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.

Trendmd

Figures/Tables 10

References 15

[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 doi: 10.1016/j.jde.2010.03.004
[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 doi: 10.1063/1.4922443
[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 doi: 10.1016/j.matpur.2017.07.019
[8]	Lai G, Sheng W C. Two-dimensional pseudosteady flows around a sharp corner. Arch Ration Mech Anal, 2021, 241(2): 805-884 doi: 10.1007/s00205-021-01665-0
[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 doi: 10.1016/j.nonrwa.2019.06.005
[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 doi: 10.1016/j.aml.2017.05.023
[12]	Lai G. On the expansion of a wedge of van der Waals gas II. Journal Differential Equations, 2016, 260: 3538-3575 doi: 10.1016/j.jde.2015.10.048
[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 doi: 10.1016/j.aml.2017.05.023
[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 doi: 10.1007/s00220-006-0033-1
[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

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 10

References 15

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Li Xiaoli,Chen Xiaoli. Stability and Exponential Decay of the 3D Boussinesq Equations with Partial Dissipation [J]. Acta mathematica scientia,Series A, 2023, 43(3): 754-770.
[2]	Zhang Mingyu. Global Existence of the Compressible and Radiative Flux with Temperature-Dependent Transport Coefficients [J]. Acta mathematica scientia,Series A, 2023, 43(2): 458-480.
[3]	Shi Yingchun, Lai Geng. Formation of Singularities in Solutions to Spherically Symmetric Relativistic Euler Equations for a Chaplygin Gas [J]. Acta mathematica scientia,Series A, 2023, 43(2): 481-490.
[4]	Changwang Xiao,Fei Guo. Global Existence and Blowup Phenomena for a Semilinear Wave Equation with Time-Dependent Damping and Mass in Exponentially Weighted Spaces [J]. Acta mathematica scientia,Series A, 2020, 40(6): 1568-1589.
[5]	Qingling Zhang,Ying Ba. The Perturbed Riemann Problem for the Pressureless Euler Equations with a Flocking Dissipation [J]. Acta mathematica scientia,Series A, 2020, 40(1): 49-62.
[6]	Lijun Pan,Xinli Han,Tong Li. The Generalized Riemann Problem for Chromatography Equations with Delta Shock Wave [J]. Acta mathematica scientia,Series A, 2019, 39(6): 1300-1313.
[7]	Jimeng Li. Oscillation Analysis of Second-Order Generalized Emden-Fowler-Type Delay Differential Equations [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1041-1054.
[8]	Changqing Tong,Jing Zheng. Periodic Solutions of a Semi-Linear Klein-Gordon Equations with High Frequencies [J]. Acta mathematica scientia,Series A, 2019, 39(3): 484-500.
[9]	Didi Hu,Xuan Wang. The Strong Time-Dependent Global Attractors for the Non-Damping Abstract Evolution Equations with Fading Memory [J]. Acta mathematica scientia,Series A, 2019, 39(1): 81-94.
[10]	Wang Li. The Inverse Problem for the Supersonic Plane Flow Past a Curved Wedge [J]. Acta mathematica scientia,Series A, 2018, 38(4): 679-686.
[11]	Luo Liping, Luo Zhenguo, Deng Yihua. Effect of Impulsive Perturbations on Oscillation of Nonlinear Delay Hyperbolic Distributed Parameter Systems [J]. Acta mathematica scientia,Series A, 2018, 38(2): 313-321.
[12]	Li Wenjuan, Tang Huo, Yu Yuanhong. Oscillation of the Neutral Emden-Fowler Differential Equation [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1062-1069.
[13]	Zeng Yunhui, Luo Liping, Yu Yuanhong. Oscillation Criteria for Generalized Neutral Emden-Fowler Equations [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1067-1081.
[14]	Song Naiqi, Zhao Jiman. Strichartz Estimates for the Wave Equation with the Full-Laplacian on the Quaternion Heisenberg Group [J]. Acta mathematica scientia,Series A, 2016, 36(1): 90-116.
[15]	Lei Qian, Li Ning, Yang Han. Blow Up and Asymptotic Behavior in the Beam Equation [J]. Acta mathematica scientia,Series A, 2015, 35(4): 738-747.