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{aligned} \frac{\partial ρ}{\partial t} + \nabla \cdot (ρ U) & = 0 \\ \frac{\partial U}{\partial t} + U \cdot \nabla U + \frac{β_{0}}{ρ} \nabla (\frac{p^{'}}{β_{0}}) & = \frac{ρ^{'}}{ρ} g \\ \nabla \cdot (β_{0} U) = 0 \end{aligned}

with $\nabla p_{0} = ρ_{0} g$ and $β_{0} = p_{0}^{1 / γ}$ .

`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

option	value	description
`cfl`	`0.8`

option	value	description
`gamma`	`1.4`	pres = rho ener (gamma - 1)

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

Low Mach number hydrodynamics

Contents

Low Mach number hydrodynamics#

lm_atm solver#

supported problems#

bubble#

`lm_atm` solver#

`bubble`#