A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions
arXiv:1609.00733 · doi:10.1007/s11207-016-0992-0
Abstract
Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin (Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.
arXiv commentAccepted for publication in Solar Physics
References in corpus (15)
- A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953
- Modeling the Subsurface Structure of Sunspots
- Non-linear numerical simulations of magneto-acoustic wave propagation in small-scale flux tubes
- The Influence of Spatial Resolution on Nonlinear Force-Free Modeling
- The Three-Dimensional Structure of a Sunspot Magnetic Field
- A self-consistent nonlinear force-free solution for a solar active region magnetic field
- Magnetic modelling and tomography: First steps towards a consistent reconstruction of the solar corona
- Optimization approach for the computation of magnetohydrostatic coronal equilibria in spherical geometry
- First nonlinear force-free field extrapolations of SOLIS/VSM data
- Numerical Models of Travel-Time Inhomogeneities in Sunspots
- Constructing semi-empirical sunspot models for helioseismology
- A Magnetostatic Grad-Rubin Code for Coronal Magnetic Field Extrapolations
- Magneto-static modelling of the mixed plasma Beta solar atmosphere based on SUNRISE/IMaX data
- The free energy of NOAA active region AR 11029
- Nonlinear force-free modeling of the corona in spherical coordinates
Cited by in corpus (10)
- Solar Force-free Magnetic Fields
- On the extrapolation of magneto-hydro-static equilibria on the sun
- Magneto-static modelling from SUNRISE/IMaX: Application to an active region observed with SUNRISE II
- Test magnetohydrostatic extrapolation with radiative MHD simulation of a solar flare
- A Magnetohydrodynamic Relaxation Method for Non-Force-Free Magnetic Field in Magnetohydrostatic Equilibrium
- Magnetohydrostatic modeling of AR11768 based on a SUNRISE/IMaX vector magnetogram
- Toward a fast and consistent approach to model solar magnetic fields in multiple layers
- Nonlinear force-free modeling of flare-related magnetic field changes at the photosphere and chromosphere
- Preprocessing of vector magnetograms for magnetohydrostatic extrapolations
- New Statistical Topology Theory Predicts Turbulent Magnetic Emergence from the Sun's Interior