Simulation of dam‐ and dyke‐break hydrodynamics on dynamically adaptive quadtree grids

Flooding due to the failure of a dam or dyke has potentially disastrous consequences. This paper presents a Godunov-type finite volume solver of the shallow water equations based on dynamically adaptive quadtree grids. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) scheme is used to evaluate interface fluxes in both wet- and dry-bed applications. The numerical model is validated against results from alternative numerical models for idealized circular and rectangular dam breaks. Close agreement is achieved with experimental measurements from the CADAM dam break test and data from a laboratory dyke break undertaken at Delft University of Technology. Copyright © 2004 John Wiley Sons, Ltd.

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

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

[3]  Pilar García-Navarro,et al.  1‐D Open‐Channel Flow Simulation Using TVD‐McCormack Scheme , 1992 .

[4]  Stephen Roberts,et al.  Numerical solution of the two-dimensional unsteady dam break , 2000 .

[5]  E. Toro,et al.  Restoration of the contact surface in the HLL-Riemann solver , 1994 .

[6]  Derek M. Causon,et al.  Numerical solutions of the shallow water equations with discontinuous bed topography , 2002 .

[7]  Masayuki Fujihara,et al.  Godunov-Type Solution of Curvilinear Shallow-Water Equations , 2000 .

[8]  Derek M. Causon,et al.  HIGH-RESOLUTION FINITE-VOLUME METHOD FOR SHALLOW WATER FLOWS , 1998 .

[9]  F. Henderson Open channel flow , 1966 .

[10]  E. Toro Shock-Capturing Methods for Free-Surface Shallow Flows , 2001 .

[11]  Masayuki Fujihara,et al.  Adaptive Q-tree Godunov-type scheme for shallow water equations , 2001 .

[12]  Pilar García-Navarro,et al.  Dam-break flow simulation : some results for one-dimensional models of real cases , 1999 .

[13]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[14]  R. Sibson A vector identity for the Dirichlet tessellation , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  S. Roberts,et al.  Catastrophic Collapse of Water Supply Reservoirs in Urban Areas , 1999 .

[16]  Derek M. Causon,et al.  A bore-capturing finite volume method for open-channel flows , 1998 .

[17]  J. A. Battjes,et al.  Coastal modelling for flood defence , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  Nikolaos D. Katopodes,et al.  Applicability of Dam‐Break Flood Wave Models , 1983 .

[19]  S. Osher Numerical Solution of Singular Perturbation Problems and Hyperbolic Systems of Conservation Laws , 1981 .

[20]  Abioala A. Akanbi,et al.  Model for Flood Propagation on Initially Dry Land , 1988 .

[21]  Peter Stansby,et al.  Unsteady surface-velocity field measurement using particle tracking velocimetry , 1995 .

[22]  Deborah Greaves,et al.  Quadtree grid generation: Information handling, boundary fitting and CFD applications , 1996 .

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

[24]  Philip L. Roe,et al.  Efficient construction and utilisation of approximate riemann solutions , 1985 .

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

[26]  Derek M. Causon,et al.  Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations , 2000 .

[27]  Paolo Mignosa,et al.  Numerical simulation and experimental verification of Dam-Break flows with shocks , 2000 .

[28]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[29]  K. Anastasiou,et al.  SOLUTION OF THE 2D SHALLOW WATER EQUATIONS USING THE FINITE VOLUME METHOD ON UNSTRUCTURED TRIANGULAR MESHES , 1997 .

[30]  Eleuterio F. Toro,et al.  Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems , 1995 .

[31]  Derek M. Causon,et al.  Calculation of shallow water flows using a Cartesian cut cell approach , 2000 .