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
- 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.
- 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.
- 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)
- Time, t = 2.0
The code and configuration files plus output for Fyris to run the 2D Noh problem are available here.
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
t = 0.0 - 2.0, 20 frames