NDLI: SEAWAT 2000: modelling unstable flow and sensitivity to discretization levels and numerical schemes

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SEAWAT 2000: modelling unstable flow and sensitivity to discretization levels and numerical schemes

Content Provider	Springer Nature Link
Author	Al Maktoumi, A. Lockington, D. A. Volker, R. E.
Copyright Year	2007
Abstract	A systematic analysis shows how results from the finite difference code SEAWAT are sensitive to choice of grid dimension, time step, and numerical scheme for unstable flow problems. Guidelines to assist in selecting appropriate combinations of these factors are suggested. While the SEAWAT code has been tested for a wide range of problems, the sensitivity of results to spatial and temporal discretization levels and numerical schemes has not been studied in detail for unstable flow problems. Here, the Elder-Voss-Souza benchmark problem has been used to systematically explore the sensitivity of SEAWAT output to spatio-temporal resolution and numerical solver choice. A grid size of 0.38 and 0.60% of the total domain length and depth respectively is found to be fine enough to deliver results with acceptable accuracy for most of the numerical schemes when Courant number (Cr) is 0.1. All numerical solvers produced similar results for extremely fine meshes; however, some schemes converged faster than others. For instance, the 3rd-order total variation-diminishing method (TVD3) scheme converged at a much coarser mesh than the standard finite difference methods (SFDM) upstream weighting (UW) scheme. The sensitivity of the results to Cr number depends on the numerical scheme as expected.Une analyse systématique montre la sensibilité des résultats obtenus avec le code SEAWAT aux différences finies en fonction du choix du dimensionnement du maillage, du pas de temps et du schéma numérique dans des problèmes d’écoulement instable. Des règles générales aidant à la sélection de combinaisons appropriées pour ces facteurs sont proposées. Si le code SEAWAT a été testé pour une large gamme de problèmes, la sensibilité des résultats aux différents niveaux de discrétisation spatiale et temporelle et aux schémas numériques n’a pas été étudiée en détail pour les problèmes d’écoulement instable. Ici, le problème de référence de Elder-Voss-Souza a été utilisée pour étudier systématiquement la sensibilité des résultats de SEAWAT en fonction du choix de la résolution spatio-temporelle et du solveur numérique. Une taille de maillage de respectivement 0.38 et 0.60% de la longueur et de la profondeur du domaine total, s’est montrée être suffisamment fine pour produire des résultats avec des précisions acceptables pour la plupart des schémas numériques pour un nombre de Courant (Cr) de 0.1. Tous les solveurs numériques ont produit des résultats similaires pour des mailles extrêmement petites, cependant, certains schémas ont convergé plus rapidement que d’autres. Par exemple, le schéma à variation totale décroissante d’ordre 3 (TVD3) a convergé pour un maillage beaucoup plus grossier que le schéma des méthodes standards de différences finies (SFDM) avec pondération amont (UW en anglais). La sensibilité des résultats au nombre de Cr dépend comme prévu du schéma numérique.Un análisis sistemático muestra como los resultados del código de diferencia finita SEAWAT son sensibles a la selección de la dimensión de la malla, el intervalo de tiempo, y el esquema numérico para problemas de flujo inestable. Se sugieren lineamientos para asistir en la selección de combinaciones apropiadas de estos factores. Mientras que el código SEAWAT se ha probado para un amplio rango de problemas, no se han estudiado en detalle la sensibilidad de resultados a los niveles de discretización temporal y espacial y los esquemas numéricos para problemas de flujo inestable. Aquí se ha usado el problema de análisis comparativo Elder-Voss-Souza para explorar sistemáticamente la sensibilidad de la salida de SEAWAT con la selección de la solución numérica y la resolución temporal y espacial. Un tamaño de malla del 0.38 y 0.6% de la profundidad y longitud del entorno total, respectivamente, se encontró que era suficientemente fina para aportar resultados con precisión aceptable para la mayoría de esquemas numéricos cuando el número de Courant (Cr) es 0.1. Todas las soluciones numéricas generaron resultados similares para mallas extremadamente finas; sin embargo, algunos esquemas convergieron más rápido que otros. Por ejemplo, el esquema del Método de Disminución de Variación de Orden Total (TVD3) convergió en una malla mucho más gruesa que la del esquema de Pesado Aguas Arriba (UW) de los Métodos de Diferencia Finita Standard (SFDM). Tal y como se esperaba la sensibilidad de los resultados del número Cr dependen del esquema numérico.
Starting Page	1119
Ending Page	1129
Page Count	11
File Format	PDF
ISSN	14312174
Journal	Hydrogeology Journal
Volume Number	15
Issue Number	6
e-ISSN	14350157
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-02-20
Publisher Institution	International Association of Hydrogeologists
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Grid sensitivity Numerical modeling Unstable flow Convection SEAWAT Waste Water Technology Water Pollution Control Water Management Aquatic Pollution Geology Hydrogeology
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences Water Science and Technology

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