Low Mach number hydrodynamics

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:

\[\begin{split}\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho U) &= 0 \\ \frac{\partial U}{\partial t} + U \cdot \nabla U + \frac{\beta_0}{\rho} \nabla \left ( \frac{p'}{\beta_0} \right ) &= \frac{\rho'}{\rho} g \\ \nabla \cdot (\beta_0 U) = 0\end{split}\]

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

lm_atm solver

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

supported problems

bubble

Initialize a buoyant bubble in a hydrostatic atmosphere. This is meant to be used to compare with the compressible solver bubble problem.

parameters:

name	default
bubble.dens_base	10.0
bubble.scale_height	2.0
bubble.x_pert	2.0
bubble.y_pert	2.0
bubble.r_pert	0.25
bubble.pert_amplitude_factor	5.0
bubble.dens_cutoff	0.01