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

Journal metrics

Journal metrics

  • IF value: 1.699 IF 1.699
  • IF 5-year value: 1.559 IF 5-year
    1.559
  • CiteScore value: 1.61 CiteScore
    1.61
  • SNIP value: 0.884 SNIP 0.884
  • IPP value: 1.49 IPP 1.49
  • SJR value: 0.648 SJR 0.648
  • Scimago H <br class='hide-on-tablet hide-on-mobile'>index value: 52 Scimago H
    index 52
  • h5-index value: 21 h5-index 21
Volume 20, issue 6
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.
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

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 F. F. Pereira et al.
  • 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.

Publications Copernicus
Download
Citation