Initialisation on (x,y) geometry

Describes different initial conditions for the simulations in \((x,y)\) geometry.

(See more on the simulation in simulations.)

Kelvin-Helmholtz instability test case

For this test case, the KelvinHelmholtzInstabilityInitialisation sets the initial conditions at

\[ f(0, x, y) = f_{\text{eq}}(x,y) + \varepsilon\cos(kx), \\ f_{\text{eq}}(x,y) = \sin(y) \]

with \(\varepsilon = 0.015\) the amplitude of perturbation and \(k = 2\pi/ L_x = 0.5\) the mode of the perturbation.

We suppose the domain periodic on \(x\) and \(y\).

These are applied in the guiding-centre equations. See in guiding-centre.