A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions

TL;DR

This paper introduces a three-dimensional fixed-point iterative numerical method for solving nonlinear magnetohydrostatic equations, extending previous approaches to include gravity, and demonstrates its effectiveness through a test case.

Contribution

Develops a novel 3D fixed-point scheme for magnetohydrostatic equations that incorporates gravity, advancing numerical modeling of solar atmospheres.

Findings

Successfully implements the method in code.

Demonstrates the method with a test case.

Extends previous 2D approaches to 3D with gravity.

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.