Computational MHD on lagrangian grids

Conservative, multidimensional, Lagrangian, staggered-grid hydrodynamics algorithms are well known[l]. Here, these principles are extended to include magnetic fields in the discretized momentum and energy equations. A magnetic vector potential, A, formulation is centered on edges so that the divergence law, ▽ · B = 0 is maintained to round-off error. The magnetic field is cell-centered. Magnetic forces from Maxwell's stress tensor are expressed in terms of the field and geometric quantities. This assures momentum and energy conservation. The method is expressed in 3D, but is generalizable to 1 or 2D. Resistive diffusion of the madoes not serve to straighten the azimuthal magnetic field lines [2]. gnetic field is handled by implicit time differencing and is solved by preconditioned, conjugate gradient methods. Multi-material, Z-pinch, test-problems are shown.