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{\large Ravi Samtaney \\
{\bf An all-speed projection method for magneto-hydrodynamics}}

Bldg 2 \\ Rm 4337 \\ KAUST \\ Thuwal 23955-6900 \\ Kingdom of Saudi Arabia
\\
{\tt Ravi.Samtaney@kaust.edu.sa}\\
Mark Adams\\
Phillip Colella\\
Daniel T. Graves\\
Terry J. Ligocki\\
Brian van Straalen\end{center}

We present an all-speed algorithm for magneto-hydrodynamics (MHD) similar
to the work of Colella & Pao (J. Comput. Phys. 1999) for low-speed
hydrodynamics. The method is based on an asymptotic ordering of scales
relevant for tokamak MHD physics. The central idea is to Hodge decompose
the velocity, and split the magnetic guide field in a manner analogous to
the pressure splitting into a thermodynamic and incompressible parts for
hydrodynamics. We present the derivation of the ideal MHD equations into
slow (advective), intermediate and fast scales. The algorithm treats the
slow advective scales using a Godunov-procedure while the intermediate
and fast scales are treated implicitly using backward Euler. Results from
numerical tests will be presented as well the challenges of designing
solvers for the intermediate scales.


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