Helicity-conservative finite element discretization for incompressible MHD systems
arXiv:2007.07516 · doi:10.1016/j.jcp.2021.110284
Abstract
We construct finite element methods for the incompressible magnetohydrodynamics (MHD) system that precisely preserve magnetic and cross helicity, the energy law and the magnetic Gauss law at the discrete level. The variables are discretized as discrete differential forms in a de Rham complex. We present numerical tests to show the performance of the algorithm.
References in corpus (5)
- Role of cross helicity in magnetohydrodynamic turbulence
- Robust Preconditioners for Incompressible MHD Models
- A Conservative Finite Element Method for the Incompressible Euler Equations with Variable Density
- Variational Integrators for Inertial Magnetohydrodynamics
- Variational Integrators for Ideal Magnetohydrodynamics
Cited by in corpus (5)
- A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume/finite element scheme for the incompressible MHD equations
- A structure-preserving finite element method for compressible ideal and resistive MHD
- An arbitrary order and pointwise divergence-free finite element scheme for the incompressible 3D Navier-Stokes equations
- Structure-preserving and thermodynamically consistent finite element discretization for visco-resistive MHD with thermoelectric effect
- A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains