4 papers
Hamiltonian formulation and matrix discretization for axisymmetric magnetohydrodynamics
Michael Roop
Equations of ideal magnetohydrodynamics (MHD) play an important role in the studies of turbulence, astrophysics, and plasma physics. These equations possess remarkable geometric st…
Structure-preserving long-time simulations of turbulence in magnetized ideal fluids
Klas Modin, Michael Roop
We address three two-dimensional magnetohydrodynamics models: reduced magnetohydrodynamics (RMHD), Hazeltine's model, and the Charney--Hasegawa--Mima (CHM) equation. These models a…
Thermal quasi-geostrophic model on the sphere: derivation and structure-preserving simulation
Michael Roop, Sagy Ephrati
We derive the global model of thermal quasi-geostrophy on the sphere via asymptotic expansion of the thermal rotating shallow water equations. The model does not rely on the asympt…
Spatio-temporal Lie-Poisson discretization for incompressible magnetohydrodynamics on the sphere
Klas Modin, Michael Roop
We give a structure preserving spatio-temporal discretization for incompressible magnetohydrodynamics (MHD) on the sphere. Discretization in space is based on the theory of geometr…