Variational Integrators for Inertial Magnetohydrodynamics
Provides a structure-preserving numerical method for plasma physics simulations, ensuring accurate long-term behavior and topological constraints.
The authors developed a variational integrator for inertial magnetohydrodynamics that preserves conservation laws (energy, modified helicities) to machine accuracy and avoids unphysical magnetic reconnection when electron inertia is neglected. Numerical examples in 2D demonstrate excellent conservation properties.
Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed. This model features a noncanonical Hamiltonian formulation with a number of conserved quantities, including the total energy and modified versions of magnetic and cross helicity. In this work, a variational integrator is presented which preserves these conservation laws to machine accuracy. As long as effects due to finite electron mass are neglected, the scheme preserves the magnetic field line topology so that unphysical reconnection is absent. Only when effects of finite electron mass are added, magnetic reconnection takes place. The excellent conservation properties of the method are illustrated by numerical examples in 2D.