Abstract
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.
Highlights
When the ratio of vertical to horizontal motion scales is not small, a nonhydrostatic approach may be necessary to accurately simulate three-dimensional free-surface flows in large aquatic ecosystems such as lakes, estuaries, reservoirs, and coastal zones [1,2,3]
The numerical experiments in the hydrodynamic solution showed that the quadratic interpolation method, using 27 node points in a single computation cell, substantially reduced the numerical diffusion in the hydrodynamic solution, which had a positive effect on the solute transport solution
The proposed combined use of the quadratic interpolation applied at Eulerian–Lagrangian method (ELM) step-ii and the flux-limiter technique substantially reduced the numerical diffusion in solving mass transport problems, showing that high-resolution methods must be implemented in the numerical solution to properly simulate more complex real situations
Summary
When the ratio of vertical to horizontal motion scales is not small (e.g., flows over abruptly changing bottom topography, orbital movements in short-wave motions, or intensive vertical circulation), a nonhydrostatic approach may be necessary to accurately simulate three-dimensional free-surface flows in large aquatic ecosystems such as lakes, estuaries, reservoirs, and coastal zones [1,2,3]. Hodges et al [16] proposed a stable non-conciliatory quadratic Lagrange interpolation for a three-dimensional mesh, where 27 grid points are used to estimate the velocity values during the particle-tracking process This technique has not yet been formally analyzed (Hodges et al [23], without any posterior record of formal analyses), previous studies successfully modeled hydrodynamic and solute transport simulations, strongly indicating that the solution satisfactorily represented internal gravity waves and may improve the ability of ELM to solve the free surface motion [16,23,24,25,26,27,28]. We used a coupled hydrodynamic solute transport model with nonhydrostatic and flux-limiter approaches to evaluate the numerical diffusion in three numerical experiments, for different purposes: (a) the first two experiments evaluated the potential for reducing the numerical diffusion in the hydrodynamic solution, by applying a nonlinear interpolator rather than a linear one, and the capability of representing the propagation of complex waves; (b) the third experiment evaluated the effect of using, or not, high-resolution schemes on the numerical diffusion of combined hydrodynamic and solute transport models
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