A structure-preserving finite element method for compressible ideal and resistive magnetohydrodynamics
Evan S. Gawlik, François Gay–Balmaz
Abstract
We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics both in the ideal and resistive cases, and in the presence of viscosity. The method is deduced from the geometric variational formulation of the equations. It preserves the balance laws governing the evolution of total energy and magnetic helicity, and preserves mass and the constraint $\text {div}B = 0$ to machine precision, both at the spatially and temporally discrete levels. In particular, conservation of energy and magnetic helicity hold at the discrete levels in the ideal case. It is observed that cross-helicity is well conserved in our simulation in the ideal case.
Topics & Concepts
PhysicsMagnetohydrodynamicsMagnetic helicityHelicityBarotropic fluidIdeal (ethics)Classical mechanicsFinite element methodMagnetohydrodynamic driveConservation lawCompressibilityMathematical analysisMagnetic fieldMechanicsQuantum mechanicsMathematicsLawPolitical scienceThermodynamicsComputational Fluid Dynamics and AerodynamicsAdvanced Numerical Methods in Computational MathematicsLattice Boltzmann Simulation Studies