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

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)

2D numerical simulation of unsteady flows for large scale floods prediction in real time

The challenge of finding a compromise between computational time and level of accuracy and robustness has traditionally expanded the use simplified models rather than full two-dimensional (2D) models for flood simulation. This work presents a GPU accelerated 2D shallow water model for the simulation of flood events in real time. In particular, an explicit first-order finite volume scheme is detailed to control the numerical instabilities that are likely to appear when used in complex topography. The model is first validated with the benchmark test case of the Toce River (Italy) and numerical fixes are demonstrated to be necessary. The model is next applied to reproduce real events in a reach of the Ebro River (Spain) in order to compare simulation results with field data. The second case deals with a large domain (744 km2) and long flood duration (up to 20 days) allowing an analysis of the performance and speed-up achieved by different GPU devices. The high values of fit between observed and simulated results as well as the computational times achieved are encouraging to propose the use of the model as forecasting system

Pseudoartrosis de escafoides carpiano tratadas mediante la técnica de Matti-Russe: estudio retrospectivo de 36 casos

Presentamos un estudio retrospectivo de una serie de 36 pacientes con pseudoartrosis de escafoides operados mediante la técnica de Matti-Russe entre 1985 y 1991. Utilizamos injerto córtico esponjoso obtenido del radio (50%), cresta ilíaca (42%) y cúbito (8%) sin diferencias en la incorporación. La tasa de curación fue mayor en las pseudoartrosis medias y distales (80%) que en las de localización proximal (54%). El 80% de los fracasos de curación en la localización media y distal eran pseudoartrosis de más de 30 meses de evolución. Los cambios degenerativos en el carpo de las pseudoartrosis no curadas fueron significativamente mayores (p< 0,001) que en las que se obtuvo la consolidación. La localización y la antiguedad de la pseudoartrosis parecen ser dos importantes factores pronósticos. La técnica de Matti-Russe presenta limitaciones en la pseudoartrosis de localización proximal y en los carpos muy degenerados.We reported a retrospective study of 36 patients with a pseudoarthrosis of the carpal scaphoid bone treated by the Matti-Russe operation from 1985 to 1991. We used radial (50%), iliac (42%) or ulnar (8%) autogenous grafts without any difference in the rate of incorporation. The rate of healing of the pseudoarthrosis was higher in mid and distal location (80%) than in proximal location (54%). In 80% of cases, healing failures in the mid and distal location occurred in old pseudoarthrosis ( >3 0 months evolution). Carpal degenerative changes were significantly higher (p < 0,01) in patients with not healed pseudoarthrosis. The location and the age of the pseudoarthrosis appear to be important prognostic factors. The Matti-Russe technique has limitations when is performed either in proximal pseudoarthrosis or in the presence of advanced radiocarpal osteoarthritis

Simulation of PID control applied to irrigation channels

Open-channel flow usually includes many hydraulic elements to help with the regulation of water supply in terms of automatic control. On the other hand, the one-dimensional Shallow Water Equations (SWE) are widely used to model and predict the flow dynamics in this kind of configurations. In this work, the unsteady SWE are used to model the water motion and they are solved using a finite volume upwind scheme able to cope with all flow regimes. Furthermore, the regulation of hydraulic structures at channels is frequently based on the PID controller. In this work, the implementation and coupling of the channel flow simulation with hydraulic elements and PID regulation is performed

Implicit 2D surface flow models performance assessment: Shallow Water Equations vs. Zero-Inertia Model

Zero-Inertia (ZI) models are used in overland flow simulation due to their mathematical simplicity, compared to more complex formulations such as Shallow Water (SW) models. The main hypothesis in ZI models is that the flow is driven by water surface and friction gradients, neglecting local accelerations. On the other hand, SW models are a complete dynamical formulation that provide more information at the cost of a higher level of complexity. In realistic problems, the usually huge number of cells required to ensure accurate spatial representation implies a large amount of computing effort and time. This is particularly true in 2D models. Hence, there is an interest in developing efficient numerical methods. In general terms, numerical schemes used to solve time dependent problems can be classified in two groups, attending to the time evaluation of the unknowns: explicit and implicit methods. Explicit schemes offer the possibility to update the solution at every cell from the known values but are restricted by numerical stability reasons. This can lead to very slow simulations in case of using fine meshes. Implicit schemes avoid this restriction at the cost of generating a system of as many equations as computational cells multiplied by the number of variables to solve. In this work, an implicit finite volume numerical scheme has been used to solve the 2D equations in both ZI and SW models. The scheme is formulated so that both quadrilateral and triangular meshes can be used. A conservative linearization is done for the flux terms, leading to a non-structured matrix for unstructured meshes thus requiring iterative methods for solving the system. A comparison between 2D SW and 2D ZI is done in terms of performance, efficiency and mesh requirements, in which both models benefit of an implicit temporal discretization in steady and nearly-steady situations

Implicit finite volume simulation of 2D shallow water flows in flexible meshes

In this work, an implicit method for solving 2D hyperbolic systems of equations is presented, focusing on the application to the 2D shallow water equations. It is based on the first order Roe''s scheme, in the framework of finite volume methods. A conservative linearization is done for the flux terms, leading to a non-structured matrix for unstructured meshes thus requiring iterative methods for solving the system. The validation is done by comparing numerical and exact solutions in both unsteady and steady cases. In order to test the applicability of the implicit scheme to real world situations, a laboratory scale tsunami simulation is carried out and compared to the experimental data. The implicit schemes have the advantage of the unconditional stability, but a quality loss in the transient solution can appear for high CFL numbers. The properties of the scheme are well suited for the simulation of unsteady shallow water flows over irregular topography using all kind of meshes

A Riemann coupled edge (RCE) 1D–2D finite volume inundation and solute transport model

A novel 1D–2D shallow water model based on the resolution of the Riemann problem at the coupled grid edges is presented in this work. Both the 1D and the 2D shallow water models are implemented in a finite volume framework using approximate Roe’s solvers that are able to deal correctly with wet/dry fronts. After an appropriate geometric link between the models, it is possible to define local Riemann problems at each coupled interface and estimate the contributions that update the cell solutions from the interfaces. The solute transport equation is also incorporated into the proposed procedure. The numerical results achieved by the 1D–2D coupled model are compared against a complete 2D model, which is considered the reference solution. The computational time is also examined