非对称Keyfitz-Kranzer方程组在压力消失过程中的质量集中和空化现象

Concentration and Cavitation Phenomena for Nonsymmetric Keyfitz-Kranzer Type in the Vanishing Pressure

研究扩展Chaplygin气体非对称Keyfitz-Kranzer方程组在压力消失过程中黎曼解的极限行为.压力消失过程中,Keyfitz-Kranzer方程组包括激波和接触间断的黎曼解收敛到一类特殊的δ激波,其传播速度和权明显不同于零压流的δ激波.为解决此问题,引入扰动Keyfitz-Kranzer方程组并证明压力消失过程中,它的解收敛到零压流.最后,呈现一组具有代表性的数值实验来验证δ激波和真空状态的形成.

This article is devoted to the study of the limit behavior for Keyfitz-Kranzer type in the vanishing pressure.The Riemann solution containing shock wave and contact discontinuity converges to a specialδshock wave whose propagation velocity and strength are different from theδshock wave of pressureless gas dynamics.To solve the problem,we introduce perturbed Keyfitz-Kranzer type,and then prove that the Riemann solution tends to zero pressure flow in the process of vanishing pressure.Finally,we present a group of representative numerical experiments to verify the formation ofδshock wave and vacuum states.