The role of quasi-conservative form for morphodynamic modelling in river flow computations

摘要

Coupling the De Saint-Venant equations with the Exner equation yields to a model for the morphohydrodynamics that can be used to describe flow in rivers the shape of which is determined by the flow itself. Modern numerical models of natural rivers are built upon synchronous solution of the above system, accounting for the strong coupling between water flow, sediment transport, and morphological evolution. Such models are described by a system of hyperbolic equations expressed in primitive (non-conservative) form, thus requiring the use of non-conservative numerical methods for its numerical solution. Methods based on the primitive formulation are known to wrongly compute both the strength and the celerity of shock waves (bores), with consequent loss of mass. Such a problem may affect the numerical solution making it completely useless, in particular for long term morphodynamic simulations. In the present contribution it is shown how a quasiconservative formulation of the governing equations may help to reduce these errors. In particular, numerical solutions are obtained using a quasi-conservative formulation of the well-known MacCormack method. To test the proposed formulation, the model is first applied to idealized benchmark problems. The robustness of the model is then tested routing severe floods through a complex river system and comparing numerical results with the measurements obtained on a physical model of the Vara River in Northern Italy.