# Low Mach number hydrodynamics solver¶

pyro’s low Mach hydrodynamics solver is designed for atmospheric flows. It captures the effects of stratification on a fluid element by enforcing a divergence constraint on the velocity field. The governing equations are:

with \(\nabla p_0 = \rho_0 g\) and \(\beta_0 = p_0^{1/\gamma}\).

As with the incompressible solver, we implement a cell-centered approximate projection method.

The main parameters that affect this solver are:

section: [driver]

option

value

description

cfl

`0.8`

section: [eos]

option

value

description

gamma

`1.4`

pres = rho ener (gamma - 1)

section: [lm-atmosphere]

option

value

description

limiter

`2`

limiter (0 = none, 1 = 2nd order, 2 = 4th order)

proj_type

`2`

what are we projecting? 1 includes -Gp term in U*

grav

`-2.0`

## Examples¶

### bubble¶

The bubble problem places a buoyant bubble in a stratified atmosphere and watches the development of the roll-up due to shear as it rises. This is run as:

```
./pyro.py lm_atm bubble inputs.bubble
```