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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 20, 1113-1125, 2013
https://doi.org/10.5194/npg-20-1113-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
17 Dec 2013
Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil
F. F. Pereira1, C. R. Fragoso Jr.2, C. B. Uvo1, W. Collischonn3, and D. M. L. Motta Marques3 1Department of Water Resources Engineering, Lund University, Lund, Sweden
2Centro de Tecnologia, Universidade Federal de Alagoas, Maceió, Brazil
3Instituto de Pesquisas Hidráulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
Abstract. 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 Guaíba River in Brazil. Their performances were evaluated by comparing mass conservation balance errors for two scenarios of a passive tracer released into the Guaíba River. The circulation model showed good agreement with observed data collected at four water level stations along the Guaíba 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 Guaíba 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.

Citation: Pereira, F. F., Fragoso Jr., C. R., Uvo, C. B., Collischonn, W., and Motta Marques, D. M. L.: Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil, Nonlin. Processes Geophys., 20, 1113-1125, https://doi.org/10.5194/npg-20-1113-2013, 2013.
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