Accurate, finite-volume methods for three dimensional magneto-hydrodynamics on Lagrangian meshes

Summary form only given. Recently developed algorithms for ideal and resistive 3D MHD calculations on Lagrangian hexahedral meshes have been generalized to work with a Lagrangian mesh composed of arbitrary polyhedral cells. This allows for mesh refinement during a calculation to prevent the well known problem of tangling in a Lagrangian mesh. Arbitrary polyhedral cells are decomposed into tetrahedrons. The action of the magnetic vector potential, A/spl middot//spl part/1, is centered on all face edges of this extended mesh. Thus, /spl nabla//spl middot/B=0 is maintained to round-off error. For ideal flow, (E=v/spl times/B), vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F=-/spl part/W/sub B///spl part/r. This assures symmetry as well as magnetic flux, momentum and energy conservation. The method is local so that parallelization by domain decomposition is natural for large meshes. In addition, a simple, ideal-gas, finite pressure term has been included. The resistive diffusion, (E=-/spl eta/J), is treated with a support operator method, to obtain an energy conservative, symmetric method on an arbitrary polyhedral mesh. The equation of motion is time-step-split. First, the ideal term is treated explicitly. Next, the diffusion is solved implicitly with a preconditioned conjugate gradient method. Results of convergence tests are presented. Initial results of an annular Z-pinch implosion problem illustrate the application of these methods to multimaterial problems.