AN IMPLICIT SCHEME FOR NONIDEAL MAGNETOHYDRODYNAMICS

A new implicit algorithm is developed for solving the time-dependent, nonideal magnetohydrodynamic equations. It can also be used as an effi cient relaxation scheme for steady state solutions. The algorithm is a finite-volume scheme that uses an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on nested control v olumes for the parabolic fluxes that arise from the non-ideal terms (i .e., resistivity and viscosity). In one dimension the scheme is second -order accurate in space and time. In two or th ree dimensions, the ac curacy is between fi rst and second order. For the class of problems c onsidered, the implicit formulation is stable for any size time step, thus allowing efficient tracking of slower transients. The implicit op erator is inverted using a lower-upper symmetric Gauss-Seidel iteratio n. Results from several test cases are presented that show good agreem ent with analytical solutions and illustrate the advantages of the sch eme. (C) 1997 Academic Press.