Boundary value problems in magnetohydrodynamics (and fluid dynamics). I. Radiation boundary condition

Numerical simulations of time-dependent phenomena involving magnetohydrodynamic (MHD) waves encounter serious problems due to artificial reflection of waves at numerical boundaries in situations where the time-dependent magnetic fields external to those boundaries are not known. A method developed for determining radiative (i.e., nonreflecting) boundary conditions for waves in ordinary fluids is generalized in this paper to treat isothermal MHD waves. A test problem is considered for which analytic results have been obtained, namely, magnetic braking of a rigidly rotating disk embedded in a differentially rotating fluid. Comparison is made between results obtained from numerical simulations, with and without the radiative boundary treatment developed here, and the analytic results.