The numerical simulation of exceptional events characterised by high hydraulic and hydrogeologic risk is an actual problem for the scientific community, working in the topic of environmental protection. In this paper a numerical code is described, for the simulation of 2D transient free-surface flows, suitable to work on both simple and complicated geometries. The proposed algorithm is based on the two-dimensional shallow water equations in their classical form. The spatial discretisation is obtained by the FVM cellcentred type method. The numerical system is solved in explicit way. The scheme is second order accurate both in space and time, trough the use of MUSCL method and a predictor-corrector approach. The scheme falls in the family of upwind methods, precisely in Godunov-type category. The local Riemann problem is solved by the Harten, Lax and Van Leer approach (HLL). The scheme is a high resolution one and the TVD (Total Variation Diminishing) property is satisfied. Particular attention is posed on the numerical treatment of source terms: the terms relative to the friction slope is discretised by a semi-implicit technique; the terms relative to the bottom slope is elaborated in an original way, based on a discretisation of their integral form. In order to test the reliability of the code, it is used for the numerical simulation of the flood-wave propagation on a portion of the Toce river valley. The basin is located on the Italian Occidental Alps. For this event, experimental data obtained by ENEL-CRIS are available.

Finite volume scheme for 2D shallow-water equations:application to a flood event in the Toce River

VALIANI, Alessandro;CALEFFI, Valerio;
1999

Abstract

The numerical simulation of exceptional events characterised by high hydraulic and hydrogeologic risk is an actual problem for the scientific community, working in the topic of environmental protection. In this paper a numerical code is described, for the simulation of 2D transient free-surface flows, suitable to work on both simple and complicated geometries. The proposed algorithm is based on the two-dimensional shallow water equations in their classical form. The spatial discretisation is obtained by the FVM cellcentred type method. The numerical system is solved in explicit way. The scheme is second order accurate both in space and time, trough the use of MUSCL method and a predictor-corrector approach. The scheme falls in the family of upwind methods, precisely in Godunov-type category. The local Riemann problem is solved by the Harten, Lax and Van Leer approach (HLL). The scheme is a high resolution one and the TVD (Total Variation Diminishing) property is satisfied. Particular attention is posed on the numerical treatment of source terms: the terms relative to the friction slope is discretised by a semi-implicit technique; the terms relative to the bottom slope is elaborated in an original way, based on a discretisation of their integral form. In order to test the reliability of the code, it is used for the numerical simulation of the flood-wave propagation on a portion of the Toce river valley. The basin is located on the Italian Occidental Alps. For this event, experimental data obtained by ENEL-CRIS are available.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1196351
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