Abstract
The one-dimensional eight-wave ideal MHD equations are used to investigate the accuracy of the proposed Runge-Kutta scheme with added TVD acting as a dissipation mechanism. This investigation is performed to establish the procedure for extension to multidimensio nal problems in MHD. A set of eigenvalues and a set of new associated eigenvectors have been developed. Three well known TVD models and several limiters for each model are investigated for their accuracy and robustness. Solutions are obtained for diffferent cases, each under the influence of a different magnetic field in order to identify the formation of wave patterns in the flow field. The numerical solutions are compared to each other and analytical solutions when available.
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