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:
\[\begin{split}\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho U) &= 0 \\
\frac{\partial U}{\partial t} + U \cdot \nabla U + \frac{\beta_0}{\rho} \nabla \left ( \frac{p'}{\beta_0} \right ) &= \frac{\rho'}{\rho} g \\
\nabla \cdot (\beta_0 U) = 0\end{split}\]
with \(\nabla p_0 = \rho_0 g\) and \(\beta_0 = p_0^{1/\gamma}\).
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