A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh

This paper presents a high-resolution numerical method for solving mass transport problems involving advection and anisotropic diffusion in shallow water based on unstructured mesh. An alternating operator-splitting technique is adopted to advance the numerical solution with advection and diffusion terms solved separately in two steps. By introducing a new r-factor into the Total Variation Diminishing (TVD) limiter, an improved finite-volume method is developed to solve the advection term with significant reduction of numerical diffusion and oscillation errors. In addition, a coordinate transformation is introduced to simplify the diffusion term with the Green-Gauss theorem used to deal with the anisotropic effect based on unstructured mesh. The new scheme is validated against three benchmark cases with separated and combined advection and diffusion transport processes involved. Results show that the scheme performs better than existing methods in predicting the advective transport, particularly when a sharp concentration front is in presence. The model also provides a sound solution for the anisotropic diffusion phenomenon. Anisotropic diffusion has been largely neglected by existing flow models based on unstructured mesh, which usually treat the diffusion process as being isotropic for simplicity. Based on the flow field provided by the ELCIRC model, the developed transport model was successfully applied to simulate the transport of a hypothetical conservative tracer in a bay under the influence of tides. 2012 Elsevier Ltd. All rights reserved. Software availability Program title: AAD (advection and anisotropic diffusion) Developers: Jun Kong, Pei Xin, Cheng-Ji Shen, Zhi-Yao Song, Ling Li Contact address: State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing (210098), China Source languages: Fortran 77 Availability: Please email your request to the first author by [email protected]. drology-Water Resources and ina. Tel.: þ86 25 83787349; ), [email protected] (P. Xin), (Z.-Y. Song), [email protected] All rights reserved. et al., A high-resolution met g & Software (2012), http://d