The eigenstructure of the equations of radiation magnetohydrodynamics

In this paper we analyze the eigenstructure of the equations of radiation magnetohydrodynamics. We wish to develop such insights as might be useful in the construction of robust and accurate higher-order Godunov schemes for their numerical solution. It is shown that the system is a hyperbolic system. The fact that the characteristic matrix for this system splits into sub-blocks is used to advantage to derive the eigenvalues and certain general properties about the eigenvectors. It is shown that the system admits an entropy wave, a pair of slow magnetosonic waves, a pair of Alfven waves, a pair of fast magnetosonic waves, a pair of radiation energy density waves and a pair of transverse radiation flux waves. A complete and orthonormal set of right and left eigenvectors is obtained. The contribution of the MHD waves to the radiative parts of the full set of equations is explicitly derived and explained with a view to improving one's intuitive understanding of these waves. The Cauchy problem for the equations of radiation magnetohydrodynamics under the locally frozen Eddington factor approximation is shown to be well-posed. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)