Streamfunction finite element method for magnetohydrodynamics

Magnetohydrodynamics (MHD) describes the macroscopic behavior of electrically conducting fluids in a magnetic field. The MHD approximation is that the electric field vanishes in the moving fluid frame, except for possible resistive effects. The study of finite element methods on an unstructured mesh for two-dimensional, incompressible MHD, using a stream function approach to enforce the divergence-free condition on magnetic and velocity fields, and an implicit time difference scheme allows for much larger time steps. The nonlinear Gauss-Seidel iterative method has no convergence guarantee, but converges well in many cases, especially for small-time step sizes in time-dependent problems. To solve linear problems in nonlinear solvers, Krylov iterative techniques are used that are suited because they can be preconditioned for efficiency. Restarted GMRES can, in principle, deal with these limitations; however, it lacks a theory of convergence and stalling is frequently observed in real applications. The tilt instability problem is defined on an unbounded domain. The simulation times according to the number of levels and processors, and plot the weak scalability. © 2007