Flash Project HEDS

This project reproduces a 2D magnetized Kelvin–Helmholtz (K–H) instability test using FLASH ver 4.8.

Initial Conditions

• Velocity:

  $\vec{v} = \left[ \frac{M}{2} \tanh\left(\frac{y}{y_0}\right),\ 0,\ 0 \right]$

• Magnetic field:

  $\vec{B} = c_a \sqrt{\rho} \left[\cos\theta,\ 0,\ \sin\theta \right]$

• Perturbation in the y-velocity:

  $v_y = v_{y0} \sin(2\pi x) \exp\left(-\frac{y^2}{\sigma^2}\right)$

Parameters (normalized MHD unit)

• Mach number: $M=1$
• Shear scale height: $y_0 = 1/20$
• Perturbation amplitude: $v_{y0} = 10^{-2}$
• Perturbation width: $\sigma = 0.1$
• Alfven speed: $c_a = 0.1$
• Domain: $[0, 1] \times [-1, 1]$
• Angle in xz plane: $\theta = \pi/3$

Reference

Mignone, A., Tzeferacos, P., & Bodo, G. (2010). High-order conservative finite difference GLM–MHD schemes for cell-centered MHD. Journal of Computational Physics, arXiv:1001.2832