wave moves with just the sonic velocity c 0 ¼ 1.18 (Arb. units). For example, let us
take the plot corresponding to t ¼ 50 in Fig. 4.13, we can observe that the forward
front has moved a distance equal to approximately 59 arbitrary units, giving a
velocity of 1.18 which is in excellent agreement with the value of c 0 . At much
later times (t > t shock ) as shown in Fig. 4.14 one can see the familiar vertical profile as
the shock wave advances down the tube.
Fig. 4.12 Uniform
acceleration of a piston to a
constant speed is shown
Fig. 4.13 Particle velocity is shown as a function of position at the times indicated for the
uniformly accelerated piston. The following parameters apply: γ ¼ 1.4, κ ¼ 1.2, Δx ¼ 0.3 and
Δt ¼ 0.05 (see text)
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4 Numerical Treatment of Plane Shocks
take the plot corresponding to t ¼ 50 in Fig. 4.13, we can observe that the forward
front has moved a distance equal to approximately 59 arbitrary units, giving a
velocity of 1.18 which is in excellent agreement with the value of c 0 . At much
later times (t > t shock ) as shown in Fig. 4.14 one can see the familiar vertical profile as
the shock wave advances down the tube.
Fig. 4.12 Uniform
acceleration of a piston to a
constant speed is shown
Fig. 4.13 Particle velocity is shown as a function of position at the times indicated for the
uniformly accelerated piston. The following parameters apply: γ ¼ 1.4, κ ¼ 1.2, Δx ¼ 0.3 and
Δt ¼ 0.05 (see text)
158
4 Numerical Treatment of Plane Shocks