| Van der Waals气体Euler方程的Riemann问题及基本波的相互作用 |
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| 引用本文： | 盛万成,王 斌. Van der Waals气体Euler方程的Riemann问题及基本波的相互作用[J]. 数学年刊A辑(中文版), 2016, 37(4): 377-396 |
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| 作者姓名： | 盛万成 王 斌 |
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| 作者单位： | 通讯作者. 上海大学理学院, 上海~200444.,上海大学理学院, 上海~200444. |
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| 基金项目： | 本文受到国家自然科学基金 (No.11371240)的资助. |
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| 摘 要： | 研究了修正的等熵Van der Waals气体动力学Euler方程Riemann问题及其基本波的相互作用.利用Maxwell提出的等面积法则,将Van der Waals气体状态方程修正为与实际相符,从而守恒律方程组从混合型转化为双曲型.利用广义特征线分析法,构造性地得到了Riemann问题的解是存在的.进一步,得到了基本波相互作用.
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| 关 键 词： | Euler方程 Van der Waals气体 Riemann问题 基本波的相互作用 |
| 收稿时间： | 2015-05-17 |
| 修稿时间： | 2016-02-04 |
Riemann Problem and Interaction of Elementary Waves to the Euler Equations for Van der Waals Gas |
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| SHENG Wancheng and WANG Bin. Riemann Problem and Interaction of Elementary Waves to the Euler Equations for Van der Waals Gas[J]. Chinese Annals of Mathematics, 2016, 37(4): 377-396 |
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| Authors: | SHENG Wancheng and WANG Bin |
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| Affiliation: | Corresponding author. College of Sciences, Shanghai University,Shanghai 200444, China. and College of Sciences, Shanghai University, Shanghai 200444, China. |
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| Abstract: | This paper deals with the Riemann problem for the Euler equations and theinteraction of elementary waves for isentropic modified Van der Waals gas.The authors modify the state equation of Van der Waals gas to agree with the reality by the area equalprinciple, which Maxwell constructed. Then the system is transformed from mixed type intohyperbolic type. By the characteristic analysis methods, the authors get the Riemann solutionsconstructively. Furthermore, the collisions of shock and another elementary waves are shown. |
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| Keywords: | Euler equations Van der Waals gas Riemann problem Interaction of elementary waves |
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