Japanese | **English**

OpenMHD is a two-dimensional finite-volume code for magnetohydrodynamics (MHD). The code is written in Fortran 90. It is parallelized by using MPI-3.1 and OpenMP.

OpenMHD was originally developed for my studies on magnetic reconnection in space physics [1,2]. Over the past 10 years, substantial improvements have been made. The code has been made publicly available in the hope that others may find it useful.

The following versions are available in .tar.gz format.

- Stable version (2019/12/27)

The source code is hosted on GitHub.

OpenMHD solves the following equations of magnetohydrodynamics. \begin{align} \frac{\partial \rho}{\partial t} &+ \nabla \cdot ( \rho \vec{v} ) = 0, \\ \frac{\partial \rho \vec{v}}{\partial t} &+ \nabla \cdot ( \rho\vec{v}\vec{v} + p_T\overleftrightarrow{I} - \vec{B}\vec{B} ) = 0, \\ \frac{\partial e}{\partial t} &+ \nabla \cdot \Big( (e+p_T )\vec{v} - (\vec{v}\cdot\vec{B}) \vec{B} + \eta \vec{j} \times \vec{B} \Big) = 0, \\ \frac{\partial \vec{B}}{\partial t} &+ \nabla \cdot ( \vec{v}\vec{B} - \vec{B}\vec{v} ) + \nabla \times (\eta \vec{j}) + \nabla \psi = 0, \\ \frac{\partial \psi}{\partial t} &+ c_h^2 \nabla \cdot \vec{B} = - \Big(\frac{c_h^2}{c_p^2}\Big) \psi, \end{align} where $p_T=p+B^2/2$ is the total pressure, $\overleftrightarrow{I}$ is the unit tensor, $e=p/(\Gamma-1) + \rho v^2/2 + B^2/2$ is the energy density, $\Gamma=5/3$ is the adiabatic index, and $\psi$ is a virtual potential for hyperbolic divergence cleaning [3]. The second-order Runge=Kutta methods, the second-order MUSCL scheme, and the HLLD flux solver [4] are employed. The source term for $\psi$ is handled by an operator splitting method and an analytic solution $\psi = \psi_0 \exp [ - ({c_h^2}/{c_p^2}) t ]$. Other numerical techniques are documented in Refs. [1,2] and references therein. The latest version incorporates further improvements such as parallel I/O.

- S. Zenitani & T. Miyoshi,
*Phys. Plasmas***18**, 022105 (2011) - S. Zenitani,
*Phys. Plasmas***22**, 032114 (2015) - A. Dedner et al.,
*J. Comput. Phys.***175**, 645 (2002) - T. Miyoshi & K. Kusano,
*J. Comput. Phys.***208**, 315 (2005)

- OpenMHD: Godunov-type code for magnetic reconnection and MHD problems (PDF 14.4MB)
- Introduction to magnetohydrodynamic simulations (PDF 13.7MB; Lecture at NAOJ 2014/2015)