Conservative numerical boundary conditions

4 Pags., 2 Figs. Trabajo originalmente presentado en International Workshop on Numerical Modelling of Hydrodynamic for Water Resources (Zaragoza. 2007)A recent technique for the numerical boundary conditions in 1D shallow water flow models is able to preserve the good properties of a conservative scheme used for the interior points. The implementation in a conservative scheme is shown in a test cases with exact solution and applied to the simulation of a real river flood wave leading to very satisfactory results.Peer reviewe

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 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

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

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

Influence of change of regulation on the goals achieved in futsal

Este artículo analiza la hipótesis de que los cambios introducidos en la normativa del fútbol sala modifican su lógica interna disminuyendo los goles totales y modificando su forma de ejecución. El objetivo de estudio es analizar los goles y manera de realizarlos en una temporada anterior y posterior al cambio de reglamentación para establecer cuantitativamente cómo el cambio de reglas del 2.006 afecta al juego. Se analizaron 3.126 goles en 442 partidos, 1.771 goles en 232 partidos en la temporada 2.002-2.003 y 1.355 goles en 210 partidos en la temporada 2.013-2.014. El método utilizado fue la metodología observacional, se utilizó el programa Lince vl.2.1. Los resultados muestran una reducción estadísticamente significativa en el número de goles de una temporada a otra. En la temporada 2.002-2.003 se lograron 1.927 goles con un promedio por equipo de 120,38 ± 28,58, y en la temporada 2.013-2.014 1.355 goles con un promedio de 90,40 ± 27,72This article analyses the hypothesis that the changes introduced in the regulation of futsal modify the inner logic of the game, what turns into a reduction of total goals and a significant variation in the form of execution. Therefore, it is set out as aim of study to analyze the goals and the way to achieve them in a previous season and in one subsequent to the change of regulation in order to establish quantitatively how the 2006 rules change has affected the game. Totally, 3126 goals were analyzed, scored in 442 matches, distributed in 1771 goals in 232 matches in season 2002-2003 and 1355 goals in 210 matches in season 2103-2014. The method used in this study was observational methodology. For the observational process, it has been used the observational software Lince vl.2.1. It has been carried out using the IBM SPSS 19.0.0 program. The results show a statistically significant reduction in the number of goals from one season to another. In season 2002-2003, 1927 goals were achieved with an average by team of 120.38±28.58, by 1355 goals in season 2013-2014 of 90.40±27.7

An efficient GPU implementation for a faster simulation of unsteady bed-load transport

Computational tools may help engineers in the assessment of sediment transport during the decision-making processes. The main requirements are that the numerical results have to be accurate and simulation models must be fast. The present work is based on the 2D shallow water equations in combination with the 2D Exner equation. The resulting numerical model accuracy was already discussed in previous work. Regarding the speed of the computation, the Exner equation slows down the already costly 2D shallow water model as the number of variables to solve is increased and the numerical stability is more restrictive. In order to reduce the computational effort required for simulating realistic scenarios, the authors have exploited the use of Graphics Processing Units in combination with non-trivial optimization procedures. The gain in computing cost obtained with the graphic hardware is compared against single-core (sequential) and multi-core (parallel) CPU implementations in two unsteady cases