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In this work, a first-order upwind and a high-order flux-limiter schemes forsolving the advection–diffusion equation on unstructured grids wereevaluated. The numerical schemes were implemented as a module of anunstructured two-dimensional depth-averaged circulation model for shallowlakes (IPH-UnTRIM2D), and they were applied to the Guaíba River inBrazil. Their performances were evaluated by comparing mass conservationbalance errors for two scenarios of a passive tracer released into theGuaíba River. The circulation model showed good agreement with observeddata collected at four water level stations along the Guaíba River, wherecorrelation coefficients achieved values up to 0.93. In addition, volumeconservation errors were lower than 1% of the total volume of theGuaíba River. For all scenarios, the higher order flux-limiter scheme hasbeen shown to be less diffusive than a first-order upwind scheme. Accumulatedconservation mass balance errors calculated for the flux limiter reached8%, whereas for a first-order upwind scheme, they were close to 18%over a 15-day period. Although both schemes have presented mass conservationerrors, these errors are assumed negligible compared with kinetic processessuch as erosion, sedimentation or decay rates

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