Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner

doi:10.1007/s10483-019-2475-6

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (5): 705-718.doi: https://doi.org/10.1007/s10483-019-2475-6

Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner

Wancheng SHENG¹, Aidi YAO^1,2

1. Department of Mathematics, Shanghai University, Shanghai 200444, China;
2. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, Anhui Province, China

收稿日期:2018-08-20 修回日期:2018-10-18 出版日期:2019-05-01 发布日期:2019-05-01
通讯作者: Wancheng SHENG E-mail:mathwcsheng@t.shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11371240 and 11771274)

Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner

Wancheng SHENG¹, Aidi YAO^1,2

1. Department of Mathematics, Shanghai University, Shanghai 200444, China;
2. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, Anhui Province, China

Received:2018-08-20 Revised:2018-10-18 Online:2019-05-01 Published:2019-05-01
Contact: Wancheng SHENG E-mail:mathwcsheng@t.shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11371240 and 11771274)

摘要/Abstract

摘要： The two-dimensional (2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar solutions for the supersonic flow around the convex corner are constructed, where the properties of the centered simple wave are used for the 2D isentropic irrotational pseudo-steady Euler equations. The geometric procedures of the center simple waves are given. It is proven that the supersonic flow turns the convex corner by an incomplete centered expansion wave or an incomplete centered compression wave, depending on the conditions of the downstream state.

关键词: composite circular cylinder, internal crack, Cauchy-type integral equation, centered expansion simple wave, centered compression simple wave, pseudo-steady flow, two-dimensional (2D) Euler equation, isothermal flow

Abstract: The two-dimensional (2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar solutions for the supersonic flow around the convex corner are constructed, where the properties of the centered simple wave are used for the 2D isentropic irrotational pseudo-steady Euler equations. The geometric procedures of the center simple waves are given. It is proven that the supersonic flow turns the convex corner by an incomplete centered expansion wave or an incomplete centered compression wave, depending on the conditions of the downstream state.

Key words: composite circular cylinder, internal crack, Cauchy-type integral equation, pseudo-steady flow, centered compression simple wave, isothermal flow, two-dimensional (2D) Euler equation, centered expansion simple wave

中图分类号:

Wancheng SHENG, Aidi YAO. Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(5): 705-718.

参考文献

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Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner

Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner

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