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 cell-centred 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 pre-dictor-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 an 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 accuracy, the stability and reliability of the code, classical test case, for which is known the exact analytical solution, are used. Afterwards the code is used for the numerical simulation of the submersion-wave propagation on the Reyran river valley in consequence of the Malpasset dam break. The valley is located in the department of Var, approximately 12 km upstream of Frejus, southern France. For this event, field data and experimental data obtained by EDF are available.

Finite volume scheme for 2D shallow-water equations:application to the Malpasset dam-break

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 cell-centred 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 pre-dictor-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 an 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 accuracy, the stability and reliability of the code, classical test case, for which is known the exact analytical solution, are used. Afterwards the code is used for the numerical simulation of the submersion-wave propagation on the Reyran river valley in consequence of the Malpasset dam break. The valley is located in the department of Var, approximately 12 km upstream of Frejus, southern France. For this event, field data and experimental data obtained by EDF are available.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1196350
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