Numerical Flood Simulation

Abstract

This contribution describes the state of the art of numerical flood simulation, in particular, the models based upon hydraulic laws. Both theory and practical aspects are discussed. In the introduction, various types of applications of these models are listed with their requirements in terms of robustness, accuracy, speed of operation, and engineering staff time. After introducing the 1D Saint Venant unsteady flow equations and describing the meaning of their terms, the concepts of kinematic and diffusive wave approximations are discussed. These provide better ways of understanding the physical behavior of flood waves and demonstrate the link between hydraulic and hydrologic flood propagation models. Numerical discretization of the unsteady flow equations is introduced with special attention given to the correct and robust modeling of rapidly varying flow, as occurring around hydraulic structures, discontinuities in channel beds, and flood‐generating breaches of river embankments and reservoir dams. Proceeding with the 2D flow description and its numerical discretization principles, the emergence of hybrid 1D/2D models is discussed with their different options of linking model components of flood‐prone areas. The quality of models also relies very much on the availability of detailed and correct data. This contribution briefly introduces the impact of new data collection techniques on numerical flood model schematization.

Efficient scheme for the shallow water equations on unstructured grids with application to the Continental Shelf

“…This is further discussed in Section 2.3. We employ a solver that combines Gaussian elimination and conjugate gradients that was developed earlier as part of the SOBEK1D2D system (Stelling and Verwey 2005). The solver is discussed in detail in Section 2.4.…”

Assessment of an ASTER-generated DEM for 2D hydrodynamic flood modeling

“…(1)-(3) are available in Stelling and Duinmeijer (2003), Stelling and Verwey (2005) and Dhondia and Stelling (2002). Adding a detailed description on the advanced numeric solver is ignored here since such is outside the scope of this work.…”

A semi-analytical model for form drag of river bedforms

“…In the calculation it is assumed that the resistance relation for steady flow is also applicable to unsteady flow (e.g. Stelling and Verwey, 2005), for instance a flood. Upstream and downstream boundary conditions, for instance, the upstream discharge as a function of time and the downstream water depth, need to be known, just as the initial flow conditions for each spatial step.…”