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2D Noh Shock Test

This 2D 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 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

Density (448kB)

Pressure (96kB)

Final State

Final Density AutoScale: (0, 16.614)	Pressure AutoScale: (0, 5.44148)
Velocity_x AutoScale: (-0.999999, 0.114766 )	Velocity Magnitude Fixed Scale: (0, 1.05)
(min max)