A second-order hydrostatic reconstruction (HR) scheme for the shallow water equations with a non-flat bottom topography and a Manning friction is presented. The framework of our reconstruction was from Chen and Noelle (2017). We extend it from first-order to second-order accuracy. The new second-order HR scheme endows with a new implicit method, which is used to cope with the friction term, can exactly preserve the physical relevant steady-state solutions and maintain the positivity of the water depth. Finally, we use several classical numerical experiments to test these properties of the new scheme and use experimental data to be used to compare with the numerical result. In all these numerical experiments, the new scheme produces satisfactory results.

提出了具有非平坦底部形貌和曼宁摩擦的浅水方程组的二阶静液压重建（HR）方案。我们的重建框架来自Chen和Noelle（2017）。我们将其从一阶精度扩展到二阶精度。新的二阶HR方案赋予了新的隐式方法，该方法用于处理摩擦项，可以精确地保留物理相关的稳态解并保持水深的正值。最后，我们使用几个经典的数值实验来测试新方案的这些特性，并使用实验数据与数值结果进行比较。在所有这些数值实验中，新方案均产生令人满意的结果。