Simulation of the St Francis dam-break flood

Numerical simulation of the 1928 St. Francis Dam failure in southern California was accomplished using a 2D Godunov-type finite-volume shallow-water algorithm run on an unstructured grid of triangular cells. The model was found to be accurate based on historical accounts, including flood maps and arrival time data, and sensitivity analysis was performed to determine factors that control the predictability of flooded area and flood arrival times. Results show that predictions of flood arrival times are sensitive to both mesh resolution and Manning coefficient (used to scale flow resistance), while predictions of flooded area were found to be relatively insensitive to the Manning coefficient. These results suggest that bed resistance controlled the speed of the St. Francis flood while flooded area was controlled by topography and the volume of released water. The study also revealed two types of previously unreported oscillatory surging in the dam-break flood. The first is due to a standing wave that develops in a tortuous reach of channel downstream of the dam. The wave is excited by reflections off canyon walls and accounts for a 30% fluctuation in discharge. The second is due to a mode-two standing wave in the reservoir. This wave is caused by the reflection of dam-break rarefaction waves off reservoir walls, and accounts for only 2-3% fluctuation in discharge. Both oscillations are therefore shown to be physically based and should not beinterpreted as spurious oscillations common to many numerical wave models

Unstructured Grid Finite-Volume Algorithm for Shallow-Water Flow and Scalar Transport with Wetting and Drying

A high-resolution, unstructured grid, finite-volume algorithm is developed for unsteady, two-dimensional, shallow-water flow and scalar transport over arbitrary topography with wetting and drying. The algorithm uses a grid of triangular cells to facilitate grid generation and localized refinement when modeling natural waterways. The algorithm uses Roe’s approximate Riemann solver to compute fluxes, a multidimensional limiter for second-order spatial accuracy, and predictor-corrector time stepping for second-order temporal accuracy. The novel aspect of the algorithm is a robust and efficient procedure to consistently track fluid volume and the free surface elevation in partially submerged cells. This leads to perfect conservation of both fluid and dissolved mass, preservation of stationarity, and near elimination of artificial concentration and dilution of scalars at stationary or moving wet/dry interfaces. Multi-dimensional slope limiters, variable reconstruction, and flux evaluation schemes are optimized in the algorithm on the basis of accuracy per computational effort

Unstructured Grid Finite Volume Algorithm for Shallow-Water Flow and Transport with Wetting and Drying

Two high-resolution, unstructured grid, finite volume algorithms are developed for unsteady, two-dimensional, shallow-water flow and scalar transport over arbitrary topography with wetting and drying. The algorithms either use grids of triangular cells (which facilitates grid generation and localized refinement when modeling natural waterways) or quadrilateral cells. The algorithms use Roe's approximate Riemann solver to compute fluxes, a multi-dimensional limiter for second-order spatial accuracy, and predictor-corrector time stepping for second-order temporal accuracy. A robust and novel procedure is introduced to consistently track fluid volume and the free surface elevation in partially submerged cells, which leads to excellent flow and scalar transport predictions in the presence of a stationary or moving wet/dry interface. The two algorithms are found to perfectly conserve both fluid and dissolved mass, preserve stationarity, and nearly eliminate artificial concentration and dilution of scalars at wet/dry interfaces

Closure to: Divergence Form for Bed Slope Source Term (DFB) in Shallow Water Equations

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Wetting and Drying of Triangular Computational Cells

A robust and novel procedure is introduced into a fixed-grid finite volume shallow-water model to consistently track fluid volume and the free surface elevation in partially submerged triangular cells, which leads to excellent flow and scalar transport predictions in the presence of a stationary or moving wet/dry interface. Using this procedure, a Roe-type finite volume scheme is found to perfectly conserve both fluid and dissolved mass, preserve stationarity, and nearly eliminate artificial concentration and dilution of scalars at wet/dry interfaces

A balanced treatment of secondary currents, turbulence and dispersion in a depth-integrated hydrodynamic and bed deformation model for channel bends

This work deals with the formulation and numerical implementation of a two-dimensional mathematical and numerical model describing open channel hydrodynamics, sediment and/or scalar transport and riverbed evolution in curved channels. It is shown that a well balanced 2D model can predict flow features, sediment and scalar concentration, and bed elevation with an accuracy that is suitable for practical river engineering. The term “balanced” implies that important physical processes are modeled with a similar degree of complexity and exhaustiveness. The starting point of the model formulation is the assumption of self-similarity of vertical velocity profiles (horizontal velocities in the longitudinal and transverse directions), that are scaled by shear velocity and streamline curvature, both resolved by the model. The former is scaled by a bed-resistance coefficient that must be estimated or calibrated – as usual – on a application-specific basis, and the latter is computed by a new, grid-based but grid orientation independent, scheme that acts on the discrete solution. All processes, including bottom shear, momentum dispersion, scalar dispersion, turbulent diffusion, bed load, and suspended load, are modeled using physically based, averaged values of empirical or semi-empirical constants, and consistently with the assumed velocity profiles (and bed-generated turbulence). Bed deformation modeling can be implemented with either an equilibrium or non-equilibrium formulation of the Exner equation, depending on the adaptation length scale, which must be taken under consideration if significantly larger than the length scale of the spatial discretization. The governing equations are solved by high-resolution, unstructured-grid Godunov method, which is elsewhere tested and shown to be reliable and second-order accurate. Application of the model to laboratory test cases, using standard parameter values and previously reported bed-resistance coefficients, gives results comparable to many 2D and 3D models previously applied to the same cases, most part of which benefit from case-specific parameter tuning. There are obviously intrinsic limits to the descriptive ability of 2D models in river modeling, but the results of this study point to the utility and cost-effectiveness of a well-designed 2D model

Evoluzione dell’alveo del Po conseguente a lavori per il miglioramento della navigabilità: simulazioni numeriche

Viene presentato un modello di simulazione numerica dell’evoluzione d’alveo in fiumi meandriformi e la sua applicazione nella valutazione degli effetti di alcune opere di regolazione sul fiume Po. Il modello, 2D, si basa sulle equazioni di De Saint Venant, nelle quali al valore della velocità mediato sulla profondità si somma un termine, supposto ad andamento lineare, corrispondente alla distribuzione sulla verticale della velocità legata alle circolazioni secondarie che si sviluppano in curva. L’evoluzione del letto è determinata dal trasporto dei sedimenti, al fondo ed in sospensione, attraverso l’equazione di continuità della fase solida. Lo schema numerico usato è ai volumi finiti, esplicito, di tipo Godunov, accurato al secondo ordine nello spazio e nel tempo. Le simulazioni riguardano gli effetti generati da alcune opere di regolazione previste sul fiume Po nei pressi di Ostiglia sull’evoluzione della topografia del fondo e sulla stabilità del tracciato di navigazione. La finalità della ricerca è l’elaborazione di uno strumento capace di valutare gli effetti, sulla scala spaziale della larghezza, di opere che interferiscono con un corso d’acqua, sia in termini di idrodinamica che di stabilità geomorfologica dell’alveo, fornendo indicazioni utili alla progettazione