ppmpy.reconstruction module

ppmpy.reconstruction module#

Routines for doing the reconstruction of the interface states from cell-average data.

class HSEPPMInterpolant(grid, p, rho, g, *, limit=True, chi_flat=None, leave_as_perturbation=False)[source]#

Bases: PPMInterpolant

PPM interpolation for pressure that subtracts off HSE

Parameters:

  • grid (FVGrid) – the grid object.

  • p (ndarray) – the pressure defined on the grid.

  • rho (ndarray) – the density defined on the grid.

  • g (ndarray) – the gravitational acceleration defined on the grid

  • limit (bool, optional) – use limiting?

  • chi_flat (ndarray, optional) – the flattening coefficient.

construct_parabola()[source]#

compute the coefficients of a parabolic interpolant for the pressure in each zone by subtracting off HSE. This will give am, the parabola value on the left edge of a zone, ap, the parabola value on the right edge of the zone, and a6, a measure of the curvature of the parabola.

class PPMInterpolant(grid, a, *, limit=True, chi_flat=None)[source]#

Bases: object

Given a fluid variable a defined on the FVGrid grid, perform the PPM reconstruction

Parameters:

  • grid (FVGrid) – the grid object.

  • a (ndarray) – the data for a single component defined on the grid.

  • limit (bool, optional) – do we use limiting?

  • chi_flat (ndarray, optional) – the flattening coefficient.

construct_parabola()[source]#

compute the coefficients of a parabolic interpolant for the data in each zone. This will give am, the parabola value on the left edge of a zone, ap, the parabola value on the right edge of the zone, and a6, a measure of the curvature of the parabola.

draw_parabola(gp, *, scale=None)[source]#

Draw the parabolas in each zone on the axes ax.

Parameters:

  • gp (GridPlot) – the grid plot object

  • scale (float, optional) – normalization factor (default is maximum data value)

integrate(sigma)[source]#

integrate under the parabola to the left edge (Im) and right edge (Ip) for a fraction sigma = lambda * dt / dx, where lambda is the characteristic speed. If sigma is not moving toward the edge, then we us the limit of the parabola in that direction.

Parameters:

sigma (ndarray) – the dimensionless wavespeed (lambda dt / dx)

Returns:

  • Im (ndarray) – the integral under the parabola from the left edge through a distance sigma.

  • Ip (ndarray) – the integral under the parabola from the right edge through a distance sigma.

mark_cubic(gp, *, scale=None)[source]#

Mark the location of the initial interface states from the cubic interpolant on the axes ax.

Parameters:

  • gp (GridPlot) – the grid plot object

  • scale (float, optional) – normalization factor (default is maximum data value)

flattening_coefficient(grid, p, u)[source]#

Compute the flattening coefficient, chi, for a shock. This works by looking for compression and a steep pressure profile. chi = 1 means no flattening. This follows Saltzman (1994).

Parameters:

  • grid (FVGrid) – the grid object.

  • p (ndarray) – the pressure defined on the grid.

  • u (ndarray) – the velocity defined on the grid

Return type:

ndarray

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