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

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Applied Mathematics and Mechanics(English Edition) 2019年第5期40卷 705-718页

作者： wancheng sheng Aidi YAO Department of Mathematics Shanghai University School of Mathematics and Big Data Anhui University of Science and Technology

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： pseudo-steady flow isothermal flow two-dimensional (2D) Euler equation centered expansion simple wave centered compression simple wave

Limits of Riemann Solutions for Isentropic MHD in a Variable Cross-Section Duct as Magnetic Field Vanishes

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Chinese Annals of Mathematics,Series B 2024年第4期45卷 637-660页

作者： wancheng sheng Tao XIAO Department of Mathematics Shanghai UniversityShanghai 200444China Shanghai Aircraft Design and Research Institute Shanghai 201210China

The stability for magnetic field to the solution of the Riemann problem for the polytropic fluid in a variable cross-section duct is *** the vanishing magnetic field method,the stable solutions are determined by comparing the limit solutions with the solutions of the Riemann problem for the polytropic fluid in a duct obtained by the entropy rate admissibility criterion.

关键词： Variable duct Magnetogasdynamics Riemann problem Stability Vanishing magnetic field method

The Riemann Problem for Chaplygin Gas Flow in a Duct with Discontinuous Cross-Section

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Chinese Annals of Mathematics,Series B 2020年第4期41卷 531-546页

作者： Liancheng DANG wancheng sheng Department of Mathematics Shanghai UniversityShanghai 200444China. Corresponding author.Department of Mathematics Shanghai UniversityShanghai 200444China.

The fluid flows in a variable cross-section duct are nonconservative because of the source ***,the Riemann problem and the interactions of the elementary waves for the compressible isentropic gas in a variable cross-section duct were *** this paper,the Riemann problem for Chaplygin gas flow in a duct with discontinuous cross-section is *** elementary waves include rarefaction waves,shock waves,delta waves and stationary waves.

关键词： Duct flow Chaplygin gas equations Nonconservative Riemann problem Delta wave Stationary wave

Centered Waves for the Two-dimensional Pseudo-Steady van der Waals Gas Satisfied Maxwell's Law Around a Sharp Corner

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Chinese Annals of Mathematics,Series B 2024年第4期45卷 537-554页

作者： Shuangrong LI wancheng sheng Department of Mathematics Shanghai UniversityShanghai 200444China Department of Mathematics Zhejiang University of Science and TechnologyHangzhou 310023China Corresponding author.Department of Mathematics Newtouch Center for Mathematics of Shanghai UniversityShanghai UniversityShanghai 200444China

In this paper,the authors study the centered waves for the two-dimensional(2D for short)pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell's law around a sharp *** view of the initial value of the specific volume and the properties of van der Waals gas,the centered waves at the sharp corner are constructed by *** is shown that the supersonic incoming flow turns the sharp corner by a centered simple wave or a centered simple wave with right-contact discontinuity or a composite wave(jump-fan,fan-jump or fan-jump-fan),or a combination of waves and constant ***,the critical angle of the sharp corner corresponding to the appearance of the vacuum phenomenon is obtained.

关键词： Two-dimensional Euler equations Van der Waals gas Centered simple wave Composite wave

The Expansion of a Wedge of Gas into Vacuum with Small Angle in Two-Dimensional Isothermal Flow

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Chinese Annals of Mathematics,Series B 2016年第3期37卷 395-404页

作者： Ju GE wancheng sheng Department of Mathematics Shanghai University Shanghai 200444 China Department of Mathematics China University of Petroleum Qingdao 266555 Shandong China

In this paper, the authors consider the expansion problem of a wedge of gas into vacuum for the two-dimensional Euler equations in isothermal flow. By the bootstrapping argument, they prove the global existence of the smooth solution through the direct method in the case 0 〈 θ 〈 -θ=arctan 1/（√2＋√5）, where θ is the half angle of the wedge. Furthermore, they get the uniform C^1,1 estimates of the solution to the expansion problem.

关键词： Hyperbolic partial differential equation 2D Riemann problem Rarefaction wave Isothermal flow

Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations

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Chinese Annals of Mathematics,Series B 2008年第6期29卷 611-622页

作者： Gan YIN wancheng sheng Department of Mathematics Shanghai University Shanghai 200433 China College of Mathematics and System Sciences Xinjiang University Urumqi 830046 Xinjiang China Department of Mathematics Shanghai University Shanghai 200433 China

The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.

关键词： Relativistic Euler equations in special relativity Pressureless relativistic Euler equations Delta shock waves Vacuum Vanishing pressure limits

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Chinese Annals of Mathematics,Series B 2007年第6期28卷 701-708页

作者： Wenhua SUN wancheng sheng School of Mathematics and Information Sciences Shandong University of Technology Zibo 255049 Shandong China Department of Mathematics Shanghai University Shanghai 200444 China

The non-selfsimilar Riemann problem for two-dimensional zero-pressure flow in gas dynamics with two constant states separated by a convex curve is considered. By means of the generalized Rankine-Hugoniot relation and the generalized characteristic analysis method, the global solution involving delta shock wave and vacuum is constructed. The explicit solution for a special case is also given.

关键词： Zero-pressure flow Non-selfsimilar Riemann problem Generalized Rankine-Hugoniot relation Entropy condition Delta shock

GLOBAL SOLUTIONS OF THE PERTURBED RIEMANN PROBLEM FOR THE CHROMATOGRAPHY EQUATIONS

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Acta Mathematica Scientia 2019年第1期39卷 57-82页

作者： Ting ZHANG wancheng sheng Department of Mathematics College of Science Shanghai University

The Riemann problem for the chromatography equations in a conservative form is considered. The global solution is obtained under the assumptions that the initial data are taken to be three piecewise constant states. The wave interaction problems are discussed in detail during the process of constructing global solutions to the perturbed Riemann problem. In addition, it can be observed that the Riemann solutions are stable under small perturbations of the Riemann initial data.

关键词： Riemann problem chromatography equation wave interactions Temple class hyperbolic conservation laws

THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS

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Acta Mathematica Scientia 2022年第4期42卷 1519-1535页

作者： Sijie LIU wancheng sheng Department of Mathematics Shanghai UniversityShanghai200444China

This paper is concerned with the pressureless Euler equations with viscous and flux *** existence of Riemann solutions to the pressureless Euler equations with viscous and flux perturbations is *** show the stability of the delta wave of the pressureless Euler equations to the perturbations;that is,the limit solution of the pressureless Euler equations with viscous and flux perturbations is the delta wave solution of the pressureless Euler equations as the viscous and flux perturbation simultaneously vanish in the case u_(-)> u_(+).

关键词： Pressureless Euler equations stability of the delta wave viscous perturbation and flux perturbation