The stability of the high-order finite volume method for hyperbolic systems is based on non-linear procedures that prevent the creation of non-physical oscillations. Traditional techniques use the a priori paradigm where the procedure is carried out with the current time step solution. The a posteriori paradigm lies on an advanced in time candidate solution and a posterior evaluation of its stability, followed by a cure when necessary. To compare the two strategies, we propose a detailed study using the non-conservative shallow-water equations as a prototype, where both techniques are applied together in the framework of second-order linear reconstruction for the sake of simplicity. Then, a hybrid version combining the most positive aspects of both methods is proposed and analysed.

双曲系统的高阶有限体积方法的稳定性基于防止产生非物理振动的非线性过程。传统技术使用先验范式，其中该过程是使用当前时间步解决方案执行的。后验范式基于先进的候选时间解及其稳定性的后验评估，必要时进行后处理。为了比较这两种策略，我们提出了一个以非保守浅水方程为原型的详细研究，为简单起见，在二阶线性重构的框架中将这两种技术一起应用。然后，提出并分析了结合了两种方法的最积极方面的混合版本。