ELLAM for the Magnetic Induction Equation in the Resistive MHD

Jiangguo (James) Liu

Email: liu@math.colostate.edu
Postal address: Department of Mathematics, Campus Delivery 1874, Colorado State University, Fort Collins, CO 80523-1874
The kinematics of magnetohydrodynamics (MHD) studies the influence of the velocity of an electrically conducting fluid (e.g., a plasma) on the magnetic field, which conserves the solenoidal property for all time.  For the 2-dim case, a scalar potential can be introduced and the magnetic field induction equation can be converted into a convection-diffusion-reaction equation, which can be efficiently solved by the Eulerian-Lagrangian localized adjoint method (ELLAM).  For the 3-dim case, locally divergence-free finite elements are used to satisfy the solenoidal property and the discontinuous Galerkin method comes into play very naturally. Simulations for some interesting MHD eddy flows will be presented, including analysis on distortion and energy evolution of the magnetic field.