一类等熵欧拉方程组的流近似

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.

Flux approximation for a class of Euler equations

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.