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TVD solves the magnetohydrodynamic (MHD) equations by updating the fluid variables along each direction using the flux-conservative, second-order, total variation diminishing (TVD), upwind scheme of Jin & Xin. The magnetic field is updated separately in two-dimensional advection-constraint steps. The electromotive force (EMF) is computed in the advection step using the TVD scheme, and this same EMF is used immediately in the constraint step in order to preserve ∇˙B=0 without the need to store intermediate fluxes. The code is extended to three dimensions using operator splitting, and Runge-Kutta is used to get second-order accuracy in time. TVD offers high-resolution per grid cell, second-order accuracy in space and time, and enforcement of the ∇˙B=0 constraint to machine precision. Written in Fortran, It has no memory overhead and is fast. It is also available in a fully scalable message-passing parallel MPI implementation.