# Shearing box in SPH

Following [Stone & Gardiner 2010](https://ui.adsabs.harvard.edu/abs/2010ApJS..189..142S/abstract), the shearing box force is:

$$
    \mathbf{f} =
        2\Omega_0 \left(  q \Omega_0 x +  v_y \right) \mathbf{e}_{x} -2\Omega_0
    v_x \mathbf{e}_{y} - \Omega_0^2 z \mathbf{e}_{z}
$$

Shear speed:

$$
\omega = q \Omega_0 L_x
$$

To add it in a runscript:

```python
xm, ym, zm = bmin
xM, yM, zM = bmax

Omega_0 = 1
eta = 0.00
q = 3.0 / 2.0

shear_speed = -q * Omega_0 * (xM - xm)

cfg = model.gen_default_config()
cfg.set_artif_viscosity_VaryingCD10(
    alpha_min=0.0, alpha_max=1, sigma_decay=0.1, alpha_u=1, beta_AV=2
)
cfg.set_boundary_shearing_periodic((1, 0, 0), (0, 1, 0), shear_speed)
cfg.set_eos_adiabatic(gamma)
cfg.add_ext_force_shearing_box(Omega_0=Omega_0, eta=eta, q=q)
cfg.set_units(shamrock.UnitSystem())
cfg.print_status()
```