OpenMHD code

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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, OpenMP, and CUDA.

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

Obtaining the code

The following version is available in .tar.gz format.

The source code is hosted on GitHub.

Basic equations

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.

  1. S. Zenitani & T. Miyoshi, Phys. Plasmas 18, 022105 (2011)
  2. S. Zenitani, Phys. Plasmas 22, 032114 (2015)
  3. A. Dedner et al., J. Comput. Phys. 175, 645 (2002)
  4. T. Miyoshi & K. Kusano, J. Comput. Phys. 208, 315 (2005)
Presentation file