High-order curvilinear finite element magneto-hydrodynamics I: A conservative Lagrangian scheme

Magneto-hydrodynamics is one of the foremost models in plasma physics with applications inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into complex physical phenomena. The classical Lagrangian typically limited low orders convergence suffer from violation divergence-free condition for magnetic field or conservation invariants. This paper first part a new series about high-order non-ideal magneto-hydrodynamics, where multi-dimensional conservative method based on curvilinear finite elements presented. zero divergence mass, momentum, flux total energy satisfied exactly. prevent entangling computational mesh its imprinting solution. A time integration applied, arbitrary order attained problems ideal magneto-hydrodynamics. resistive diffusion solved by implicit scheme. Description given multiple test demonstrating properties scheme performed. construction possible future directions development discussed.