ppmpy.euler module

ppmpy.euler module#

The main Euler solver classes.

class Euler(nx, C, *, fixed_dt=None, bc_left_type='outflow', bc_right_type='outflow', gamma=1.4, init_cond=None, grav_func=None, params=None, use_hse_reconstruction=False, hse_as_perturbation=False, use_limiting=True, use_flattening=True)[source]#

Bases: object

A 1D compressible Euler solver using the piecewise parabolic method (PPM), following the original Colella & Woodward ideas

Parameters:

  • nx (int) – the number of zones

  • C (float) – the CFL number

  • fixed_dt (float, optional) – a fixed timestep to use for every step. In this case we do not estimate the timestep using the CFL criteria.

  • bc_left_type (str) – boundary condition type at the left edge. Allowed values are: “reflect”, “outflow”, “periodic”

  • bc_left_type – boundary condition type at the right edge. Allowed values are: “reflect”, “outflow”, “periodic”

  • init_cond (function) – the function to call to initialize the conserved state. This has the signature init_cond(euler) where euler is an Euler object.

  • grav_func (function) – the function to call to compute the gravitational acceleration. This has the signature: g = grav_func(grid, rho, params), where grid is a FVGrid`, rho is the density (array), and params is a dict of option parameters needed to interpret gravity.

  • params (dict, optional) – a dictionary of parameters that is passed to the initial condition and gravity functions. The ratio specific heats can be set here as “gamma”.

  • use_hse_reconstruction (bool, optional) – do we subtract off HSE from pressure before doing the parabolic reconstruction?

  • hse_as_perturbation (bool, optional) – do we do the characteristic tracing on p’ – the pressure perturbation?

  • use_limiting (bool, optional) – do we limit the parabola coefficients?

  • use_flattening (bool, optional) – do we apply flattening to the shock to smear them out?

advance_step()[source]#

Advance the conserved state through a single timestep

compute_fluxes(q_left, q_right)[source]#

given the left and right states, solve the Riemann problem to get the interface state and return the fluxes

Parameters:

  • q_left (ndarray) – the left primitive variable state on the interface.

  • q_right (ndarray) – the right primitive variable state on the interface.

Returns:

flux – the conserved flux through each interface.

Return type:

ndarray

cons_flux(state)[source]#

given an interface state, return the conservative flux

Parameters:

state (RiemannState) – the interface state from the Riemann solver.

Returns:

flux – the conserved flux through the interface for the input state.

Return type:

ndarray

cons_to_prim()[source]#

Convert the conserved variable state to primitive variables

Returns:

q – the primitive variable array.

Return type:

ndarray

construct_parabola()[source]#

Create the parabola reconstruction of the primitive variables

draw_prim(gp, ivar)[source]#

Draw the parabola for a primitive variable (ivar) on a GridPlot object

Parameters:

  • gp (GridPlot) – the grid plot object for the figure

  • ivar (int) – the index of the primitive variable to plot

draw_waves(gp)[source]#

Draw the domains seen by each of the 3 characteristic waves and the interface they interact with

Parameters:

gp (GridPlot) – the grid plot object for the figure

estimate_dt()[source]#

compute the Courant-limited timestep from the current fluid state

evolve(tmax, *, verbose=True)[source]#

The main evolution driver to advance the state to time tmax

Parameters:

  • tmax (float) – maximum simulation time to evolve to

  • verbose (bool, optional) – enable / disable verbosity

interface_states()[source]#

Trace the primitive variables to the interfaces by integrating under the parabola and doing a characteristic projection

Returns:

  • q_left (ndarray) – the left primitive variable state on the interface.

  • q_right (ndarray) – the right primitive variable state on the interface.

plot_prim(*, ivar=None)[source]#

Plot the primitive variable(s) for the current solution.

Parameters:

ivar (int) – the index of the variable to plot (None plots rho, u, p)

Return type:

matplotlib.pyplot.Figure

class FluidVars[source]#

Bases: object

A simple container that holds the integer indices we will use to refer to the different fluid components

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