Numerical simulation of runoff from extreme rainfall events in a mountain water catchment

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

Estudio geológico del sector de Puerto-López (Granada, zona subbética)

La geología del sector de Puerto-López, situado al NW de Granada, ofrece varios aspectos de interés. Hemos podido establecer la sucesión  estratigráfica, con términos comprendidos entre el Lías y el Senonense, con dataciones muchas veces precisas gracias a las faunas de Ammonites. La estructura es relativamente violenta y son de destacar los pliegues vergentes al S y las fallas inversas del mismo sentido. Por la naturaleza de la serie y por su posición en el Subbético medio, se ha llegado a la correlación de la serie establecida con otras series subbéticas, de la transversal de Granada

Estudio geológico del sector de Puerto-López (Granada, zona subbética)

La geología del sector de Puerto-López, situado al NW de Granada, ofrece varios aspectos de interés. Hemos podido establecer la sucesión  estratigráfica, con términos comprendidos entre el Lías y el Senonense, con dataciones muchas veces precisas gracias a las faunas de Ammonites. La estructura es relativamente violenta y son de destacar los pliegues vergentes al S y las fallas inversas del mismo sentido. Por la naturaleza de la serie y por su posición en el Subbético medio, se ha llegado a la correlación de la serie establecida con otras series subbéticas, de la transversal de Granada

Formulation of exactly balanced solvers for blood flow in elastic vessels and their application to collapsed states

In this work, numerical solvers based on extensions of the Roe and HLL schemes are adapted to deal with test cases involving extreme collapsing conditions in elastic vessels. To achieve this goal, the system is transformed to provide a conservation–law form, allowing to define Rankine–Hugoniot conditions. The approximate solvers allow to describe the inner states of the solution. Therefore, source term fixes can be used to prevent unphysical values of vessel area and, at the same time, the eigenvalues of the system control stability. Numerical solvers of different order are tested using a wide variety of Riemann problems, including extreme vessel collapse and blockage. In all cases, the robustness of the approximate solvers presented here is checked using first and third order methods in time and space, using the WENO reconstruction scheme in combination with the TVDRK3 method

Coupled method for the numerical simulation of 1D shallow water and Exner transport equations in channels with variable cross-section

This work is focused on the a numerical finite volume scheme for the resulting coupled shallow water-Exner system in 1D applications with arbitrary geometry. The mathematical expression modeling the the hydrodynamic and morphodynamic components of the physical phenomenon are treated to deal with cross-section shape variations and empirical solid discharge estimations. The resulting coupled system of equations can be rewritten as a nonconservative hyperbolic system with three moving waves and one stationary wave to account for the source terms discretization. But, even for the simplest solid transport models as the Grass law, to find a linearized Jacobian matrix of the system can be a challenge if one considers arbitrary shape channels. Moreover, the bottom channel slope variations depends on the erosion-deposition mechanism considered to update the channel cross-section profile. In this paper a numerical finite volume scheme is proposed, based on an augmented Roe solver (first order accurate in time and space) and dealing with solid transport flux variations caused by the channel geometry changes. Channel crosssection variations lead to the appearance of a new solid flux source term which should be discretized properly. Comparison of the numerical results for several analytical and experimental cases demonstrate the effectiveness, exact wellbalanceness and accuracy of the scheme

A large time step 1D upwind explicit scheme (CFL > 1): Application to shallow water equations

It is possible to relax the Courant–Friedrichs–Lewy condition over the time step when using explicit schemes. This method, proposed by Leveque, provides accurate and correct solutions of non-sonic shocks. Rarefactions need some adjustments which are explored in the present work with scalar equation and systems of equations. The non-conservative terms that appear in systems of conservation laws introduce an extra difficulty in practical application. The way to deal with source terms is incorporated into the proposed procedure. The boundary treatment is analysed and a reflection wave technique is considered. In presence of strong discontinuities or important source terms, a strategy is proposed to control the stability of the method allowing the largest time step possible. The performance of the above scheme is evaluated to solve the homogeneous shallow water equations and the shallow water equations with sourc

Validación experimental de un modelo computacional unidimensional para el cálculo de ondas de avenida

[ES] El objetivo principal de este artículo es validar un modelo numérico para el cálculo computacional de ondas de avenida en cauces fluviales, en aproximación unidimensional. Se presenta la comparación de resultados frente a los datos experimentales de un ensayo de laboratorio, y la comparación con un caso test propuesto y resuelto por otros autores.Villanueva, I.; García, P.; Zorraquino, V. (1999). Validación experimental de un modelo computacional unidimensional para el cálculo de ondas de avenida. Ingeniería del Agua. 6(1):55-62. https://doi.org/10.4995/ia.1999.2777SWORD556261Abbott M. B. (1992). Computational Hydraulics. Ashgate, Aldershot, U.K.Bellos C.V., Soulis J.V., Sakkas J.G. (1992). Experimental investigation of two-dimensional dam-break induced flows. Journal of Hydraulic Research, Vol. 30, Num. 1Chow V. T. (1959), Open channel Hydraulics, McGraw-Hill Book Co. IncCunge J.A., Holly F.M., Verwey A. (1980). Practical aspects of computational river hydraulics, Pitman, London, U.K.Fread D.L. (1985). Channel routing. Hidrological forecasting. M. G. Anderson and T.P. Burt, eds., Jhon Wiley and Sons Ltd. N.Y.García-Navarro P. (1989). Estudio de la propagación de ondas en cursos fluviales, tesis doctoral, U. de Zaragoza.García-Navarro P., Alcrudo F. (1995). Simulación de flujo transitorio en cauces naturales. Ingeniería del Agua. Vol. 2, Num. 1.García-Navarro P., Alcrudo F., Savirón J.M. (1992). 1-D Open-channel flow simulation using TVD-Mac-Cormack scheme. Journal of Hydraulic Engeenering. Vol. 118, Num. 10.Jin M., Fread D.L. (1997). Dynamic flood routing with explicit and implicit numerical solution schemes. Journal of Hydraulic Engeenering. Vol. 123, Num. 3.Mahmood K., Yevjevich, V. (1975). Unsteady flow in open channels, Water Resources Publications, US

Diffusion–dispersion numerical discretization for solute transport in 2D transient shallow flows

The 2D solute transport equation can be incorporated into the 2D shallow water equations in order to solve both flow and solute interactions in a coupled system of equations. In order to solve this system, an explicit finite volume scheme based on Roe’s linearization is proposed. Moreover, it is feasible to decouple the solute transport equation from the hydrodynamic system in a conservative way. In this case, the advection part is solved in essence defining a numerical flux, allowing the use of higher order numerical schemes. However, the discretization of the diffusion–dispersion terms have to be carefully analysed. In particular, time-step restrictions linked to the nature of the solute equation itself as well as the numerical diffusion associated to the numerical scheme used are question of interest in this work. These improvements are tested in an analytical case as well as in a laboratory test case with a passive solute (fluorescein) released from a reservoir. Experimental measurements are compared against the numerical results obtained with the proposed model and a sensitivity analysis is carried out, confirming an agreement with the longitudinal coefficients and an underestimation of the transversal ones, respectively

A 1D numerical model for the simulation of unsteady and highly erosive flows in rivers

This work is focused on a numerical finite volume scheme for the coupled shallow water-Exner system in 1D applications with arbitrary geometry. The mathematical expressions modeling the hydrodynamic and morphodynamic components of the physical phenomenon are treated to deal with cross-section shape variations and empirical solid discharge estimations. The resulting coupled equations can be rewritten as a non-conservative hyperbolic system with three moving waves and one stationary wave to account for the source terms discretization. Moreover, the wave celerities for the coupled morpho-hydrodyamical system depend on the erosion-deposition mechanism selected to update the channel cross-section profile. This influence is incorporated into the system solution by means of a new parameter related to the channel bottom variation celerity. Special interest is put to show that, even for the simplest solid transport models as the Grass law, to find a linearized Jacobian matrix of the system can be a challenge in presence of arbitrary shape channels. In this paper a numerical finite volume scheme is proposed, based on an augmented Roe solver, first order accurate in time and space, dealing with solid transport flux variations caused by the channel geometry changes. Channel cross-section variations lead to the appearance of a new solid flux source term which should be discretized properly. The stability region is controlled by wave celerities together with a proper reconstruction of the approximate local Riemann problem solution, enforcing positive values for the intermediate states of the conserved variables. Comparison of the numerical results for several analytical and experimental cases demonstrates the effectiveness, exact well-balancedness and accuracy of the scheme

Use of internal boundary conditions for levees representation: application to river flood management

River floods can be simulated with the 2D shallow water system of equations using finite volume methods, where the terrain is discretized in cells that form the computational mesh. Usually a proper treatment of wet/dry fronts is required. River levees can be modelled as part of the topography by means of sufficiently small cells of higher elevation than the rest of the bed level in locally refined meshes. This procedure is associated with a large computational time since the time step depends directly on the cell size. The alternative proposed in this work includes the levees as internal boundary conditions in the 2D numerical scheme. In particular, levees have been defined by a weir law that, depending on the relative values of water surface levels on both sides, can formulate the discharge for different situations (i.e. free flow and submerged flow). In addition, having identified numerical difficulties in cases of low discharge under free flow conditions, a novel procedure to avoid oscillations has been developed and called volume transport method. The validation and comparison between methods has been carried out with benchmark test cases and, in addition, with a real flood event in the Ebro River (Spain)