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Seminars

Analysis Seminar

Interaction of fan-shock-fan composite waves in 2D pseud-steady flows of van der Waals gases

2025/04/29 (Tue.) 10:00~13:00
  • Date : 2025/04/29 (Tue.) 10:00~13:00
  • Location : online
  • Speaker : Geng Lai (Shanghai University)
  • Organizer : Tai-Ping Liu (AS)
  • Abstract : We study the expansion into vacuum of a wedge of gas at rest. This problem catches several important classes of wave interactions in the context of 2D Riemann problems. When the gas at rest is a non-ideal gas (e.g., van der Waals gas), the gas away from the sharp corner of the wedge may expand into the vacuum as two symmetrical planar fan waves, shock-fan composite waves, or fan-shock-fan composite waves. Then the expansion in vacuum problem can be reduced to three types of wave interactions: interaction of fan waves, interaction of shock-fan waves, and interaction of fan-shock-fan waves. In this talk, i will introduce the interaction of fan-shock-fan waves. This interaction involves shock waves in the interaction region and is actually a shock free boundary problem. We find that the shocks in the interaction region are envelopes of one of the acoustic families of characteristics of the flow behind them, and not characteristics. This results in that the flow behind the shocks is not C^1 smooth up to the shock boundaries. By virtue of the hodograph transformation method and the characteristic decomposition method, we construct a global piecewise smooth solution to the expansion in vacuum problem for the third case. 【Registration】Online participants must fill the application form below. A link to the meeting will be distributed on a first-come, first-serve basis, due to device limitations.

Click here to register: https://forms.gle/xpZsvpvr9wfVU9aN9 (Deadline: 4pm, Apr. 28)
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