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Equations

Though equations eq.(13)-(18) and one of eq.(19)-(21) give the governing equations of the MHD system, we can easily see that we can not use them in MHD simulation, as we can not derive the time evolution of each parameters from them directly. It is necessary for us to change these equations to other time-variant forms. There are several transformations for eq.(13)-(18) and one of eq.(19)-(21). Though these transformations are mathematically the same, they have different numerical characteristics in MHD simulations. So it is necessary for us to know the numerical characteristics of each of them before we can know which one to choose for certain problems. The followings are some of the transformations to eq. (13)-(18) and (20).