−1
−0.5
0
0.5
1
1.5
2
− 1
− 0.9
− 0.8
− 0.7
− 0.6
− 0.5
− 0.4
− 0.3
− 0.2
− 0.1
0
0.1
Particle velocity at t=1
Position, x
−1
−0.5
0
0.5
1
1.5
2
Position, x
−1
−0.5
0
0.5
1
1.5
2
Position, x
0.103
1.183
0.2
0.4
0.6
0.8
1
1.2
Pressure at t=1
Pressure (Arb. units)
Density (Arb. units)
Particle velocity (Arb. units)
0.103
1.183
0.2
0.4
0.6
0.8
1
1.2
Density at t=1
0.103
1.183
Fig. A.4 Particle velocity, pressure and density (solid lines) obtained numerically for the piston
withdrawal problem. The broken lines give the variations in these parameters within the expansion
fan according to the method of characteristics (see text)
Appendix A
321
−0.5
0
0.5
1
1.5
2
− 1
− 0.9
− 0.8
− 0.7
− 0.6
− 0.5
− 0.4
− 0.3
− 0.2
− 0.1
0
0.1
Particle velocity at t=1
Position, x
−1
−0.5
0
0.5
1
1.5
2
Position, x
−1
−0.5
0
0.5
1
1.5
2
Position, x
0.103
1.183
0.2
0.4
0.6
0.8
1
1.2
Pressure at t=1
Pressure (Arb. units)
Density (Arb. units)
Particle velocity (Arb. units)
0.103
1.183
0.2
0.4
0.6
0.8
1
1.2
Density at t=1
0.103
1.183
Fig. A.4 Particle velocity, pressure and density (solid lines) obtained numerically for the piston
withdrawal problem. The broken lines give the variations in these parameters within the expansion
fan according to the method of characteristics (see text)
Appendix A
321