Accurate, Finite-Volume Methods for 3D MHD and Applications
Abstract
Recently developed algorithms for 3D MHD calculations on a structured, Lagrangian, hexahedral mesh are described. The magnetic field B is described in terms of the magnetic flux through each hex face. Vertex forces are derived by the variation of magnetic energy with respect to vertex positions. This assures symmetry, magnetic flux, momentum, and energy conservation, as well as maintaining an exact vanishing divergence of B. It is shown that the form of the ideal dispersion relation may be preserved by an appropriate choice of volume, and volume averages, so that the well known stiffness is resolved without pollution of the low-frequency modes. Resistive diffusion is calculated using the support operator method, to obtain an energy conservative, symmetric method on an arbitrary mesh. Implicit time difference equations are solved by preconditioned, conjugate gradient methods. Results of convergence tests are presented. Initial results of a liner implosion problem illustrate the application of these methods to multi-material problems. Applications to electromagnetism on arbitrary 3D hex meshes are also discussed.
- Publication:
-
APS Meeting Abstracts
- Pub Date:
- August 1997
- Bibcode:
- 1997APS..CPC..Q308B