A non-negative and high-resolution finite volume method for the depth-integrated solute transport equation using an unstructured triangular mesh

作者：Ye, Ronghui; Zhang, Chenming; Kong, Jun^*; Jin, Guangqiu; Zhao, Hongjun; Song, Zhiyao; Li, Ling

来源：Environmental Fluid Mechanics, 2018, 18(6): 1379-1411.

DOI：10.1007/s10652-018-9598-4

• Scalar transport
• Anisotropic diffusion
• TVD scheme
• Finite volume method
• Unstructured triangular mesh
• Shallow water dynamics

This paper proposes a new high-resolution finite volume method for solving the two-dimensional (2D) solute transport equation using an unstructured mesh. A new simple r-factor algorithm is introduced into the Total Variation Diminishing flux limiter to achieve a more efficient yet accurate high-resolution scheme for solving the advection term. To avoid the physically-meaningless negative solutions resulted from using the Green-Gauss theorem, a nonlinear two-point flux approximation scheme is adopted to deal with the anisotropic diffusion term. The developed method can be readily coupled with a two-dimensional finite-volume-based flow models under unstructured triangular mesh. By integrating with the ELCIRC flow model, the proposed method was verified using three idealized benchmark cases (i.e., advection of a circle-shaped solute field, advection in a cyclogenesis flow field and transport of a initially square-shaped solute plume), and further applied to simulate the non-reactive solute transport process driven by irregular tides in the Deep Bay, eastern Pearl River Estuary of China. These cases are also simulated by models using other existing methods, including different r-factor for advection term and the Green-Gauss theorem for diffusion term. The comparison between the results from the new method and those from other existing methods demonstrated the new method could describe advection induced concentration shock and discontinuities, and anisotropic diffusion at high resolution without providing spurious oscillations and negative values.

• 出版日期2018-12
• 单位南京师范大学; 珠江水利委员会珠江水利科学研究院; 河海大学; 水文水资源与水利工程科学国家重点实验室