2D HD Test: Rayleigh Taylor Instability

The Rayleigh-Taylor instability problem. This instability occurs in a gravitational field when a dense fluid lies above a less dense fluid.

Location

demo/hd2d_rayleigh_taylor/

Geometry

\(-0.25 \leq x \leq 0.25\)
\(-0.5 \leq y \leq 0.5\).

Force

A constant gravity is applied in the negative \(y\) direction. The gravitational acceleration is set to \(g=0.1\).

\[ \frac{\partial \rho v_y}{\partial t} = [...] - \rho g \]

Initial Conditions

The initial condition is described by the upper and lower states separated at \(y=0.0\). The density is \(\rho = 2\) in the upper region (\(y \geq 0\)) and \(\rho =1\) in the lower region (\(y < 0\)). The pressure is \(p =p_0 - \rho g y\). The ratio of specific heats is \(\gamma = 1.4\).

Boundary Conditions

A periodic boundary condition is imposed in the \(x\) direction, and a symmetric boundary condition is imposed on all variables in the \(y\) direction. Only \(V_y\) is set antisymmetric at \(y=\pm0.5\). Note that if you set the periodic boundary flag in the \(x\) direction to true in config.yaml, the symmetric boundary condition no longer works.

domain:
  periodic:
    x: true  # when this flag is true, the symmetric boundary condition does not work

Results

A Python script for visualization is provided. The plots of the results are saved in demo/hd2d_rayleigh_taylor/figs.

cd demo/hd2d_rayleigh_taylor
python plot_data.py

hd2d_rayleigh_taylor

3D Version

The extension to 3D is achieved simply by setting k_size to a value larger than 1 in the configuration file config.yaml.

# config.yaml
grid:
  i_size: 512
  j_size: 512
  k_size: 512 # change from 1 to 512