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Nonlinear Magnetohydrodynamics: Numerical Concepts
Volume 49 · Number 2T · February 2006 · Pages 139-146
Technical Paper · Plasma and Fusion Energy Physics - Equilibrium and Instabilities
R. Keppens
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The ideal MagnetoHydroDynamic (MHD) equations accurately describe the macroscopic dynamics of a perfectly conducting plasma. Adopting a continuum, single fluid description in terms of the plasma density  , velocity v, thermal pressure p and magnetic field B, the ideal MHD system expresses conservation of mass, momentum, energy, and magnetic flux. This nonlinear, conservative system of 8 partial differential equations enriches the Euler equations governing the dynamics of a compressible gas with the dynamical influence - through the Lorentz force - and evolution - through the additional induction equation - of the magnetic field B. In multi-dimensional problems, the topological constraint expressed by the Maxwell equation [nabla]  B = 0, represents an additional complication for numerical MHD. Basic concepts of shock-capturing high-resolution schemes for computational MHD are presented, with an emphasis on how they cope with the thight physical demands resulting from nonlinearity, compressibility, conservation, and solenoidality.
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