The first results have been obtained with a Reynolds number equal to 1000. They are reported in the section "Graphics with Re=1000" at different times between 0,2 and 0,5. The evolution of the wave front during the time shows that it becomes a discontinuity about at t=0.2. As we can expect, the shock is straight and it is convected with a constant velocity in y direction. We note that it dissipates itself when it propagates. This phenomenon is principally a physical dissipation due to the second order terms in the equation, and not a numerical dissipation. To veriffy that, we just raffine the grid in order to decrease any numerical dissipation.
In order to study the influence of Reynolds number, we also solve equations with a Reynolds number equal to 100.
In this case, results are differents because the shock wave never appears. We can see that on the corresponding graphics located in the section "Graphics with Re=100'' at the same times. We note that the wave front stiffened until a particular time, after for dissipates itself, due to the diffusion effects great in front of the advection effects.
Click here to see animations of the steepening and the propagation of the wave front with Re=1000 and Re=100.