# Buoyant Flows (Variable-Density and Fire-Induced)

Flows where large temperature differences make the density itself a variable of the
solution, beyond the small-perturbation Boussinesq limit of the {ref}`thermal cases <vc_differentially_heated_cavity>`. Here the density is slaved to the ideal-gas
equation of state $\rho = P/(rT)$ (the Tier-3 variable-density low-Mach closure of
{footcite:t}`taha2024fire`), the buoyancy is the exact $(\rho - \rho_\infty)\,g$ force,
and the energy field is transported alongside the LBM. This is the regime of buoyant
plumes and fires, where the hot gas can be several times lighter than the ambient and
the Boussinesq approximation no longer holds.

The cases build up in physical complexity:

- a closed-form-free **sanity check** that the closure runs stably and rises a warm
  bubble (the closure in isolation);
- a **non-reactive buoyant plume** (helium into air) that isolates the variable-density
  closure at a realistic density ratio, with no combustion;
- an **internally-heated open compartment** (the Steckler room fire) that adds a heat
  source, open ventilation and wall heat loss;
- a **reacting pool fire** (methane) that stacks single-step combustion and radiation on
  top of the closure.

```{important}
The variable-density bubble runs as a closure-stability sanity check. The helium
plume, Steckler room fire and methane pool fire are planned cases: each README
gives the intended setup, dimensionless matching and reference data, and lists the
solver capabilities the case depends on under a Prerequisites subsection.
```

```{toctree}
---
maxdepth: 1
---
01_lowmach_bubble/README.md
02_sandia_helium_plume/README.md
03_steckler_room_fire/README.md
04_sandia_methane_pool_fire/README.md
```

```{footbibliography}
```