(bc_inlet)=

# Inlet

The inlet of a flow is usually defined by a pressure gradient or an imposed velocity. The simplest case, a prescribed uniform velocity and pressure, is a local lattice-Boltzmann boundary condition and is described below. The harder case, a *turbulent* inlet that reproduces a realistic atmospheric boundary layer, is a topic in its own right and is covered in the {ref}`Turbulent inflow <theory_inflow>` chapter (the synthetic eddy method and PODFS precursor replay).

## Uniform Velocity

This boundary condition forces a uniform velocity and pressure profile.
Its implementation consists of setting the populations to their equilibrium, fixing the velocity and pressure values.

$$
f_{\bar{i}}\left(t+\Delta t\right)=f_{i}^{\mathrm{eq}}\left(\rho,\mathbf{u}\right)
$$ (uniform_velocity)

```{admonition} Use case
Uniform velocity is used to assure a constant velocity and density inlet, which increases the simulation stability and allows for the calculation of the pressure coefficient.
```

```{eval-rst}
.. footbibliography::
```