Pressure profiles at time around the shock discontinuity for the Mach 10 (top), 100 (middle), and 1000 (bottom) experiments. The result of the numerical solution is shown as diamonds; the red symbol highlights the position of the shock cell given by a shock finder algorithm. The solid line is the exact numerical solution. We see that the numerical shock tends to broaden with increasing Mach number, and given the largest error made on the post- and pre-shock regions, the error on the evaluated Mach number becomes larger for a small kernel (ncell,max = 2).
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