In this paper, we introduce a new locally implicit sonic point processing algorithm for one-dimensional shallow-water equations. The algorithm is based on transferring the shallow-water invariants along the characteristics around the sonic point, and it can be coupled with conservative-characteristic methods, which have problems modelling the transonic flows. For each sonic point, a system of two non-linear equations should be solved, which allows to use the proposed method with explicit methods for subsonic or supersonic flows without noticeable increase in calculation time. The important features of the algorithm include the second order of approximation in time and space and the property of time reversibility if monotonization procedures are disabled. Coupled with the CABARET scheme, the proposed method has been tested on several Riemann problems, including the Toro tests for transonic flows. The results have shown that the algorithm allows to obtain solutions with accurate transonic rarefaction and shock waves in both cases of wet and dry beds.

在本文中，我们为一维浅水方程式引入了一种新的局部隐式声波点处理算法。该算法基于沿声波点周围的特征传递浅水不变量，并且可以与保守特征方法耦合，这些方法存在跨声速流建模的问题。对于每个声波点，应该解决两个非线性方程组的问题，这允许将本方法与显式方法一起用于亚音速或超音速流动，而不会显着增加计算时间。该算法的重要特征包括在时间和空间上的二阶逼近以及如果禁用单调过程则具有时间可逆性。结合CABARET方案，所提出的方法已在多个Riemann问题上进行了测试，包括跨音速流动的Toro测试。结果表明，该算法可以在湿床和干床的情况下获得具有精确跨音速稀疏和冲击波的解。