multishocked gasdynamic flows. This is due to their robustness for strong shock wave calculations. A general Shock-capturing methods have become an effective tool for the solution of hyperbolic partial differential equations. Both upwind discussion of the modern high-resolution shock-capturing and symmetric TVD schemes in the framework of the shock-capturmethods and their application for a variety of gasdynamic ing approach are thoroughly investigated and applied with great problems can be found in [1, 2]. The extension of these success to a number of complicated multidimensional gasdynamic schemes to the equations of the ideal magnetohydrodyproblems. The extension of these schemes to magnetohydrodynamics (MHD) is not straightforward. First, the exact solunamic (MHD) equations is not a simple task. First, the exact solution of the MHD Riemann problem is too multivariant to be used in tion [3] of the MHD Riemann problem is too multivariant regular calculations. On the other hand, the extensions of Roe's to be used in regular calculations. Second, several different approximate Riemann problem solvers for MHD equations in genapproximate solvers [4-9], applied to MHD equations are eral case are nonunique and need further investigation. That is why, now at the stage of investigation and comparison. some simplified approaches should be constructed. In this work,
The schemes [4][5][6][7] are based on the MHD extensions the second order of accuracy in time and space high-resolution of Roe's linearization procedure [10]. In [4], the attempt Lax-Friedrichs type scheme is suggested that gives a drastic simplification of the numerical algorithm comparing to the precise characof such extension was made and the second-order upwind teristic splitting of Jacobian matrices. The necessity is shown to scheme was constructed that demonstrated several advansolve the full set of MHD equations for modeling of multishocked tages in comparison with Lax-Friedrichs, Lax-Wendroff, flows, even when the problem is axisymmetric, to obtain evolutionand flux-corrected transport schemes. Roe's procedure, ary solutions. For the numerical example, the MHD Riemann probnevertheless, turned out to be realizable only for the special lem is used with the initial data consisting of two constant states lying to the right and to the left from the centerline of the computacase with the specific heat ratio อฒ ฯญ 2. The reason for such tional domain. If the problem is solved as purely coplanar, a slow behavior of MHD equations is that there is not any single compound wave appears in the self-similar solution obtained by averaging procedure to find a frozen Jacobian matrix for any shock-capturing scheme. If the full set of MHD equations is the system. That is why a simple arithmetic average of gas used and a small uniform tangential disturbance is added to the dynamic parameters was used for the calculation of fluxes magnetic field vector, a rotational jump splits from the compound wave, and it degrades into a slow shock. The reconstruction process on cell surfaces. This implies that the stationary discontinuof the nonevolutionary compound wave into evolutionary shocks ities are no longer steady solutions of the resulting numeriis investigated. Presented results should be taken into account in the cal scheme (see [2] for the regular mathematical backdevelopment of shock-capturing methods for MHD flows. แฎ 1996 ground). However, they still can be resolved within several Academic Press, Inc. mesh cells. Another linearization approach is used in [5][6][7], where the linearized Jacobian matrix is not a function of a single averaged set of variables, but it depends in a