Introduction

Lagoon Schematization

The most important problem to get meaningful results from the applications of mathematical models consists in determining the number of the finite element to be used in the schematization of the hydrodynamic system. Particularly, two conflicting requirements collide: the first is to increase how much it is possible the sizes of the finite elements and, consequently, to decrease the number of the nodes in which the solution is calculated (in order to diminish the computational effort); the second is to increase the finite elements number and the points of calculation in order to simulate with greater detail and precision the real morphological situation of the lagoon. To contemporarily satisfy both necessities, the Venice lagoon has been schematized through 24000 triangular finite elements, corresponding to a seeding of over 14000 nodes.

The finite elements' grid has been therefore perfectly fitted to the real contours of the channels, of the islands and of the external lagoon boundaries, allowing, in this way, a rapid distinction among the elements' typology and a consequent straightforward attribution of parameters like bathymetry and friction. With the purpose to assign the finite elements' altitudes, a particular procedure implemented among the preprocessor PreM2d commands has allowed assigning automatically the depths of the finite elements perfectly adherent to the real lagoon, on the base of the depth measurements effectively relieved in the most recent executed measurement campaigns.

To the goals of a correct interpretation of the characteristics of resistance to the tidal propagation in the lagoon, the triangular finite element have been divided in three different typologies (‘lagoon', ‘channel', ‘barena'). Keeping into account considerations of hydraulic character, have been assumed some coefficients of resistance to the motion differentiated for the three different systems of elements above mentioned, generally assigning for them values comprised within those suggested in the classical hydraulic.

Assessment of results from MEFH Model

The assessment of results from MEFH model was realized considering the tidal event in the period October 1 st -6 th 1986, when changes in level were recorded in a number of measurement stations spread throughout the lagoon basin.

After having realized the verification process with the hydrodynamic model through a number of sensibility tests using different values of finite element friction coefficients, it was decided to confirm the values of 30, 35, 20 [m 1/3 s 1 ] in Gauckler-Strickler's formula for the system of lagoon {1}, channel {2} and barena {3} elements, respectively.

As an example of the achieved results, in Charts 3 to 8 measurements are compared to simulated data, on period October 1 st -3 rd , 1996, for 6 different stations of measurement:

1 - Cason Figheri;

2 - Torson di Sotto;

3 - Fusina;

4 - Punta Salute;

5 - S. Erasmo;

6 - Val Dogà.

These hydrometric stations, located at relative considerable distance and belonging to the three different basins afferent Chioggia, Malamocco and Lido mouths (fig. 2), are to be considered extremely meaningful to show the possible ability, by the mathematical model, to simulate the hydrodynamic propagation process of the tide in the whole lagoon system.

Comparisons between simulated values and measured data confirm the accuracy of simulation throughout the measurement stations.

A further aspect, which is crucial to prove the relevance of the results, is the ability of MEFH to preserve water volume entered through inlets, within the lagoon hydrodynamic system. For this purpose in Charts 9 and 10 the values of some variables were represented, showing how precisely MEFH is able to resolve the equation of mass continuity. In particular, Chart 9 compares the total inflows from sea mouths and the simultaneous change in water volume inside the lagoon, in the unity of time, while Chart 10 compares the graphs of the total volumes entered from the mouths and those varied in lagoon, calculated, cumulatively, from the beginning of the simulation.

Nella fig. 9 il volume "Entrato Bocche" viene determinato valutando dapprima la portata complessiva che entra dalle bocche a mare, in corrispondenza di un certo istante di calcolo, moltiplicando poi tale valore per il passo temporale di calcolo del modello (pari a 180 [s]); il volume "Variazione Laguna" viene calcolato valutando prima la variazione di volume subita, durante lo stesso passo temporale di calcolo, dai singoli 12800 elementi finiti in cui é stato suddiviso il bacino lagunare e sommando poi tutti i contributi degli stessi elementi.

Questi risultati ottenuti forniscono la prova definitiva sulla precisione dei risultati forniti dal modello idrodinamico MfhLag. Infatti, considerando che l'oscillazione dello specchio liquido lagunare risulta essere, in ogni punto e in ogni istante, quasi aderente ai livelli forniti dal modello (fig. 3÷8), la precisione con cui viene conservata la massa nel bacino lagunare garantisce, altresì, l'altrettanto perfetta coincidenza tra il campo delle velocità, medie sulla verticale, ottenuto e quello realmente presente in laguna.

Conclusions

BIBLIOGRAPHY

[1] Garzon, A., ”Modello idrodinamico 2-D agli elementi finiti: Documentazione Scientifica“, Studio A.2.8, Consorzio Venezia Nuova, July 1988.

[2] Garzon, A., CREA s.r.l., ”Taratura e calibrazione del modello idrodinamico 2-D agli elementi finiti“, Consorzio Venezia Nuova, January 1995.

[3] Garzon, A., Cecconi, G., ”A Two Dimensional Semi-Implicit Finite Element Model for Tidal Propagation in the Venice Lagoon”, Proceedings of the Ninth International Conference on ”FINITE ELEMENTS in FLUIDS, New Trends and Applications”, Venice, 15-21 October 1995.

[4] “Sezione di lavoro 20 - Batimetria della laguna. 2° stralcio: studio dell'evoluzione morfologica - Rapporto Finale”, Consorzio Venezia Nuova, 1994.