In this paper, we present a general framework to construct section-averaged models when the flow is constrained – e.g. by topography – to be almost one-dimensional. These models are consistent with the two-dimensional shallow water equations. After rewriting the two-dimensional shallow water equations in a suitable set of coordinates allowing to take care of a meandering configuration, we consider the quasi one-dimensional regime. Then, we expand the water elevation and velocity field in the spirit of the diffusive wave equations and establish a set of one-dimensional equations made of a mass, momentum and energy equations, which are close to the ones usually used in hydraulic engineering. Our model reduces to classical shallow water models with variable sections found in the literature. Out of these configurations, there is an $\mathcal{O}\left(1\right)$ deviation of our model from the classical ones. Finally, we present the main mathematical properties of our model and carry out numerical simulations to validate our approach by comparing the results to the full two-dimensional shallow water equations.

在本文中，我们提出了一个通用的框架，当流量（例如，受地形影响）几乎为一维时，可构造截面平均模型。这些模型与二维浅水方程是一致的。在将二维浅水方程式改写为一组适当的坐标后，它们可以照顾到弯曲的构造，然后考虑准一维状态。然后，我们本着扩散波方程的精神扩展水高程和速度场，并建立了一个由质量，动量和能量方程组成的一维方程组，该方程组与水利工程中通常使用的方程组非常接近。我们的模型简化为文献中发现的具有可变截面的经典浅水模型。在这些配置之外，还有一个$\mathcal{Ø}（\mathrm{1个}）$我们的模型与经典模型的偏差。最后，我们介绍了模型的主要数学性质，并通过将结果与完整的二维浅水方程进行了比较，进行了数值模拟，以验证我们的方法。