Summary
A three dimensional hydrodynamic model has been developed in boundary fitted coordinates for application to shelf and coastal sea circulation. The momentum and continuity equations are solved on a space staggered grid system using a semi-implicit finite-difference solution algorithm for the exterior vertically averaged flow and an explicit procedure for the interior flow. The vertical coordinate, transformed by the local depth, is approximated by a series of permeable layers. The interior momentum equations are solved explicitly with the exception that the vertical diffusive terms employ an implicit specification to ease the time step restriction. The model has been tested in a two dimensional mode against analytic solutions for a standing wave in a closed basin, tidal flow in a annular basin with constant depth and wind driven flow in a elliptic cylindrical basin. Three dimensional tests of the code include wind and density forcing in a rectangular basin. All simulations show excellent agreement with the analytic solutions.
Zusammenfassung
Ein dreidimensionales hydrodynamisches Modell in randwert-angepaßten Koordinaten wurde entwickelt zur Berechnung der Zirkulation in Schelf- und Randmeeren.
Die Impuls- und Kontinuitätsgleichungen werden in einem räumlich verschachtelten Gitter mit einem halbimpliziten finiten Differenzenverfahren für den externen Anteil der vertikal integrierten Strömung und einem expliziten Verfahren für den internen Anteil gelöst. Die Vertikalkoordinate wird nach Transformation mit der lokalen Wassertiefe mit einer Reihe permeabler Schichten approximiert. Die Impulsgleichung des internen Anteils wird explizit gelöst mit Ausnahme des vertikalen Diffusionsterms. Dieser wird implizit behandelt, um die Begrenzung durch den Zeitschritt zu vermeiden. Das Modell wurde in einer zweidimensionalen Version getestet und die Ergebnisse verglichen mit den analytischen Lösungen einer stehenden Welle in einem geschlossenen Becken, einer Gezeitenströmung in einem Ringkanal mit konstanter Tiefe und windinduzierter Strömung in einem elliptischen und zylindrischen Becken. Der Test des dreidimensionalen Modells berücksichtigt Wind und Massenaufbau in einem Rechteckbecken. Alle Simulationen zeigen eine sehr gute Übereinstimmung der Ergebnisse mit der analytischen Lösung.
Résumé
Un modèle hydrodynamique tri-dimensionnelle avec un système de coordonnées adapté aux frontières a été développé pour simuler les courants côtiers et du plateau continental. Les équations de mouvement et de continuité sont résolues sur des grilles spatiales séparées et emboitées en utilisant un schema semi-implicite aux différences finies pour le courant barotrope et un schema explicite pour le courant barocline. La coordonnée verticale est adaptée à la prodondeur locale et est approximée en utilisant une série de couches perméables. Les équations de mouvement interne pour les vitesses baroclines sont résolues explicitement à l'exception des termes diffusifs verticaux qui utilisent un schema implicite pour pallier les contraintes de pas de temps. Le modèle a été testé en mode bi-dimensionnel en comparaison avec des solutions analytiques pour une onde stationnaire en bassin clos, pour un courant de marée en bassin annulaire de profondeur constante et pour un courant du au vent dans un bassin cylindrique de section elliptique. Des tests tri-dimensionnels du code de calcul en bassin rectangulaire font intervenir des variations de densité et de force du vent. Toutes ces simulations fournissent d'excellentes concordances avec les solutions analytiques.
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Craig Swanson, J., Spaulding, M., Mathisen, JP. et al. A three dimensional boundary fitted coordinate hydrodynamic model, part I: Development and testing. Deutsche Hydrographische Zeitschrift 42, 169–186 (1989). https://doi.org/10.1007/BF02226293
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DOI: https://doi.org/10.1007/BF02226293