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

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 smbullet delta1, is centered on all faces edges of this extended mesh. Thus, triangledown sm-bullet B = 0 is maintained to round-off error. For ideal flow, (E = v x B), vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F = -partial deriv.WB/partial deriv. 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 = -ηJ), 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 multi-material problems