; Bx = 5/√4π; p = 1; γ = 1.4. The initial conditions for the rotating cylinder of radius r0=0.1, centered at [0.5, 0.5], are: ρ = 10; Ux = -U0*(y − 0.5)*r0; Uy = U0*(x−0.5)*r0. The conditions out of the rotating cylinder are: Ux = Uy=0 with a density ρ = 1.
