A hybrid first-order and WENO scheme for the high-resolution and computationally efficient modeling of pollutant transport. (15th July 2021) - Hu, Yuying; Hu, Peng; Li, Wei; Liao, Weihong
Highlights: A hybrid first-order and WENO scheme is proposed for pollutant transport modeling. The new model achieves comparable quantitative accuracy as compared to the WENO method but has significantly reduced computational cost. A threshold value for switching between first-order and WENO schemes is recommended. Abstract: 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 ∼ 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.