A control volume finite elements approach to flood plain inundation modelling

The paper describes the development of CVFE a 1-D/2-D Control Volume Finite Elements model within the frame of the D e cision Support system for Inundation Risk Evaluation and Emergencies management (DESIREE) project. The CVFE approach addresses and solves the discretisation problem, by defining a double mesh: the first one is a triangular mesh of FEs over which the momentum equations can be lumped and the second one is a IFD polygonal mesh over which mass balance can be lumped. This approach can handle isotropic and anisotropic problems and overcomes the lack of capability of standard Finite Element approach to locally preserve the mass balance equation, which generally results into heavy oscillations of the solution. In addition, the introduction of the CVFE method permits a physical interpretation of the quantities that describe the flow terms and allows for the 1-D representation of the river and channel flows. The paper will also show that the CVFE may be regarded as a synthesis of the Finite Elements and of the Integrated Finite Differences combining their advantages. The CVFE method is locally conservative (like the IFD method) and permits an accurate description of complex geometry and of pronounced heterogeneity and anisotropy (like the FE method). The final result of the project will be a software package running on a (MIMD) parallel computer, imbedded into the DESIREE based Decision Support System. CVFE will be tested and validated on the Magra river basin, chosen for its dangerous high flood risk situation.