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The two-dimensional adiabatic relaxation method for MHD modelling. (English) Zbl 0632.76126
The adiabatic relaxation method is extended to two dimensions using a moving finite element model. The MHD equations are split into ideal and diffusion parts by employing a fractional timestep. The ideal equations are expressed in variational form using Hamilton’s principle. Finite element discretisation of the variational principle leads to equations for studying equilibria, time dependent MHD and stability. It is shown that conjugate gradient accelerated SSOR is effective in solving the nonlinear minimisation problem arising in finding equilibria. Aligning the finite elements with flux surfaces causes surface averaged transport to emerge naturally from the diffusion part of the timestep.
MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76T99 Multiphase and multicomponent flows
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
70H99 Hamiltonian and Lagrangian mechanics
Software:
ERATO
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