二维范德瓦尔斯气体磁流体绕凸拐角的超声流动

Abstract

Abstract:

In this paper, we study the supersonic flow of two-dimensional isentropic van der Waals magnetic fluid around convex corners. According to the value of the specific volume of the incoming flow, the flow at the convex corner is discussed by classification. It is shown that the supersonic incoming flow can turn the convex corner by a centered rarefaction wave, a sonic shock or a composite wave of them, and the critical angle of the corner corresponding to the appearance of the vacuum phenomenon is obtained.

Key words: Convex corner, Van der Waals gas, Composite wave, Vacuum.

CLC Number:

O175.27

Wang Kefeng,You Shouke. Supersonic Flow of Two-dimensional Van Der Waals Gas Magnetic Fluid Around Convex Corner[J].Acta mathematica scientia,Series A, 2023, 43(4): 1170-1178.

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References

[1]	Courant R, Friedrichs K. Supersonic Flow and Shock Waves. New York: Interscience, 1948
[2]	Sheng W C, You S K. The two-dimensional unsteady supersonic flow around a convex corner. Journal of Hyperbolic Differential Equtions, 2018, 15: 443-461
[3]	Sheng W C, Yao A D. Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner. Applied Mathematics and Mechanics, 2019, 40(5): 117-130
[4]	Chen S X, Qu A F. Interaction of rarefaction waves in jet stream. Journal Differential Equations, 2010, 248(12): 2931-2954
[5]	Lai G. Interaction of fan-jump-fan composite waves in a two-dimensional steady jet for van der Waals gases. Journal of Hyperbolic Differential Equations, 2017, 14(1): 74-134
[6]	Lai G. Interaction of jump-fan composite waves in a two-dimensional jet for van der Waals gases. Journal of Mathematical Physics, 2015, 56(6): 061504
[7]	Sheng W C, You S K. Interaction of a centered simple wave and a planar rarefaction wave of the two-dimensional Euler equations for pseudo-steady compressible flow. Journal de Mathématiques Pures et Appliquées, 2018, 114: 29-50
[8]	Lai G, Sheng W C. Two-dimensional pseudosteady flows around a sharp corner. Arch Ration Mech Anal, 2021, 241(2): 805-884
[9]	Yao A D, Sheng W C. Two-dimensional pseudo-steady supersonic flow around a sharp corner. Journal of Applied Mathematics and Mechanics, 2022, 102(2): e201800270
[10]	Chen J J, Yin G, You S K. Expansion of gas by a sharp corner into vacuum for 2-D pesudo-steady compressible magnetohydrodynamics system. Nonlinear Analysis Real World Applications, 2019, 52: 102955
[11]	Chen J J, Sheng W C. Simple waves of the two dimensional compressible Euler equations in magnetohydrodynamics. Applied Mathematics Letters, 2018, 75: 24-29
[12]	Lai G. On the expansion of a wedge of van der Waals gas II. Journal Differential Equations, 2016, 260: 3538-3575
[13]	Chen J J, Sheng W C. Simple waves of the two dimensional compressible Euler equations in magnetohydrodynamics. Applied Mathematics Letters, 2017, 75: 24-49
[14]	Li J Q, Zhang T, Zheng Y X. Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations. Communications in Mathematical Physics, 2006, 267(1): 1-12
[15]	Cramer M S, Sen R. Exact solutions for sonic shocks in van der Waals gases. Physics of Fluids, 1987, 30(2): 377-385

Supersonic Flow of Two-dimensional Van Der Waals Gas Magnetic Fluid Around Convex Corner

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