2-D Noh shock test

This 2-D L&W test consists of a circular infinite strength shock propagating out from the origin on a square Cartesian grid. There is an analytical solution, and with Gamma = 5/3 it is as follows:

The shock front expands at velocity V_s = 1/3

Inside the shocked region: (r < t/3)

  • Density = 16
  • Pressure = 16/3
  • Velocity = 0

Outside the shock: (r > t/3)

  • Density = 1.0 + t/r
  • Pressure = 0.0
  • Radial velocity = -1.0
 

Initial conditions

  • Adiabatic index: Gamma = 5/3
  • The density is uniform, d = 1.0 everywhere
  • Pressure is set to P = 1.0e-6 everywhere, as an approximation to zero pressure.
  • The radial velocity, v(r), is -1.0 (ie flowing towards the origin). This gives an isothermal Mach number, M_i = (v * d)/ P = 1000.0.
 

Grid

  • 400 x 400 cells
  • Domain: 0.0 < x < 1.0, 0.0 < y < 1.0 , 1st quadrant.
  • Left and bottom boundaries are reflecting
  • Top and Right boundaries are updated each cycle with the analytical solution for the density, plus fixed inflow velocity and pressure - to allow the inflow to continue for an extended period of time.
 

Algorithm settings

  • CFL number: 0.8
  • Striping correction on, artificial viscosity parameter: alpha = 0.05
  • DivV threshold: 1.0, Scale: 1.0 (standard)
  • Flattening: minimum 0.0, maximum 1.0 (standard)
 

Ending condition

  • Time, t = 2.0

The code and configuration files plus output for Fyris to run the 2D Noh problem are available here.

 

Results

  • L1 Norms w.r.t. Analytical model at t = 2.0

    • L1 norm Density : 0.74 per cent

    • L1 norm Pressure : 0.87 per cent

QuickTime movies

t = 0.0 - 2.0, 20 frames

 

Final state

min  max

 (0, 16.614)

Final density

Auto scale: (0, 16.614)

 (-0.999999, 0.114766 )

Final velocity_x

Auto scale: (-0.999999, 0.114766 )

 (0, 5.44148)

Final pressure

Auto scale: (0, 5.44148)

 (0, 1.05)

Final velocity magnitude

Fixed scale: (0, 1.05)

 

Updated:  19 October 2017/Responsible Officer:  RSAA Director/Page Contact:  Webmaster