# 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

## 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

Final density

Auto scale: (0, 16.614)

Final velocity_x

Auto scale: (-0.999999, 0.114766 )

Final pressure

Auto scale: (0, 5.44148)

Final velocity magnitude

Fixed scale: (0, 1.05)