A new modified Engquist–Osher-type flux-splitting scheme is proposed to approximate the scalar conservation laws with discontinuous flux function in space. The fact that the discontinuity of the fluxes in space results in the jump of the unknown function may be the reason why it is difficult to design a high-order scheme to solve this hyperbolic conservation law. In order to implement the WENO flux reconstruction, we apply the new modified Engquist–Osher-type flux to compensate for the discontinuity of fluxes in space. Together the third-order TVD Runge–Kutta time discretization, we can obtain the high-order accurate scheme, which keeps equilibrium state across the discontinuity in space, to solve the scalar conservation laws with discontinuous flux function. Some examples are given to demonstrate the good performance of the new high-order accurate scheme.

中文翻译：

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空间不连续通量守恒律的高阶精确通量分裂方案

提出了一种新的改进的Engquist-Osher型通量分裂方案，以近似空间中具有不连续通量函数的标量守恒律。空间中通量的不连续性导致未知函数的跳跃这一事实可能是为什么难以设计高阶方案来解决该双曲守恒律的原因。为了实现WENO通量重构，我们应用了新的改进的Engquist-Osher型通量来补偿空间中通量的不连续性。结合三阶TVD Runge-Kutta时间离散，我们可以获得高阶精确方案，该方案在空间的不连续点之间保持平衡状态，以解决具有不连续通量函数的标量守恒定律。