応用水文 = Applied hydrology

High resolution schemes for hyperbolic conservation laws

This paper reviews state-of-the-art empirical, hydrodynamic and simple conceptual models for determining flood inundation. It explores their advantages and limitations, highlights the most recent advances and discusses future directions. It addresses how uncertainty is analysed in this field with the various approaches and identifies opportunities for handling it better. The aim is to inform scientists new to the field, and help emergency response agencies, water resources managers, insurance companies and other decision makers keep up-to-date with the latest developments. Guidance is provided for selecting the most suitable method/model for solving practical flood related problems, taking into account the specific outputs required for the modelling purpose, the data available and computational demands. Multi-model, multi-discipline approaches are recommended in order to further advance this research field. This paper reviews state-of-the-art flood inundation models.It explores their advantages and limitations.It highlights the most recent advances and discusses future directions.It addresses how uncertainty is analysed and identifies opportunities for handling it better.

Flood inundation modelling

The surface gradient method for the treatment of source terms in the shallow-water equations

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

A 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 discretisation 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.

A high-resolution godunov-type scheme in finite volumes for the 2d shallow-water equations

A numerical technique for the modelling of shallow water flow in one and two dimensions is presented in this work along with the results obtained in different applications involving unsteady flows in complex geometries. A cell-centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured cells is presented. The discretization of the bed slope source terms is done following an upwind approach. In some applications a problem arises when the flow propagates over adverse dry bed slopes, so a special procedure has been introduced to model the advancing front. The applications presented are mainly related with unsteady flow problems

A numerical model for the flooding and drying of irregular domains

On numerical treatment of the source terms in the shallow water equations

Flux difference splitting and the balancing of source terms and flux gradients

A wetting-drying condition (WDC) for unsteady shallow water flow in two dimensions leading to zero numerical error in mass conservation is presented in this work. Some applications are shown which demonstrate the effectiveness of the WDC in flood propagation and dam break flows over real geometries. The WDC has been incorporated into a cell centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured meshes. Previous wetting-drying condition based on steady-state conditions lead to numerical errors in unsteady cases over configurations with strong variations on bed slope. A modification of the wetting-drying condition including the normal velocity to the cell edge enables to achieve zero numerical errors. The complete numerical technique is described in this work including source terms discretization as a complete and efficient 2D river flow simulation tool

Pilar García-Navarro

Papers

A high-resolution godunov-type scheme in finite volumes for the 2d shallow-water equations

A numerical model for the flooding and drying of irregular domains

On numerical treatment of the source terms in the shallow water equations

Flux difference splitting and the balancing of source terms and flux gradients

Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topography