摘要
研究了一类带有流扰动的一般压力等熵欧拉方程组的黎曼问题,获得了包含5种不同结构的黎曼解.证明了当包含压力的3-参数流扰动消失时,任何包含2个激波的黎曼解收敛于零压流系统的狄拉克激波解;任何包含2个稀疏波的黎曼解收敛于零压流系统的真空解.还证明了当包含压力的2-参数流扰动消失时,任何满足一定初值条件的2-激波黎曼解收敛于一类Chaplygin型气体方程组的狄拉克激波解.最后,对狄拉克激波和真空状态的形成过程进行了数值模拟.
The Riemann problem for a class of flux-perturbation Euler equations with general pressure is solved,and five kinds of Riemann solutions of different structures are obtained.It is shown that when the three-parameter flux perturbations including pressure disappear,any Riemann solution containing two shock waves converges to a delta-shock solution of the zero-pressure flow;any Riemann solution including two rarefaction waves converges to the vacuum solution of the zero-pressure flow.It is also proved that when the two-parameter flux perturbations including pressure disappear,any two-shock Riemann solution satisfying certain initial values converges to a delta-shock solution of a type of Chaplygin gas equations.Finally,the formation processes of the delta-shocks and vacuum states are simulated numerically.
作者
杨汉春
袁宏丹
张月航
YANG Han-chun;YUAN Hong-dan;ZHANG Yue-hang(School of Mathematics and Statistics,Yunnan University,Kunming 650500,Yunnan,China)
出处
《云南大学学报（自然科学版）》
CAS
CSCD
北大核心
2023年第2期239-255,共17页
Journal of Yunnan University(Natural Sciences Edition)
基金
国家自然科学基金(12061084)
云南省科技厅应用基础研究计划(2019FY003007).
作者简介
通信作者:杨汉春(1968−),男,云南人,博士,教授,主要研究偏微分方程.E-mail:hyang@ynu.edu.cn。
