By the flux-approximation method, we study limits of Riemann solutions to the Brio system with two independent parameters. The Riemann problem of the perturbed system is solved analytically, and four kinds of solutions are obtained constructively. It is shown that, as the two-parameter flux perturbation vanishes, any two-shock-wave and two-rarefaction-wave solutions of the perturbed Brio system converge to the delta-shock and vacuum solutions of the transport equations, respectively. In addition, we specially pay attention to the Riemann problem of a perturbed simplified system of conservation laws derived from the perturbed Brio system by neglecting some quadratic term. As one of the parameters of the perturbed Brio system goes to zero, the solution of which consisting of two shock waves tends to a delta-shock solution to this simplified system. By contrast, the solution containing two rarefaction waves converges to a contact discontinuity and a rarefaction wave of the simplified system. What is more, the formation mechanisms of delta shock waves under flux approximation with both two parameters and only one parameter are clarified. Some numerical simulations presenting the formation processes of delta shock waves and vacuum states are also presented to confirm the theory analysis.

通过通量近似方法，我们研究了具有两个独立参数的Bie系统的黎曼解的极限。解析地解决了摄动系统的黎曼问题，并建设性地获得了四种解。结果表明，随着两参数通量扰动的消失，被扰动的Brio系统的任何两个激波解和两个反射波解都分别收敛于输运方程的δ激波解和真空解。此外，我们特别注意通过忽略一些二次项，从扰动的Brio系统中得到的扰动的守恒律简化系统的黎曼问题。当扰动的Brio系统的参数之一趋于零时，由两个冲击波组成的解决方案趋向于对该简化系统的delta-shock解决方案。相反，包含两个稀疏波的解收敛到简化系统的接触不连续和稀疏波。此外，阐明了两个参数且只有一个参数的通量近似下的三角激波的形成机理。一些数值模拟给出了三角波冲击波和真空状态的形成过程，也证实了理论分析。