The interface flux plays an important role in designing numerical methods for scalar conservation laws with discontinuous flux function in space. Based on the $(A,B)$-type entropy solutions defined by Bürger et al. (2009), we introduce a new modified Local Lax–Friedrichs interface flux to approximate this system. The interface flux is Lipschitz continuous and monotone with respect to its two variables. Moreover, we present some numerical experiments to demonstrate the efficiency of our method.

中文翻译：

---

具有不连续通量的标量守恒律的新改良的本地Lax–Friedrichs方案

界面通量在设计具有不连续通量函数的标量守恒律的数值方法时起着重要作用。基于$（\mathrm{一种}，乙）$Bürger等人定义的B型熵解。（2009），我们引入了一个新的改进的Local Lax–Friedrichs界面通量来近似该系统。相对于两个变量，界面通量为Lipschitz连续和单调。此外，我们提出了一些数值实验来证明我们方法的有效性。