Finite volume method for simulating extreme flood events in natural channels

The need for mitigating damages produced by extreme hydrologie events has stimulated the European Community to fund several projects. The Concerted Action on Dam-break Modelling workgroup (CADAM) performed a considerable work for the development of new codes and for the adequate verification of their performance. In the context of the CADAM project, a new 2D computer code is developed, tested and applied, as described in the present paper. The algorithm is obtained through the spatial discretisation of the shallow water equations by a finite volume method, based on the Godunov approach. The HLL Riemann solver is used. A second order accuracy in space and time is achieved, respectively by MUSCL and predictor-corrector techniques. The high resolution requirement is ensured by satisfaction of TVD property. Particular attention is posed to the numerical treatment of source terms. Accuracy, stability and the reliability of the code are tested on a selected set of study cases. A grid refinement analysis is performed. Numerical results are compared with experimental data, obtained by the physical modelling of a submersion wave on a portion of the Toce river valley, Italy, performed by ENEL-HYDRO and considered as representative of a real life flood occurrence.

[1]  M. Hanif Chaudhry,et al.  Explicit Methods for 2‐D Transient Free Surface Flows , 1990 .

[2]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .

[3]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow , 1977 .

[4]  Davide Carlo Ambrosi,et al.  Approximation of shallow water equations by Roe's Riemann solver , 1995 .

[5]  Jaw-Yen Yang,et al.  Computation of free surface flows. Part III. Steady supercritical flow using a generalized lagrangian method , 1996 .

[6]  S. Osher,et al.  Upwind difference schemes for hyperbolic systems of conservation laws , 1982 .

[7]  A. Valiani.  Rapid transients in free-surface flows with movable bed: a 2-D numerical solution , 1992 .

[8]  Mohammed Louaked,et al.  TVD scheme for the shallow water equations , 1998 .

[9]  J. S. Wang,et al.  FINITE-DIFFERENCE TVD SCHEME FOR COMPUTATION OF DAM-BREAK PROBLEMS , 2000 .

[10]  Ming-Hseng Tseng.  Explicit finite volume non-oscillatory schemes for 2D transient free-surface flows , 1999 .

[11]  Pilar García-Navarro,et al.  Flux difference splitting and the balancing of source terms and flux gradients , 2000 .

[12]  D. Zhao,et al.  Finite‐Volume Two‐Dimensional Unsteady‐Flow Model for River Basins , 1994 .

[13]  J. V. Soulis,et al.  Computation of two-dimensional dam-break-induced flows , 1991 .

[14]  Pilar García-Navarro,et al.  International Journal for Numerical Methods in Fluids Two-dimensional Dam Break Flow Simulation , 2022 .

[15]  P. García-Navarro,et al.  On numerical treatment of the source terms in the shallow water equations , 2000 .

[16]  Marinko Nujić,et al.  Efficient implementation of non-oscillatory schemes for the computation of free-surface flows , 1995 .

[17]  P. Lax,et al.  On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[18]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme I. The quest of monotonicity , 1973 .

[19]  A. Gosman,et al.  High resolution NVD differencing scheme for arbitrarily unstructured meshes , 1999 .

[20]  Stanley Osher,et al.  Convergence of Generalized MUSCL Schemes , 1985 .

[21]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[22]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[23]  Paul Glaister.  Approximate Riemann solutions of the shallow water equations , 1988 .

[24]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[25]  Pilar García-Navarro,et al.  Flux difference splitting for 1D open channel flow equations , 1992 .

[26]  Pilar García-Navarro,et al.  A HIGH-RESOLUTION GODUNOV-TYPE SCHEME IN FINITE VOLUMES FOR THE 2D SHALLOW-WATER EQUATIONS , 1993 .

[27]  B. V. Leer,et al.  Towards the Ultimate Conservative Difference Scheme , 1997 .

[28]  Valerio Caleffi,et al.  Case Study: Malpasset Dam-Break Simulation using a Two-Dimensional Finite Volume Method , 2002 .

[29]  E. F. Toro,et al.  Riemann problems and the WAF method for solving the two-dimensional shallow water equations , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[30]  M. Berzins,et al.  An unstructured finite-volume algorithm for predicting flow in rivers and estuaries , 1998 .