Related papers: MRX: A differentiable 3D MHD equilibrium solver wi…
A new conservative finite element solver for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations is presented.The solver utilizes magnetic vector potential and current density as solution variables, which are…
In magnetohydrodynamics (MHD), the magnetic field is evolved by the induction equation and coupled to the gas dynamics by the Lorentz force. We perform numerical smoothed particle magnetohydrodynamics (Spmhd) simulations and study the…
This paper constructs the first mixed finite element for the linear elasticity problem in 3D using $P_3$ polynomials for the stress and discontinuous $P_2$ polynomials for the displacement on tetrahedral meshes under some mild mesh…
Magnetohydrodynamic (MHD) solvers used to study dynamic plasmas for magnetic confinement fusion typically rely on initial conditions that describe force balance, which are provided by an equilibrium solver based on the Grad-Shafranov (GS)…
Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic…
We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Rung-Kutta…
This paper is concerned with existence of solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in there-dimensional (3D) periodic domains (in Lagrangian coordinates).…
For the representation of axi-symmetric plasma configurations, it is natural to use cyl. coordinates (R,Z,$\phi$), where $\phi$ is an independent coordinate. The same cyl. coordinates have also been widely used for representing 3D MHD…
We present a discussion of two-dimensional magneto-hydrodynamics (MHD) configurations, concerning the equilibria of accretion disks of a strongly magnetized astrophysical object. We set up a viscoresistive scenario which generalizes…
The first paper of this series presents a discretely entropy stable discontinuous Galerkin (DG) method for the resistive magnetohydrodynamics (MHD) equations on three-dimensional curvilinear unstructured hexahedral meshes. Compared to other…
We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the…
Compressible vortex sheets are fundamental waves in entropy solutions to the multidimensional hyperbolic systems of conservation laws. For the Euler equations in 2-D gas dynamics, the classical linearized stability analysis on compressible…
Four different approximate approaches used to model the stressing of coronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The…
We present a new magnetohydrodynamic (MHD) code for the simulation of wave propagation in the solar atmosphere, under the effects of electrical resistivity, but not dominant, and heat transference in a uniform 3D grid. The code is based on…
In this series of papers we examine magnetic reconnection in a domain where the magnetic field does not vanish and the non-ideal region is localised in space. In a previous paper we presented a technique for obtaining analytical solutions…
We extend the recently introduced explicit divergence-free DG scheme for incompressible hydrodynamics [arXiv:1808.04669]. to the incompressible magnetohydrodynamics (MHD). A globally divergence-free finite element space is used for both the…
Ideal magnetohydrodynamic (MHD) equilibria on a Riemannian 3-manifold satisfy the stationary Euler equations for ideal fluids. A stationary solution $X$ admits a large set of ``adapted" metrics in $M$ for which $X$ solves the corresponding…
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects…
Many astrophysical and terrestrial scenarios involving magnetic fields can be approached in axial geometry. Although the smoothed particle hydrodynamics (SPH) technique has been successfully extended to magneto-hydrodynamics (MHD), a…
Context. For the last thirty years, most of the studies on the relaxation of stressed magnetic fields in the solar environment have onlyconsidered the Lorentz force, neglecting plasma contributions, and therefore, limiting every equilibrium…