An Accurate and Efficient Semi-Implicit Method for Section Averaged Free Surface Flow Modelling

Code:
12/2007
Title:
An Accurate and Efficient Semi-Implicit Method for Section Averaged Free Surface Flow Modelling
Date:
Friday 27th July 2007
Author(s):
Deponti, Alberto; Bonaventura, Luca; Rosatti; Giorgio, Garegnani, Giulia
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Abstract:
An accurate, efficient and robust numerical method for the solution of the section averaged equations of open channel flow is presented and discussed. The method allows for river sections of arbitrary shape and for arbitrary bottom topography. The continuity equation is formulated in a conservative fashion, while a non conservative form is chosen for the momentum equation, thus avoiding the need for well balanced schemes to handle rapidly varying bathymetry. In order to achieve unconditional stability with respect to flow celerity, a semi-implicit time discretization is introduced, which requires the solution of a weakly nonlinear system for the free surface at each time step by a fixed point iteration technique. A semi-Lagrangian discretization is introduced, to achieve full unconditional stability and increase efficiency at no accuracy loss in subcritical flow regimes. An appropriate upwind discretization is also introduced for the momentum equation, which allows to recover correct solutions also in presence of discontinuities and strong gradients. Numerical experiments show that the semi-Lagrangian method yields indeed accurate results also in the case of stationary hydraulic jumps. The model is validated in a wide range of idealised test cases, highlighting its accuracy and efficiency characteristics, especially for long time range simulations of subcritical river flow. Finally, a first model validation on realistic data is presented, concerning simulations of flooding events of the Adda river.
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G. Rosatti, L. Bonaventura, A. Deponti, G. Garegnani, An Accurate and Efficient Semi-Implicit Method for Section Averaged Free Surface Flow Modelling, International Journal of Numerical Methods in Fluids, Vol. 65, pp. 448-473, 2011