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Open AccessArticle

Combined Use of High-Resolution Numerical Schemes to Reduce Numerical Diffusion in Coupled Nonhydrostatic Hydrodynamic and Solute Transport Model

Hydraulic Research Institute, Federal University of Rio Grande do Sul, Porto Alegre 91501-970, RS, Brazil
Center of Technology, Federal University of Alagoas, Maceió 57072-970, AL, Brazil
UMR 228 Espace-DEV, Institut de Recherche pour le Développement, 13001 Marseille, France
Author to whom correspondence should be addressed.
Water 2019, 11(11), 2288;
Received: 4 September 2019 / Revised: 20 October 2019 / Accepted: 21 October 2019 / Published: 31 October 2019
(This article belongs to the Special Issue Hydraulic Dynamic Calculation and Simulation)
In three-dimensional simulations of free-surface flow where the vertical velocities are relevant, such as in lakes, estuaries, reservoirs, and coastal zones, a nonhydrostatic hydrodynamic approach may be necessary. Although the nonhydrostatic hydrodynamic approach improves the physical representation of pressure, acceleration and velocity fields, it is not free of numerical diffusion. This numerical issue stems from the numerical solution employed in the advection and diffusion terms of the Reynolds-averaged Navier–Stokes (RANS) and solute transport equations. The combined use of high-resolution schemes in coupled nonhydrostatic hydrodynamic and solute transport models is a promising alternative to minimize these numerical issues and determine the relationship between numerical diffusion in the two solutions. We evaluated the numerical diffusion in three numerical experiments, for different purposes: The first two experiments evaluated the potential for reducing numerical diffusion in a nonhydrostatic hydrodynamic solution, by applying a quadratic interpolator over a Bilinear, applied in the Eulerian–Lagrangian method (ELM) step-ii interpolation, and the capability of representing the propagation of complex waves. The third experiment evaluated the effect on numerical diffusion of using flux-limiter schemes over a first-order Upwind in solute transport solution, combined with the interpolation methods applied in a coupled hydrodynamic and solute transport model. The high-resolution methods were able to substantially reduce the numerical diffusion in a solute transport problem. This exercise showed that the numerical diffusion of a nonhydrostatic hydrodynamic solution has a major influence on the ability of the model to simulate stratified internal waves, indicating that high-resolution methods must be implemented in the numerical solution to properly simulate real situations. View Full-Text
Keywords: numerical diffusion; Eulerian–Lagrangian method; interpolation; flux limiter numerical diffusion; Eulerian–Lagrangian method; interpolation; flux limiter
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Cunha, A.H.F.; Fragoso, C.R., Jr.; Tavares, M.H.; Cavalcanti, J.R.; Bonnet, M.-P.; Motta-Marques, D. Combined Use of High-Resolution Numerical Schemes to Reduce Numerical Diffusion in Coupled Nonhydrostatic Hydrodynamic and Solute Transport Model. Water 2019, 11, 2288.

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