SUMMARYA high-order Godunov-type scheme based on MUSCL variable extrapolation and slope limiters is presented for the resolution of 2D free-surface flow equations. In order to apply a finite volume technique of integration over body-fitted grids, the construction of an approximate Jacobian (Roe type) of the normal flux function is proposed. This procedure allows conservative upwind discretization of the equations for arbitrary cell shapes. The main advantage of the model stems from the adaptability of the grid to the geometry of the problem and the subsequent ability to produce correct results near the boundaries.Verification of the technique is made by comparison with analytical solutions and very good agreement is found. Three cases of rapidly varying two-dimensional flows are presented to show the efficiency and stability of this method, which contains no terms depending on adjustable parameters. It can be considered well suited for computation of rather complex free-surface two-dimensional problems.KEY WORDS Free-surface flow Two-dimensional modelling Finite volumes MUSCL approach Upwind differencing
A description of the Tous Dam break as a case study for flood model development and validation purposes is presented. The corresponding data set was put together during a joint European project named Investigation of extreMe flood Processes And unCerTainty (IMPACT) with the aim of testing numerical models of flood propagation, including the treatment of urban areas. The case study is based upon the failure of Tous Dam in Spain and the flooding of Sumacárcel, a small town located 5 km downstream. Tous Dam broke due to overtopping on October 20, 1982. This event exemplifies the failure of a major flood control structure with considerable risk for population and damage to properties. The paper describes Tous Dam, the event that led to its breaching, the effects of the flood downstream and the inundation of the town of Sumacárcel. The information provided together with the referenced data set allows for mathematical modelling of the breaching and flooding processes, including the town, and can be used for validation of mathematical models against real-life data.
RÉSUMÉCet article décrit la rupture du barrage de Tous (Espagne) en tant que cas test pour le développement de modèles de propagation de crues et pour leur validation. Les données ont été rassemblées dans le cadre du projet européen IMPACT (Investigation of extreMe flood Processes And unCerTainty) dans le but de tester des modèles numériques de propagation de crues, en y incluant le traitement de zones urbaines. Ce cas test est basé sur la rupture du barrage de Tous et sur l'inondation de Sumacárcel, une petite ville située 5 km à l'aval du barrage. Le barrage de Tous s'est rompu par submersion le 20 octobre 1982. Cet événement constitue un exemple de rupture d'un ouvrage majeur destiné à contrôler les crues, rupture entraînant des risques considérables pour les populations et pour les biens à l'aval. Le barrage de Tous, l'événement conduisant à sa rupture, les effets de l'onde de submersion ainsi que l'inondation de Sumacárcel sont décrits dans le texte. Les informations et données fournies avec ce cas test permettent de tester la modélisation mathématique de la formation de brèche et d'une rupture progressive, ainsi que de propagation des crues. Ces données peuvent donc être utilisées pour la validation de modèles numériques incluant les zones urbanisées à partir d'un cas réel.
To cite this version:Slah Sahmim, Fayssal Benkhaldoun, Francisco Alcrudo. A sign matrix based scheme for nonhomogeneous PDE's with an analysis of the convergence stagnation phenomenon. Journal of Computational Physics, Elsevier, 2007, 226 (2)
AbstractThis work is devoted to the analysis of a finite volume method recently proposed for the numerical computation of a class of non homogenous systems of partial differencial equations of interest in fluid dynamics. The stability analysis of the proposed scheme leads to the introduction of the sign matrix of the flux jacobian. It appears that this formulation is equivalent to the VFRoe scheme introduced in the homogeneous case and has a natural extension here to non homogeneous systems. Comparative numerical experiments for the Shallow Water and Euler equations with source terms, and a model problem of two phase flow (Ransom faucet) are presented to validate the scheme. The numerical results present a convergence stagnation phenomenon for certain forms of the source term, notably when it is singular. Convergence stagnation has been also shown in the past for other numerical schemes. This issue is addressed in a specific section where an explanation is given with the help of a linear model equation, and a cure is demonstrated.
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