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

Pereira, Fabio LU ; Fragoso Jr, Carlos ; Bertacchi Uvo, Cintia LU ; Collischonn, Walter and Motta Marques, David (2013) In Nonlinear Processes in Geophysics 20(6). p.1113-1125
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... (More)
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. (Less)
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organization
publishing date
type
Contribution to specialist publication or newspaper
publication status
published
subject
categories
Popular Science
in
Nonlinear Processes in Geophysics
volume
20
issue
6
pages
1113 - 1125
publisher
European Geosciences Union
external identifiers
  • wos:000329043300017
  • scopus:84890498312
ISSN
1023-5809
DOI
10.5194/npg-20-1113-2013
language
English
LU publication?
yes
id
443c6d24-5011-4abe-8018-e39a0a1158d5 (old id 4196252)
date added to LUP
2016-04-01 10:48:12
date last changed
2020-01-12 05:40:34
@misc{443c6d24-5011-4abe-8018-e39a0a1158d5,
  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.},
  author       = {Pereira, Fabio and Fragoso Jr, Carlos and Bertacchi Uvo, Cintia and Collischonn, Walter and Motta Marques, David},
  issn         = {1023-5809},
  language     = {eng},
  number       = {6},
  pages        = {1113--1125},
  publisher    = {European Geosciences Union},
  series       = {Nonlinear Processes in Geophysics},
  title        = {Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil},
  url          = {https://lup.lub.lu.se/search/ws/files/2148894/4219527.pdf},
  doi          = {10.5194/npg-20-1113-2013},
  volume       = {20},
  year         = {2013},
}