pencil.calc.shocktube

Contains the classes containing the SOD analytic data

Classes

SodShock

SodShock -- holds shock profiles and coordinate arrays

Functions

sod(*args, **kwargs)

Solve Sod shock tube for given parameters and resolution

Module Contents

pencil.calc.shocktube.sod(*args, **kwargs)

Solve Sod shock tube for given parameters and resolution

Signature:

calc_shocktube(xarr, time, par=list(), lreference=False, DEBUG=False,

lplot=False, itplot=0, magic=[‘ee’,’tt’,’Ms’])

Parameters:

  • *xarr* (Coordinate vector (the initial discontinuity is always at x=0))

  • *time* (Time after membrane snapped.)

  • *par* (Param object)

  • *lreference* (Use default parameters for Sod's reference problem.)

  • *DEBUG* (Flag to switch on output)

  • *lplot* (Plot first snapshot profiles)

  • *itplot* (Iteration index of snaphot to plot)

  • *magic* (Optional profiles to include in Sod object.)

Return type:

Class containing coordinates and shock profiles

Notes

Adapted from IDL script shocktube.pro Analytical solution of the shocktube problem

Initial state (pressure jump)

——————+——————

pl | pr

——————+——————

0

Evolved state: membrane has snapped, four domains

x x x x 1 2 3 4

Velocity

-**********——————–***—

Nomenclature pl, pr - pressure far left/right from the shock structure p2 - pressure in the expansion wave p3=p4 - no pressure jump across the contact discontinuity p: pressure, T: temperature, rho: density, u: flow velocity, cs: sound speed

gamma (adiabatic index) is assumed to be constant

The borders between the different domains are x1, x2, x3, x4 and move at velocities ul-csl, u4-c4, u2, u3, u4, respectively.

Warning: This works so far only in the case ul=ur=0

Examples

>>> shock = pc.calc.sod()
>>> shock.keys()
t
x
rho
ux
pp
ee
tt
Ms
class pencil.calc.shocktube.SodShock

Bases: object

SodShock – holds shock profiles and coordinate arrays

Fill members with default values

t
keys()
calc_shocktube(xarr, time, par=list(), lreference=False, DEBUG=False, lplot=False, itplot=0, magic=['ee', 'tt', 'Ms'])

xarr: Coordinate vector (the initial discontinuity is always at x=0)

time: Time after membrane snapped.

par: Param object

lreference: Use default parameters for Sod’s reference problem.

DEBUG: Flag to switch on output

lplot: Plot first snapshot profiles

itplot: Iteration index of snaphot to plot

magic: Optional profiles to include in Sod object.