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.