Interaction of Rarefaction Waves and Vacuum in a Convex Duct

Chen, Shuxing; Qu, Aifang

doi:10.1007/s00205-014-0738-9

Cited by 17 publications

(10 citation statements)

References 9 publications

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“…Remark 5. For the case that Riemann invariants are both constants on Γ in which is a straight segment vertical to the velocity of the incoming flow, the problem has been solved by Chen and Qu in [5]. Here we extend their work to a more general case.…”

Section: Remarkmentioning

confidence: 89%

“…On the other hand, if the rotation is involved, in the general case, due to the possible compression of gases, the smooth solutions will blow up and the shock is formed (see [6], [20], [21] and [23]). Meanwhile, if the gases are suitably expanded or expanded into the vacuum, the global solutions can exist(see [4], [5], [10], [11], [22], [24] and [27]- [29]).…”

Section: Remark 3 For the M-d Compressiblementioning

confidence: 99%

“…Preliminaries. In this section, we start with some basic structures of the steady plane isentropic flow, which can be characterized by the Euler system (5).…”

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confidence: 99%

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The global supersonic flow with vacuum state in a 2D convex duct

Shen

2021

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This paper concerns the motion of the supersonic potential flow in a two-dimensional expanding duct. In the case that two Riemann invariants are both monotonically increasing along the inlet, which means the gases are spread at the inlet, we obtain the global solution by solving the problem in those inner and border regions divided by two characteristics in (x, y)-plane, and the vacuum will appear in some finite place adjacent to the boundary of the duct. In addition, we point out that the vacuum here is not the so-called physical vacuum. On the other hand, for the case that at least one Riemann invariant is strictly monotonic decreasing along some part of the inlet, which means the gases have some local squeezed properties at the inlet, we show that the C 1 solution to the problem will blow up at some finite location in the non-convex duct.

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Section: Remarkmentioning

confidence: 89%

Section: Remark 3 For the M-d Compressiblementioning

confidence: 99%

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The global supersonic flow with vacuum state in a 2D convex duct

Shen

2021

era

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“…(1.9) see Figure 2. Global smooth isentropic irrotational supersonic flows in the semi-infinite divergent duct were constructed in [2,14,15]. In [15], the authors also constructed a global smooth transonic solution in a De Laval nozzle.…”

Section: Introductionmentioning

confidence: 99%

“…In order to prove that the global solution can be constructed after solving a finite number of Gourst problems and slip boundary problems, the method of hodograph transformation in [2] does not work here, since we do not have Riemann invariants for the 2D steady full Euler system. In this paper, we use characteristic angles α and β.…”

Section: Introductionmentioning

confidence: 99%

Global non-isentropic rotational supersonic flows in a semi-infinite divergent duct

Lai

2019

Preprint

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Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global non-isentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the duct, and the state of the flow is given at the inlet of the duct. The solution is constructed by the method of characteristics. The main difficulty for the global existence is that uniform a priori C 1 norm estimate of the solution is hard to obtain, especially when the solution tends to vacuum state. We derive a group of characteristic decompositions for the 2D steady full Euler system. Using these decompositions, we obtain the uniform a priori estimates of the derivatives of the solution. A sufficient condition for the appearance of vacuum is given. We also show that if there is a vacuum then the vacuum is always adjacent to one of the walls, and the interface between gas and vacuum must be straight.

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Global Continuous Sonic–Supersonic Flows in Two-Dimensional Semi-infinite Divergent Ducts

Lai

2021

J. Math. Fluid Mech.

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Interaction of Rarefaction Waves and Vacuum in a Convex Duct

Cited by 17 publications

References 9 publications

The global supersonic flow with vacuum state in a 2D convex duct

The global supersonic flow with vacuum state in a 2D convex duct

Global non-isentropic rotational supersonic flows in a semi-infinite divergent duct

Global Continuous Sonic–Supersonic Flows in Two-Dimensional Semi-infinite Divergent Ducts

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