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- W196207890 abstract "The problem of modelling both the unsteady hydrodynamics and the bed morphological variations in natural channels is generally performed by solving the De Saint Venant balance equations for the liquid phase together with the Exner continuity equation for the sediments carried as bed-load. This thesis focuses on the development of an high-order accurate centred scheme of the finite volume type for the numerical solution of the coupled De Saint Venant-Exner system. A new scheme, called PRICE-C, is proposed. It solves the system of equations in a non-conservative form, however it has the important characteristic of reducing automatically to a conservative scheme if the underlying PDE system is a conservation law. It is applied to the shallow water equations in the presence of either a fix or a movable bed. The scheme is first introduced in a one-dimensional framework, and it is then extended to the two-dimensional case. The extension is not straightforward in the case of an unstructured mesh, since averages over suitable edge-based control volumes have to be performed. The scheme is extended to high order of accuracy in space and time via the ADER-WENO and MUSCL technique respectively for the one- and twodimensional case. The well-balanced property of the scheme is proven, i.e. the ability to reach steady states also in the presence of discontinuous water surface or discontinuous bottom profile. The scheme can deal with subcritical and supercritical flows, as well as transcritical situations. Moreover the proposed approach leads to a correct estimate of the celerity of surface discontinuities as well sediment bores and small bottom perturbations. The main characteristic of the scheme is its simplicity: it is based on a simple centred approach, that means that the knowledge of the eigenvalues of the matrix of the system is not required. This is important since the interaction between sediment transport and water flow not always admits detailed knowledge of the eigenstructure. Hence this scheme can be useful to engineers since they need simple numerical tools that can be easily used without entering in the mathematical detail of the differential hyperbolic system under consideration. Moreover the centred strategy gives generality to the scheme: in fact, it can be applied without modification to any kind of hyperbolic equations with non-conservative terms." @default.
- W196207890 created "2016-06-24" @default.
- W196207890 creator A5082110607 @default.
- W196207890 date "2010-11-22" @default.
- W196207890 modified "2023-09-27" @default.
- W196207890 title "Numerical Modelling of Alluvial Rivers by Shock Capturing Methods" @default.
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