This report contains the graphs for shock-contact interaction problem and Sod problem.( The one Yuri did) From the diffusion of contact discontinuity study which I did ( Report 1) shows that even for shock -contact interaction the code behaves as second order near the contact discontinuity in the slow fast case but not in fast slow case i.e width of contact varies as t^1/3.But the second verification that the density is given by the formulae given for different order by Yanenko and Vorohztsov apply for the initial condition of Sod problem as is shown in the graphs for second case. The point where the contact dicontinuity curve for different resolutions meet is very close to what is predicted by theory. Though in essence the shock contact interaction problem behaves the same when shock paases by but the initial conditions are different and hence the second condition that at contact rho=(rho1+2*rho2)/3 is not satisfied because the density the same as initial and the velocity and pressures will also be different from the initial conditions.


Plot of contact discontinuity with resolution in shock -contact interaction problem

Mach number M=2.0
For fast slow case:density ratio(eeta)=7.0
For slow fast case:density ratio(eeta)=0.14
Gamma = 1.20886
Ambient density = 1.0
The plots are for time t=0.3



Contact discontinuty in FS case for 1D run
The curves for different resolutions meet at density=22.3

Contact discontinuty in SF case for 1D run
The curves for different resolutions meet at density=0.92


Contact discontinuty in FS case for y invariant 2D run
Curves for different resolution meet at density = 21.5

Contact discontinuty in SF case for y invariant 2D run
Curves for different resolution meet at density = 0.89


Contact discontinuty in FS case for 2D run with theta=30 degrees

Curves for different resolution don't meet at one point. This may be due to the shock because the case without shock, this doesn't happen



Contact discontinuty in SF case for 2D run with theta = 30 degrees

Curves for different resolution don't meet at one point



Plots of Contact discontinuity with resolution without any shock

In this case, whole domain was initialised with a constant velocity and no shock
Initial velocity u0=1.5
The plots are at time t=0.3


Contact discontinuty in FS case for 1D run
Curves for different resolutions meet at density =5.8



Contact discontinuty in SF case for 1D run
Curves for different resolution meet at density=0.4.


Contact discontinuty in FS case for y invariant 2D run
Curves for different resolution meet at density = 5.875



Contact discontinuty in SF case for y invariant 2D run
Curves for different resolution meet at density =0.45


Contact discontinuty in FS case for 2D run with theta=30 degrees
Curves for different resolution meet at density = 6.2



Contact discontinuty in SF case for 2D run with theta=30 degrees
Curves for different resolution meet at density =0.45

The value predicted by the theoretical arguements of Yanenko for the two cases will be:
For slow fast case (eeta=0.14) (1+2*0.14)/3= 0.4266
For fast slow case (eeta=7.0) (1+2*7.0)/3= 5.0

The results obtained from the Sod problem( Without any shock) match very closely with the one we obtain with PPM. This is the case Yuri did. If we do the shock - contact interaction problem, I doubt that because of the different initial conditions which change because shock passes by will not give us the same results even if we find the post shock densities and use them. The velocity and pressure will no longer be uniform. But we can still present an arguement that the this case also behaves like the Sod problem as the diffusion of contact discontinuity varies as t^(1/3) as for this case.

The images can be saved by rigt clicking and saving the picture.