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In this poster, we present multidimensional simulations of the magnetohydrodynamic (MHD) Kelvin-Helmholtz instability in a compressible ideal flow. Simulations have been performed with a multidimensional MHD code, based on the Total Variation Diminishing scheme (Harten 1983) which is a second-order-accurate extension of the Roe-type upwind scheme. The one-dimensional version of the code utilizes an approximate Riemann solver described in Brio and Wu (1987). Multiple spatial dimensions are treated through a Strang-type operator splitting, and the constraint of a divergence-free field is enforced exactly by calculating a correction via a gauge transformation in each time step. Utilizing the analytical formulation of Miura and Pritchett (1982), we have established an initial sheared flow with field configurations transverse or parallel to the initial flow direction which is unstable against the Kelvin-Helmholtz mode. Through numerical simulations typically using 256x256 cells or 512x512 cells, we have confirmed first the linear stability criterion and recover the linear growth rates of wave modes excited as initial conditions. Then, the simulations have extended well beyond the nonlinear flow regime by evolving up to ten dynamical times or more. In the nonlinear regime, we have observed the development of large eddies whose size is comparable to the wavelength of the most unstable mode in the linear regime. However, after the evolution of several dynamical times, the large eddies become less dominant and smaller scale structures appear making the whole structure look turbulent. One of the results from these calculations is that the code can accurately model the nonlinear evolution of complex multidimensional MHD flows. This work was supported in part by NSF, NASA and the University of Minnesota Supercomputer Institute. DR also acknowledges the support by the Non-Directed Research Fund of the Korea Research Foundation 1993.
{\noindent References: Harten, A., 1983, J.~ Comp.~ Phys., 49, 357.\hfil\break Brio, M.~and Wu, C.~C., 1988, J.~ Comp.~ Phys., 75, 500.\hfil\break Miura, A.~and Pritchett, P.~L., 1982, J.~Geophys.~Res., 87, 7431. }
