2D MHD Test: Orszag-Tang Vortex

The Orszag-Tang vortex problem [Orszag and Tang, 1979] is a standard test problem for magnetohydrodynamics (MHD) codes. This problem involves the interaction of two vortices in a magnetized medium, and forms complex structures and turbulence.

Location

demo/mhd2d_vortex/

Geometry

\(0 \leq x \leq 1\)
\(0 \leq y \leq 1\).

Initial Conditions

The initial condition is set as follows. The ratio of specific heats is \(\gamma = 5/3\).

\[\begin{split} \begin{align*} \rho &= 1, \\ p &= \frac{1}{\gamma}, \\ v_x &= -v_0 \sin(2\pi y), \\ v_y & = v_0 \sin(2\pi x), \\ v_z & = 0, \\ B_x & = B_0 \sin(2\pi y),\\ B_y & = B_0 \sin(4\pi x),\\ B_z & = 0, \end{align*} \end{split}\]

Here \(v_0 = 1\) and \(B_0 = \sqrt{4\pi}/\gamma\).

Boundary Conditions

A periodic boundary condition is imposed on all variables at all boundaries.

Results

A Python script for visualization is provided. The plots of the results are saved in demo/mhd2d_vortex/figs.

cd demo/mhd2d_vortex
python plot_data.py

mhd2d_vortex