@inproceedings{Abdolmaleki04,

  author = {K. Abdolmaleki and K. P. Thiagarajan and M. T. Morris-Thomas},

  title = {Simulation of The Dam Break Problem and Impact Flows Using a Navier-Stokes Solver},

  booktitle = {Proceedings of the Fifteenth Australasian Fluid Mechanics Conference},

  publisher = {The University of Sydney},

  year = {2004},

  keywords = {dam-break; model},

  abstract = {The impact flow on a vertical wall resulting from a dam break problem is simulated using a Navier-Stokes (NS) solver. The NS solver uses an Eulerian finite volume method (FVM) along with a volume of fluid (VOF) scheme for phase interface capturing. The purpose of this study is to assess the accuracy of the solver for problems in the category of wave impacts. Previous experiments and other numerical solution techniques are compared with the solver's results. Different aspects of the flow such as free-surface elevation before and after the initial impact have been studied in depth. The pressure peak due to water impact on the vertical wall has also been analyzed. Water viscosity and air compressibility effects have been assessed. The significance of the time step and grid resolution are also discussed. Results show favorable agreement with experiments before water impact on the wall. However, both impact pressure and freesurface elevations after the impact depart from the experiments significantly. Hence the code is assessed to be good only for qualitative studies.},

  file = {Abdolmaleki04.pdf:Abdolmaleki04.pdf:PDF}

}

@article{Afzalimehr01,

  author = {H. Afzalimehr and F. Anctil},

  title = {Friction velocity associated to a non-uniform flow and an intermediate scale roughness},

  journal = {Journal of Hydraulic Research},

  year = {2001},

  volume = {39},

  number = {2},

  pages = {181--186},

  abstract = {This work consists of an experimental study of the resistance associated with non-uniform flows over cobble-bed channels, leading to an intermediate scale roughness. Friction velocity is estimated for twelve cases of accelerating and decelerating flows. Four estimation methods are compared: Reynolds stress, logarithmic law, parabolic law and a global approach. They are all in close agreement. The observed mean longitudinal velocity profiles are consistent with observations reported in the literature for non-uniform flows over gravel-bed channels with small relative roughness. Accelerating flows produce smaller friction velocities than decelerating flows, which is contrary to observations reported in the literature.},

  file = {Afzalimehr01.pdf:Afzalimehr01.pdf:PDF}

}

@techreport{Audusse04a,

  author = {E. Audusse},

  title = {A multilayer Saint-Venant model},

  year = {2004},

  number = {5249},

  keywords = {Free surface Navier-Stokes equations; shallow water assumption; hydrostatic approximation; Saint-Venant system; multilayer model; viscosity},

  abstract = {We introduce a new variant of the multilayer Saint-Venant system. The classical Saint-Venant system is a well-known approximation of the incompressible Navier-Stokes equations for shallow water flows with free moving boundary. Its efficiency, robustness and low computational cost make it very commonly used. Nevertheless its range of application is limited and it does not allow to access to the vertical profile of the horizontal velocity. Hence and thanks to a precise analysis of the shallow water assumption we propose here a new approximation of the Navier-Stokes equations which consists in a set of coupled Saint-Venant systems, extends the range of validity and gives a precise description of the vertical profile of the horizontal velocity while preserving the computational efficiency of the classical Saint-Venant system. We validate the model through some numerical examples.},

  file = {Audusse04a.pdf:Audusse04a.pdf:PDF}

}

@phdthesis{Audusse04b,

  author = {E. Audusse},

  title = {Modélisation hyperbolique et analyse numérique pour les écoulements en eaux peu profondes},

  school = {Université Paris VI -- Pierre et Marie Curie},

  year = {2004},

  note = {196~pages},

  keywords = {shallow water equations; source terms; multilayer model; transport equation; scalar conservation law; discontinuous flux; finite volumes; well-balanced scheme; kinetic interpretation; hydrostatic reconstruction; Kruzkov's entropies},

  abstract = {In this work we study some hyperbolic conservation laws related to shallow water flows. First we consider the Saint-Venant system with source terms and we develop a second order bidimensional well-balanced finite volumes scheme that is based on a kinetic interpretation of the system and on a hydrostatic reconstruction of the interfaces values. The scheme is consistent and conservative and it preserves the non-negativity of the water height. Then we extend the kinetic interpretation to the coupling with a transport equation. We construct a two time steps scheme that takes into account all the eigenvalues of the problem. This approach preserves the stability properties of the system and reduces the numerical diffusion and the computational cost. We also present a new multilayer Saint-Venant system that allows us to obtain non constant vertical velocity profiles while preserving an invariant two dimensional domain of calculation. We present the derivation of the system and we study its stability-energy, hyperbolicity. We also investigate its relation with other fluid models and we perform its numerical implementation. Finally we prove a uniqueness theorem for scalar conservation laws with discontinuous flux. Our proof uses a new family of entropies that are a natural way to adapt classical Kruzkov's entropies to the discontinuous case. This new method avoids the making of some classical hypothesis on the flux such as convexity, BV bounds or finite number of discontinuities and does not need the definition of some interface condition.},

  file = {Audusse04b.pdf:Audusse04b.pdf:PDF}

}

@article{Audusse04c,

  author = {E. Audusse and F. Bouchut and M.-O. Bristeau and R. Klein and B. Perthame},

  title = {A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows},

  journal = {SIAM J. Sci. Comput.},

  year = {2004},

  volume = {25},

  number = {6},

  pages = {2050--2065},

  keywords = {shallow water equations; finite volume schemes; well-balanced schemes},

  abstract = {We consider the Saint-Venant system for shallow water flows, with nonflat bottom. It is a hyperbolic system of conservation laws that approximately describes various geophysical flows, such as rivers, coastal areas, and oceans when completed with a Coriolis term, or granular flows when completed with friction. Numerical approximate solutions to this system may be generated using conservative finite volume methods, which are known to properly handle shocks and contact discontinuities. However, in general these schemes are known to be quite inaccurate for near steady states, as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions. This difficulty can be overcome by using the so-called well-balanced schemes. We describe a general strategy, based on a local hydrostatic reconstruction, that allows us to derive a well-balanced scheme from any given numerical flux for the homogeneous problem. Whenever the initial solver satisfies some classical stability properties, it yields a simple and fast well-balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality.},

  file = {Audusse04c.pdf:Audusse04c.pdf:PDF},

  doi = {http://dx.doi.org/10.1137/S1064827503431090}

}

@article{Audusse05,

  author = {E. Audusse and M.-O. Bristeau},

  title = {A well-balanced positivity preserving "second-order" scheme for shallow water flows on unstructured meshes},

  journal = {Journal of Computational Physics},

  year = {2005},

  volume = {206},

  pages = {311--333},

  keywords = {Saint-Venant system; shallow water flow; finite volume; Kinetic solver; hydrostatic reconstruction; well-balanced scheme; positivity preserving scheme; second-order extension},

  abstract = {We consider the solution of the Saint-Venant equations with topographic source terms on 2D unstructured meshes by a finite volume approach. We first present a stable and positivity preserving homogeneous solver issued from a kinetic representation of the hyperbolic conservation laws system. This water depth positivity property is important when dealing with wet-dry interfaces. Then, we introduce a local hydrostatic reconstruction that preserves the positivity properties of the homogeneous solver and leads to a well-balanced scheme satisfaying the steady-state condition of still water. Finally, a formally second-order extension based on limited reconstructed values on both sides of each interface and on an enriched interpretation of the source terms satisfies the same properties and gives a noticeable accuracy improvement. Numerical examples on academic and real problems are presented.},

  file = {Audusse05.pdf:Audusse05.pdf:PDF},

  doi = {http://dx.doi.org/10.1016/j.jcp.2004.12.016}

}

@techreport{Audusse00,

  author = {E. Audusse and M.-O. Bristeau and B. Perthame},

  title = {Kinetic schemes for Saint-Venant equations with source terms on unstructured grids},

  year = {2000},

  number = {3989},

  keywords = {Saint-Venant system; shallow water system; unstructured grid; finite volume method; kinetic schemes; source terms; equilibrium scheme},

  abstract = {We consider the Saint-Venant (or Shallow Water) system which is an usual model to describe the flows in rivers or coastal areas. This hyperbolic system of conservation laws is solved on unstructured meshes by a kinetic scheme based on a finite volume approach. An important property of this scheme is the preservation of the water height positivity when applications with dry areas are considered. Following some hypothesis an entropy inequality is proved. The standard kinetic scheme is modified to deal with varying bed slope and particularly to preserve aquilibrium states such as still water. Moreover the source terms due to arbitrary bottom topography have to be discretized in such a way to balance the flux gradients for these equilibriums. We illustrate the properties of the scheme on different test cases for which exact solutions are available and on more realistic applications.},

  file = {Audusse00.pdf:Audusse00.pdf:PDF}

}

@phdthesis{Augeard06,

  author = {B. Augeard},

  title = {Mécanisme de genèse du ruissellement sur sol agricole drainé sensible à la battance. Etudes expérimentales et modélisation},

  school = {ENGREF},

  year = {2006},

  abstract = {This study aims at describing and organizing into a hierarchy the processes leading to surface runoff on artificially subsurface drained area, by considering not only the perched water table fluctuations, but also the possible soil surface sealing. Three complementary research issues have been developed. First, the evolution of the tilled layer structure during rainfall in the presence of a shallow water table was observed using laboratory rainfall simulation. Bulk density profiles measured by X-ray radiography show that the increase of bulk density due to sealing and slumping are more significant in the wettest conditions. The proposed bulk density evolution model correctly reproduces this effect. Second, seal hydraulic properties were determined from a model based on bulk density profiles using other simulated rainfall experiments. The estimation of model parameters by inverse method led to an accurate simulation of the measured flows and water pressures, and conformed to the measured bulk density profiles. Hydraulic conductivity greatly decreases at the soil surface due to sealing process. The third issue was based on a drained field investigation in Mélarchez watershed (Seine et Marne) associated to flow modelling (Hydrus 2D). Data recorded in winter 2003-2004 show that drainage limits surface runoff amount. Saturation excess runoff is the most frequent observed process, even if soil sealing, especially due to saturation excess surface runoff, increases runoff amount. Other rainfall conditions were tested using Hydrus 2D. The condition of water table reaching soil surface was particularly analysed in terms of infiltration-runoff flows and return time of the corresponding rainfalls.},

  file = {Augeard06.pdf:Augeard06.pdf:PDF}

}

@techreport{Augeard08b,

  author = {Bénédicte Augeard and Cédric Chaumont and Yves Nédelec},

  title = {Mesure de ruissellement sur deux directions à  petite échelle sur une parcelle agricole de Goins (bassin de l'Orgeval)},

  year = {2008},

  note = {11 pages},

  keywords = {ANR METHODE, overland flow, field experiment, furrow, tillage, plot},

  file = {Augeard08b.pdf:Augeard08b.pdf:PDF}

}

@phdthesis{Balayn01,

  author = {P. Balayn},

  title = {Contribution à la modélisation numérique de l'évolution morphologique des cours d'eau aménagés lors de crues},

  school = {Université Claude Bernard--Lyon 1},

  year = {2001},

  file = {Balayn01.pdf:Balayn01.pdf:PDF}

}

@article{Barrenechea02,

  author = {G. R. Barrenechea and P. Le Tallec and F. Valentin},

  title = {New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains},

  journal = {Mathematical Modelling and Numerical Analysis},

  year = {2002},

  volume = {36},

  number = {2},

  pages = {177--203},

  abstract = {Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once. Numerical tests are presented to validate and compare the proposed boundary conditions.},

  file = {Barrenechea02.pdf:Barrenechea02.pdf:PDF}

}

@article{Bathurst02,

  author = {J. C. Bathurst},

  title = {At-a-site variation and minimum flow resistance for mountain rivers},

  journal = {Journal of Hydrology},

  year = {2002},

  volume = {269},

  number = {1-2},

  pages = {11--26},

  keywords = {bed material size distribution; boulder-bed channels; channel slope; field data; flow resistance; mountain rivers; GRAVEL-BED RIVERS; HIGH-GRADIENT STREAMS; VELOCITY; CHANNELS; HYDRAULICS; ROUGHNESS; DISCHARGE},

  abstract = {Existing flow resistance relationships for mountain rivers maybe in error by typically 30%. In part this is because flow resistance is a complex phenomenon, not easy to quantify with the available data. However, a further reason is the reliance of past analyses on fitting relationships to data from multiple sites, hence emphasizing an averaging between-site variation. A more scientific approach is to derive separate at-a-site relationships and investigate how they can be collapsed into a single formula. Twenty-seven carefully selected field datasets from seven literature sources are therefore analysed empirically to show at-a-site variations in resistance, with the aim of improving the accuracy and applicability of mountain river flow resistance relationships. Considering only the bed grain roughness, the principal factors likely to determine flow resistance are identified as relative submergence d/D-84 (where d is depth and D-84 is the bed material 84-percentile size), bed material size, distribution and channel slope. The dependency of the resistance function (8/f)(1/2) (where f is the Darcy-Weisbach resistance coefficient) on d/D84 is more accurately described by a power law than by a semi-logarithmic law, especially at high flows. From observations of coincident at-a-site datasets, two equations are derived, distinguished largely according to channel slope S. For S < 0.8%, (8/f)(1/2) = 3.84(d/D-84)(0.547) (r(2) = 0.986). For S > 0.8% (8/f)(1/2) = 3.10(d/D-84)(0.93) (r(2) = 0.959). These equations appear to define minimum values for flow resistance, probably for ideal conditions of bed grain roughness and uniform flow. Deviations from this ideal (because of form roughness, nonuniform flow or bank effects) will increase resistance in a manner which is not yet quantified. The equations therefore have a very specific applicability and are not generally applicable to all flows. The cause of the slope dependency remains unclear, nor is any dependency on bed material size distribution identified. Nevertheless the high correlation coefficients suggest an improved accuracy compared with other field-based relationships. The equations are derived for in-bank flows with d/D-84 < 11 and slopes in the range 0.2-4%.},

  file = {Bathurst02.pdf:Bathurst02.pdf:PDF},

  doi = {http://dx.doi.org/10.1016/S0022-1694(02)00191-9}

}

@mastersthesis{Becque08,

  author = {S. Becque},

  title = {Etude expérimentale et numérique de l'influence d'une rugosité orientée sur le ruissellement},

  school = {Ecole Polytechnique Universitaire Pierre et Marie Curie},

  year = {2008},

  note = {51 pages. Encadrants : Yves Nédélec, Bénédicte Augeard, Frédéric Darboux},

  keywords = {ANR Methode, experiment, metrology, depth, flow, laboratory},

  abstract = {The objective of my six months training course at the Cemagref of Antony was to carry out a laboratory experimentation of dripping flow on drill, and then to construct a mathematical model to describe this kind of flow. Results of this experimentation will be used by the model makers of the project METHODE. Because of very small flow depth, the traditional measuring methods of flow velocity and flow depth can not be used. We carried out experimental protocols to measure these variables with good precision. We used an instantaneous-profile laser to measure flow depth. The instantaneous profile laser usually measured soil surface elevation. In this work; it was used to measure the depth of a mix flow of water and paint. Flow velocity was measured with two conductimetry sensors set along the flow and salt solution drops dribbling upstream. A one dimensional flow experiment was carried out in a rectangular gutter and a polystyrene drilled surface was used for the two dimensional flow one. The mathematical one dimensional model developed in this work is based on the Manning- Strickler and the Darcy-Weisbach laws. It was applied to simulate flow in the gutter and in one drill of the drilled surface. The model simulations were compared with data of the experiments.},

  file = {Becque08.pdf:Becque08.pdf:PDF}

}

@article{Beecham05,

  author = {S. Beecham and M. H. Khiadani and J. Kandasamy},

  title = {Friction factors for spatially varied flow with increasing discharge},

  journal = {Journal of Hydraulic Engineering},

  year = {2005},

  volume = {131},

  pages = {792--799},

  keywords = {friction factor; water discharge; channel flow; slopes; flow resistance},

  abstract = {This paper describes an experimental investigation of how friction factors change for spatially varied flow in sloping channels receiving lateral inflow. The results are compared with those of Beij in 1934, and it is concluded that uniform flow resistance coefficients are not always appropriate for spatially varied flow. Moreover, the common technique of assuming a constant friction factor over the entire length of the channel has been found to have little theoretical justification. The method of Keulegan in 1952 for calculating friction factors in spatially varied flow gives a better estimate, but does not explicitly take account of the lateral inflow rate or velocity. Beij's 1934 experimental data, which was used by Keulegan does not show a systematic variation of friction factor with lateral inflow rate for a constant Reynolds number although this may be due to the low flowrates used. The results of the present study indicate that the friction factor increases with lateral inflow rate for a constant Reynolds number in the experiments that included subcritical and supercritical flow conditions. A method for calculating friction factors which allows for lateral inflow is presented as a precursor to the development of a general method of evaluating friction factors for spatially varied flow with increasing discharge.},

  file = {Beecham05.pdf:Beecham05.pdf:PDF},

  doi = {http://dx.doi.org/10.1061/(ASCE)0733-9429(2005)131:9(792)}

}

@mastersthesis{Elbouajaji07,

  author = {Mohamed El Bouajaji},

  title = {Modélisation des écoulements à surface libre~: étude du ruissellement des eaux de pluie},

  school = {Université Louis Pasteur},

  year = {2007},

  note = {Encadrants~: Fabrice Dupros et Olivier Cerdan},

  keywords = {Shallow flow equations; 2d; infiltration; Saint-Venant; ANR METHODE; Green-Ampt; hydrostatic reconstruction; finite volume; well-balanced scheme},

  file = {Elbouajaji07.pdf:Elbouajaji07.pdf:PDF}

}

@book{Bouchut04,

  author = {F. Bouchut},

  title = {Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources},

  publisher = {Birkhäuser Basel},

  year = {2004},

  volume = {2/2004},

  keywords = {conservation laws; hyperbolic systems; kinetic solvers; numerical analysis; partial differential equations;},

  abstract = {This book is devoted to finite volume methods for hyperbolic systems of conservation laws. It differs from previous expositions on the subject in that the accent is put on the development of tools and the design of schemes for which one can rigorously prove nonlinear stability properties. Sufficient conditions for a scheme to preserve an invariant domain or to satisfy discrete entropy inequalities are systematically exposed, with analysis of suitable CFL conditions. The monograph intends to be a useful guide for the engineer or researcher who needs very practical advice on how to get such desired stability properties. The notion of approximate Riemann solver and the relaxation method, which are adapted to this aim, are especially explained. In particular, practical formulas are provided in a new variant of the HLLC solver for the gas dynamics system, taking care of contact discontinuities, entropy conditions, and including vacuum. In the second half of the book, nonconservative schemes handling source terms are analyzed in the same spirit. The recent developments on well-balanced schemes that are able to capture steady states are explained within a general framework that includes analysis of consistency and order of accuracy. Several schemes are compared for the Saint Venant problem concerning positivity and the ability to treat resonant data. In particular, the powerful and recently developed hydrostatic reconstruction method is detailed.},

  doi = {http://dx.doi.org/10.1007/b95203}

}

@article{Bradford01,

  author = {S. F. Bradford and N. D. Katopodes},

  title = {Finite volume model for nonlevel basin irrigation},

  journal = {Journal of Irrigation and Drainage Engineering},

  year = {2001},

  volume = {127},

  number = {4},

  pages = {216--223},

  abstract = {A finite volume model for unsteady, two-dimensional, shallow water flow is developed and applied to simulate the advance and infiltration of an irrigation wave in two-dimensional basins of complex topography. The fluxes are computed with Roe's approximate Riemann solver and the monotone upstream scheme for conservation laws is used in conjunction with predictor-corrector time-stepping to provide a second-order accurate solution. Flux-limiting is implemented to eliminate spurious oscillations and the model incorporates an efficient and robust scheme to capture the wetting and drying of the soil. Model predictions are compared with experimental data for one- and two-dimensional problems involving rough, impermeable, and permeable beds, including a poorly leveled basin.},

  file = {Bradford01.pdf:Bradford01.pdf:PDF}

}

@inproceedings{Braschi94,

  author = {G. Braschi and F. Dadone and M. Gallati},

  title = {Plain flooding: near field and far field simulations},

  booktitle = {Modelling of flood propagation over initially dry areas},

  publisher = {American Society of Civil Engineers, New York, USA},

  year = {1994},

  pages = {45--59},

  keywords = {dam-break; experiment; depth; flood; velocity},

  file = {Braschi94.pdf:Braschi94.pdf:PDF}

}

@article{Braud05,

  author = {I. Braud and D. De Condappa and J. M. Soria and R. Haverkamp and R. Angulo-Jaramillo and S. Galle and M. Vauclin},

  title = {Use of scaled forms of the infiltration equation for the estismation of unsatured soil hydraulic properties (the Beerkan method)},

  journal = {European Journal of Soil Science},

  year = {2005},

  volume = {56},

  pages = {361--374},

  abstract = {Water movement in soil can be described accurately at the local scale, provided that soil hydraulic properties can be determined with precision. Traditional methods for characterizing soil are often time consuming, and large areas cannot be sampled easily. We present a simple method for overcoming these difficulties. It is easy to implement and cheap. It is known as the Beerkan method, and it relies on particle-size analysis, dry bulk density and simple infiltration tests in cylinders. We describe the experimental protocol and the method of data analysis, leading to the estimation of parameters describing hydraulic properties. Shape parameters depend on soil texture and are derived from particle-size data. Normalization parameters depend on soil structure. They are derived by inverse modelling and optimization from the infiltration tests. The theoretical background relies on the sorptivity concept and scaled forms of the infiltration equation. The formalism for one- and three-dimensional analysis is described. We assess the accuracy of the method using published data and simulated values, showing the soundness of the approach. For the purpose of illustration, we implemented a simple optimization technique on two bounding cases.},

  file = {Braud05.pdf:Braud05.pdf:PDF},

  doi = {http://dx.doi.org/10.1111/j.1365-2389.2004.00660.x}

}

@techreport{Bristeau01,

  author = {M.-O. Bristeau and B. Coussin},

  title = {Boundary conditions for the shallow water equations solved by kinetic schemes},

  year = {2001},

  number = {4282},

  keywords = {shallow water system; finite volume method; kinetic solver; friction; boundary conditions},

  abstract = {We consider the Saint-Venant system for Shallow Water which is an usual model to describe the flows in rivers, coastal areas or floodings. The hyperbolic system of conservation laws is solved on unstructured meshes using a finite volume method together with a kinetic solver. We add ti this system a friction term, the role of which is important when small water depths are considered. In this paper we address the treatment of the boundary conditions, the difficulty is due to the fact that in some cases (fluvial flows) the given boundary conditions are not sufficient to apply directly the scheme, we discuss here how to treat these boundary conditions using a Riemann invariant. Some numerical results illustrate the ability of the method to treat complex problems like the filling up or the draining off of a river bed.},

  file = {Bristeau01.pdf:Bristeau01.pdf:PDF}

}

@article{Brufau03,

  author = {P. Brufau and P. Garcìa-Navarro},

  title = {Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique},

  journal = {Journal of Computational Physics},

  year = {2003},

  volume = {186},

  pages = {503--526},

  keywords = {multidimensional upwind; shallow water; unsteady flow; source terms},

  abstract = {In the context of numerical techniques for solving unsteady free surface problems, finite element and finite volume approximations are widely used. A class of upwind methods which attempts to model the equations in a genuinely multidimensional manner has been recently introduced as an alternative. Multidimensional upwind schemes (MUS) were developed initially for the approximation of steady-state solutions of the two-dimensional Euler equations on unstructured grids, although they can be applicable to any system of hyperbolic conservation laws, such as the shallow water equations. The formal analogy between the two systems of equations is useful for simple cases. However, in practical applications of interest in hydraulics, complex geometries and bottom slope variation can lead to important numerical errors produced by an inadequate source term discretization. This problem has been analyzed and, in this work, the necessity of a multidimensional upwind discretization of the source terms is justified. The basis of the numerical method is stated and the particular adaptation to unsteady shallow water flows over irregular geometry is described. As test cases, laboratory experimental data are used together with academic tests for validation.},

  file = {Brufau03.pdf:Brufau03.pdf:PDF},

  doi = {http://dx.doi.org/10.1016/S0021-9991(03)00072-X}

}

@article{Burguete04,

  author = {J. Burguete and P. Garcìa-Navarro},

  title = {Implicit schemes with large time step for non-linear equations : application to river flow hydraulics},

  journal = {International Journal for Numerical Methods in Fluids},

  year = {2004},

  volume = {46},

  pages = {607--636},

  keywords = {implicit schemes; upwind discretization; shallow water; unsteady flow with shocks; non-linear equations; high CFL number},

  abstract = {In this work, first-order upwind implicit schemes are considered. The traditional tridiagonal scheme is rewritten as a sum of two bidiagonal schemes in order to produce a simpler method better suited for unsteady transcritical flows. On the other hand, the origin of the instabilities associated to the use of upwind implicit methods for shock propagations is identified and a new stability condition for non-linear problems is proposed. This modification produces a robust, simple and accurate upwind semi-explicit scheme suitable for discontinuous flows with high Courant-Friedrichs-Lewy (CFL) numbers. The discretization at the boundaries is based on the condition of global mass conservation thus enabling a fully conservative solution for all kind of boundary conditions. The performance of the proposed technique will be shown in the solution of the inviscid Burgers' equation, in an ideal dambreak test case, in some steady open channel flow test cases with analytical solution and in a realistic flood routing problem, where stable and accurate solutions will be presented using CFL values up to 100.},

  file = {Burguete04.pdf:Burguete04.pdf:PDF},

  doi = {http://dx.doi.org/10.1002/fld.772}

}

@article{Burguete02,

  author = {J. Burguete and P. Garcìa-Navarro and R. Aliod},

  title = {Numerical simulation of runoff from extreme rainfall events in a mountain water catchment},

  journal = {Natural Hazards and Earth System Sciences},

  year = {2002},

  volume = {2},

  pages = {109--117},

  abstract = {A numerical model for unsteady shallow water flow over initially dry areas is applied to a case study in a small drainage area at the Spanish Ebro River basin. Several flood mitigation measures (reforestation, construction of a small reservoir and channelization) are simulated in the model in order to compare different extreme rainfall-runoff scenarios.},

  file = {Burguete02.pdf:Burguete02.pdf:PDF}

}

@article{Caleffi03,

  author = {V. Caleffi and A. Valiani and A. Zanni},

  title = {Finite volume method for simulating extreme flood events in natural channels},

  journal = {Journal of Hydraulic Research},

  year = {2003},

  volume = {41},

  number = {2},

  pages = {167--177},

  keywords = {SWE; FVM; HLL approximate Riemann solver; source terms; overland flood flow; Toce river},

  abstract = {The need for mitigating damages produced by extreme hydrologic 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.}

}

@article{Castro07,

  author = {M. J. Castro and A. Pardo and C. Parès},

  title = {Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique},

  journal = {Mathematical Models and Methods in Applied Sciences},

  year = {2007},

  volume = {17},

  number = {12},

  pages = {2065--2113},

  keywords = {nonconservative products; finite volume method; well-balanced schemes; approximate Riemann solvers; Godunov methods; Roe methods; relaxation methods; high order methods},

  abstract = {The goal of this paper is to generalize the hydrostatic reconstruction technique introduced in Ref. 2 for the shallow water system to more general hyperbolic systems with source term. The key idea is to interpret the numerical scheme obtained with this technique as a path-conservative method, as defined in Ref. 35. This generalization allows us, on the one hand, to construct well-balanced numerical schemes for new problems, as the two-layer shallow water system. On the other hand, we construct numerical schemes for the shallow water system with better well-balanced properties. In particular we obtain a Roe method which solves exactly every stationary solution, and not only those corresponding to water at rest.},

  file = {Castro07.pdf:Castro07.pdf:PDF}

}

@phdthesis{Cerdan01,

  author = {O. Cerdan},

  title = {Analyse et modélisation du transfert de particules solides à l'échelle de petits bassins versants cultivés},

  school = {Université d'Orléans},

  year = {2001},

  file = {Cerdan01.pdf:Cerdan01.pdf:PDF}

}

@phdthesis{Chahinian04,

  author = {N. Chahinian},

  title = {Paramétrisation multi-critère et multi-échelle d'un modèle hydrologique spatialisé de crue en milieu agricole},

  school = {université de Montpellier II--sciences et techniques de Languedoc},

  year = {2004},

  file = {Chahinian04.pdf:Chahinian04.pdf:PDF}

}

@article{Chanson06,

  author = {Hubert Chanson},

  title = {Solutions analytiques de l'onde de rupture de barrage sur plan horizontal et incliné},

  journal = {La Houille Blanche},

  year = {2006},

  number = {3},

  pages = {76--86},

  keywords = {Dam break wave; Analytical solutions; Saint-Venant equations; Turbulent and laminar flows; horizontal and sloping channels; shallow flow equations},

  abstract = {Dam break waves have been responsible for numerous losses and tragedies. The present work is focused on simple solutions of the dam break wave problem using the Saint-Venant equations Theoretical solutions are developed for instantaneous dam break of semi-infinite reservoir in initially-dry channels. Both laminar and turbulent flow conditions are considered. Solutions for horizontal inverts are compared successfully with previous experimental results, and they are then extended to sloping channels. The results yield a series of simple analytical solutions that are well-suited for educational purposes as well as for emergency services.},

  file = {Chanson06.pdf:Chanson06.pdf:PDF},

  doi = {http://dx.doi.org/10.1051/lhb:200603012}

}

@inbook{Chow88a,

  author = {Ven Te Chow and David R. Maidment and Larry W. Mays},

  title = {Applied hydrology},

  publisher = {McGraw-Hill Book Company},

  year = {1988},

  pages = {272--309},

  keywords = {MacCormack; hydrology; scheme; shallow flow equation},

  file = {Chow88a.pdf:Chow88a.pdf:PDF}

}

@techreport{Cordier07,

  author = {Stéphane Cordier and Frédéric Darboux and Olivier Delestre and François James},

  title = {Etude d'un modèle de ruissellement 1D},

  year = {2007},

  keywords = {shallow flow equations; ANR METHODE; finite volume; model; hydrostatic reconstruction; well-balanced scheme},

  file = {Cordier07.pdf:Cordier07.pdf:PDF}

}

@phdthesis{Crossley99,

  author = {A. J. Crossley},

  title = {Accurate and efficient numerical solutions for the Saint Venant equations of open channel flow},

  school = {university of Nottingham},

  year = {1999},

  abstract = {Within the field of hydraulics there is a growing trend towards the use of computer based models, which have proven to be an invaluable tool in engineering. A range of commercial packages is available which encompass different mathematical models and a variety of solution strategies. A number of problems can be identified with the software currently available, and as aresult, research continues into developing better numerical techniques for computational hydraulics. The issues most often addressed by researchers consider the application of faster and more accurate numerical methods, many of which were originally developed for gas dynamics problems. There has been a growing trend in favour of Riemann based methods constructed within the finite volume framework. Such methods are noted for their good conservation and shock capturing capabilities. However, the computational cost of employing these algorithms can lead to excessively long run times, particularly when higher order mathematical models are used. This often is as a result of stability constraints placed upon explicit schemes, which require the smallest possible time step permitted throughout the grid, to be applied globally. One possibillility for improving this situation is to use local time stepping, whereby individual cells are advanced by their own maximum allowable time steps. To incorporate this concept into a transient model requires the development of a suitable integration strategy, to ensure that the solution remains accurate in time. Two such strategies developed for the Euler equations are considered within this thesis for application to the Saint Venant equations of open channel flow. Both techniques