To improve the modeling quality of pollutant transport in shallow waters, different reconstruction schemes have been proposed to better link the edge values to the centroid values of a pollutant concentration in finite-volume shallow water models: a scheme of higher (lower) order generally has a better (poorer) quantitative accuracy but lower (higher) computational efficiency. Here, a numerical comparative study of several classical schemes is first conducted under a variety of pollutant distribution conditions. The results reveal that, for the condition of relatively uniform pollutant distribution, the numerical accuracy of a lower-order scheme (such as the first-order scheme or the MUSCL scheme) may be similar to that of a higher-order scheme (such as the WENO scheme). The second-order derivative of the concentration, here termed the nonlinear indicator (NI), correlates well with the discrepancies between the numerical solutions and analytical solutions. A threshold value of approximately ${10}^{-7}\sim {10}^{-6}$ m^-2 for the NI is identified, above which a higher-order scheme may be required. Based on this understanding, a hybrid first-order and WENO scheme is proposed. Numerical case studies show that the hybrid scheme can successfully combine the efficiency of the first-order scheme with the high accuracy of the WENO scheme for pollutant modeling.

为了提高浅水污染物输送的建模质量，已提出了不同的重建方案，以更好地将有限体积浅水模型中的边值与污染物浓度的质心值联系起来：通常，较高（较低）阶的方案具有更好（较差）的定量精度，但较低（较高）的计算效率。在这里，首先在各种污染物分布条件下对几种经典方案进行了数值比较研究。结果表明，在污染物分布相对均匀的条件下，低阶方案（如一阶方案或MUSCL方案）的数值精度可能与高阶方案（如WENO方案）。浓度的二阶导数 这里称为非线性指标（NI），它与数值解和解析解之间的差异密切相关。阈值约为${10}^{-7}〜{10}^{-6}$确定用于NI的 m ^-2，在此之上，可能需要更高阶的方案。基于此理解，提出了一种混合的一阶WENO方案。数值案例研究表明，该混合方案可以成功地将一阶方案的效率与WENO方案的高精度结合起来用于污染物建模。