Notes on the eigensystem of magnetohydrodynamics

The eigenstructure of the equations governing one-dimensional ideal magnetohydrodynamics is examined, motivated by the wish to exploit it for construction of high-resolution computational algorithms. The results are given in simple forms that avoid indeterminacy or degeneracy whenever possible. The unavoidable indeterminacy near the magnetosonic (or triple umbilic) state is analysed and shown to cause no difficulty in evaluating a numerical flux function. The structure of wave paths close to this singularity is obtained, and simple expressions are presented for the structure coefficients that govern wave steepening.