lm_atm package¶

The pyro solver for low Mach number atmospheric flow. This implements as second-order approximate projection method. The general flow is:

create the limited slopes of rho, u and v (in both directions)
get the advective velocities through a piecewise linear Godunov method
enforce the divergence constraint on the velocities through a projection (the MAC projection)
predict rho to edges and do the conservative update
recompute the interface states using the new advective velocity
update U in time to get the provisional velocity field
project the final velocity to enforce the divergence constraint.

The projections are done using multigrid

Subpackages¶

lm_atm.problems package
- Submodules
- lm_atm.problems.bubble module

Submodules¶

lm_atm.LM_atm_interface module¶

lm_atm.LM_atm_interface.get_interface_states[source]¶

Compute the unsplit predictions of u and v on both the x- and y-interfaces. This includes the transverse terms.

Note that the gradp_x, gradp_y should have any coefficients already included (e.g. \(\beta_0/\rho\))

Parameters:

ng : int: The number of ghost cells
dx, dy : float: The cell spacings
dt : float: The timestep
u, v : ndarray: x-velocity and y-velocity
ldelta_ux, ldelta_uy: ndarray: Limited slopes of the x-velocity in the x and y directions
ldelta_vx, ldelta_vy: ndarray: Limited slopes of the y-velocity in the x and y directions
gradp_x, gradp_y : ndarray: Pressure gradients in the x and y directions
source : ndarray: Source terms

Returns:

out : ndarray, ndarray, ndarray, ndarray, ndarray, ndarray, ndarray, ndarray: unsplit predictions of u and v on both the x- and y-interfaces

lm_atm.LM_atm_interface.is_asymmetric[source]¶

Is the left half of s asymmetric to the right half?

Parameters:	ng : int The number of ghost cells nodal: bool Is the data nodal? s : ndarray The array to be compared
Returns:	out : int Is it asymmetric? (1 = yes, 0 = no)

lm_atm.LM_atm_interface.is_asymmetric_pair[source]¶

Are sl and sr asymmetric about an axis parallel with the y-axis in the center of domain the x-direction?

Parameters:	ng : int The number of ghost cells nodal: bool Is the data nodal? sl, sr : ndarray The two arrays to be compared
Returns:	out : int Are they asymmetric? (1 = yes, 0 = no)

lm_atm.LM_atm_interface.is_symmetric[source]¶

Is the left half of s the mirror image of the right half?

Parameters:	ng : int The number of ghost cells nodal: bool Is the data nodal? s : ndarray The array to be compared
Returns:	out : int Is it symmetric? (1 = yes, 0 = no)

lm_atm.LM_atm_interface.is_symmetric_pair[source]¶

Are sl and sr symmetric about an axis parallel with the y-axis in the center of domain the x-direction?

Parameters:	ng : int The number of ghost cells nodal: bool Is the data nodal? sl, sr : ndarray The two arrays to be compared
Returns:	out : int Are they symmetric? (1 = yes, 0 = no)

lm_atm.LM_atm_interface.mac_vels[source]¶

Calculate the MAC velocities in the x and y directions.

Parameters:

ng : int: The number of ghost cells
dx, dy : float: The cell spacings
dt : float: The timestep
u, v : ndarray: x-velocity and y-velocity
ldelta_ux, ldelta_uy: ndarray: Limited slopes of the x-velocity in the x and y directions
ldelta_vx, ldelta_vy: ndarray: Limited slopes of the y-velocity in the x and y directions
gradp_x, gradp_y : ndarray: Pressure gradients in the x and y directions
source : ndarray: Source terms

Returns:

out : ndarray, ndarray: MAC velocities in the x and y directions

lm_atm.LM_atm_interface.rho_states[source]¶

This predicts rho to the interfaces. We use the MAC velocities to do the upwinding

Parameters:	ng : int The number of ghost cells dx, dy : float The cell spacings rho : ndarray density u_MAC, v_MAC : ndarray MAC velocities in the x and y directions ldelta_rx, ldelta_ry: ndarray Limited slopes of the density in the x and y directions
Returns:	out : ndarray, ndarray rho predicted to the interfaces

lm_atm.LM_atm_interface.riemann[source]¶

Solve the Burger’s Riemann problem given the input left and right states and return the state on the interface.

This uses the expressions from Almgren, Bell, and Szymczak 1996.

Parameters:	ng : int The number of ghost cells q_l, q_r : ndarray left and right states
Returns:	out : ndarray Interface state

lm_atm.LM_atm_interface.riemann_and_upwind[source]¶

First solve the Riemann problem given q_l and q_r to give the velocity on the interface and: use this velocity to upwind to determine the state (q_l, q_r, or a mix) on the interface).

This differs from upwind, above, in that we don’t take in a velocity to upwind with).

Parameters:	ng : int The number of ghost cells q_l, q_r : ndarray left and right states
Returns:	out : ndarray Upwinded state

lm_atm.LM_atm_interface.states[source]¶

This is similar to mac_vels, but it predicts the interface states of both u and v on both interfaces, using the MAC velocities to do the upwinding.

Parameters:

ng : int: The number of ghost cells
dx, dy : float: The cell spacings
dt : float: The timestep
u, v : ndarray: x-velocity and y-velocity
ldelta_ux, ldelta_uy: ndarray: Limited slopes of the x-velocity in the x and y directions
ldelta_vx, ldelta_vy: ndarray: Limited slopes of the y-velocity in the x and y directions
source : ndarray: Source terms
gradp_x, gradp_y : ndarray: Pressure gradients in the x and y directions
u_MAC, v_MAC : ndarray: MAC velocities in the x and y directions

Returns:

out : ndarray, ndarray, ndarray, ndarray: x and y velocities predicted to the interfaces

lm_atm.LM_atm_interface.upwind[source]¶

upwind the left and right states based on the specified input velocity, s. The resulting interface state is q_int

Parameters:	ng : int The number of ghost cells q_l, q_r : ndarray left and right states s : ndarray velocity
Returns:	q_int : ndarray Upwinded state

lm_atm.simulation module¶

class lm_atm.simulation.Basestate(ny, ng=0)[source]¶

Bases: object

jp(shift, buf=0)[source]¶

v(buf=0)[source]¶

v2d(buf=0)[source]¶

v2dp(shift, buf=0)[source]¶

class lm_atm.simulation.Simulation(solver_name, problem_name, rp, timers=None)[source]¶

Bases: simulation_null.NullSimulation

dovis()[source]¶: Do runtime visualization

evolve()[source]¶: Evolve the low Mach system through one timestep.

initialize()[source]¶: Initialize the grid and variables for low Mach atmospheric flow and set the initial conditions for the chosen problem.

make_prime(a, a0)[source]¶

method_compute_timestep()[source]¶

The timestep() function computes the advective timestep (CFL) constraint. The CFL constraint says that information cannot propagate further than one zone per timestep.

We use the driver.cfl parameter to control what fraction of the CFL step we actually take.

preevolve()[source]¶: preevolve is called before we being the timestepping loop. For the low Mach solver, this does an initial projection on the velocity field and then goes through the full evolution to get the value of phi. The fluid state (rho, u, v) is then reset to values before this evolve.

read_extras(f)[source]¶: read in any simulation-specific data from an h5py file object f

write_extras(f)[source]¶: Output simulation-specific data to the h5py file f