Assessment of numerical schemes for solving the advection-diffusion equation on unstructured grids: case study of the Guaiba River, Brazil

作者：Pereira F F^*; Fragoso C R Jr; Uvo C B; Collischonn W; Motta Marques D M L

来源：Nonlinear Processes in Geophysics, 2013, 20(6): 1113-1125.

DOI：10.5194/npg-20-1113-2013

In this work, a first-order upwind and a high-order flux-limiter schemes for solving the advection-diffusion equation on unstructured grids were evaluated. The numerical schemes were implemented as a module of an unstructured two-dimensional depth-averaged circulation model for shallow lakes (IPH-UnTRIM2D), and they were applied to the Guaiba River in Brazil. Their performances were evaluated by comparing mass conservation balance errors for two scenarios of a passive tracer released into the Guaiba River. The circulation model showed good agreement with observed data collected at four water level stations along the Guaiba River, where correlation coefficients achieved values up to 0.93. In addition, volume conservation errors were lower than 1% of the total volume of the Guaiba River. For all scenarios, the higher order flux-limiter scheme has been shown to be less diffusive than a first-order upwind scheme. Accumulated conservation mass balance errors calculated for the flux limiter reached 8 %, whereas for a first-order upwind scheme, they were close to 18% over a 15-day period. Although both schemes have presented mass conservation errors, these errors are assumed negligible compared with kinetic processes such as erosion, sedimentation or decay rates.

• 出版日期2013