一类具有非等熵 Dusty 气体的两相流模型 Riemann 解的压力消失极限

摘要/Abstract

图/表 5

参考文献 42

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摘要：

该文研究一类具有非等熵 Dusty 气体的两相流模型 Riemann 解在压力消失时的极限行为. 首先, 针对该模型的黎曼问题, 利用特征分析法得到基本波的表达式并在 $(p, u, s)$ 坐标系中构造了黎曼熵解. 然后, 证明了在压力消失时该模型的黎曼解收敛于带相同初值的一维常压力流体模型的黎曼解. 最后, 对该模型的黎曼解在压力消失过程中 $\delta$ -激波和真空状态的形成进行数值模拟, 验证了上述理论分析的结果.

关键词: 非等熵, 两相流模型, 压力消失极限, 黎曼解, $\delta$ -激波, 真空状态

Abstract:

This paper studies the cavitation and concentration phenomena of the Riemann solutions for a reduced two-phase mixtures model with non-isentropic dusty gas state as the pressure vanishes. Firstly, we construct the Riemann entropy solutions by characteristic analysis method in $(p, u, s)$ coordinate system. Secondly, we conclude that, the pressureless limit of Riemann solutions for the reduced two-phase mixtures model is just the Riemann solutions for the reduced 2-dimensional pressureless gas dynamics model. Finally, we present numerical simulations which are consistent with our theoretical analysis.

Key words: non-isentropic, two-phase mixtures model, pressureless limit, Riemann problem, Delta shock wave, vacuum state

中图分类号:

O175.23

金岱广,何劭弘,吴雨嫣,蒋伟峰. 一类具有非等熵 Dusty 气体的两相流模型 Riemann 解的压力消失极限[J]. 数学物理学报, 2025, 45(2): 371-388.

Daiguang Jin,Shaohong He,Yuyan Wu,Weifeng Jiang. The Vanishing Pressure Limit of Riemann Solutions for a Class of Two-Phase Flow Models with Non-Isentropic Dusty Gases[J]. Acta mathematica scientia,Series A, 2025, 45(2): 371-388.

图1

以 $(p_l, u_l, s_l)$ 和 $(p_l, u_l, s_1)$ 为中心的基本波投影"

图1

图2

图3

$(\varepsilon, \theta)$ 取不同值时方程 (1.1) 和 (5.1) 的黎曼解"

图3

图4

$(\varepsilon, \theta)$ 取不同值时方程 (1.1) 和 (5.2) 的黎曼解"

图4

图5

$(\varepsilon, \theta)=(0.03, 0.005)$ 时方程 (1.1) 和 (5.2) 黎曼解中密度的局部细节"

图5

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