Van der Waals气体Euler方程的活塞问题

The Piston Problem of the Euler Equations for Van der Waals Gas

研究了修正的Van der Waals气体Euler方程的活塞问题.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合,从而将方程从混合型转会化为双曲型.利用特征分析法,给出修正的Van der Waals气体Euler方程的Riemann问题前向波的所有解,从而进一步给出了推拉活塞时气体的所有运动.

This paper is devoted to the piston problem of the Euler equations for isentropic modified Van der Waals gas.The modified Van der Waals gas state equation agrees with the reality,which was constructed by Maxwell using area equal principle.Then the system transforms mixed type into hyperbolic type.By the characteristic analysis methods,the forward wave solutions of the Euler equations for the modified Van der Waals gas are given.Thereby further,the motions of gas caused by pushing and pulling the piston are shown.