Balaguer Beser, Ángel Antonio
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Balaguer Beser
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Ángel Antonio
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- PublicationA well-balanced high-resolution shape-preserving central scheme to solve one-dimensional sediment transport equations(ELSEVIER SCI LTD, 2012) Capilla Romá, Maria Teresa; Balaguer Beser, Ángel Antonio; Dpto. de Matemática Aplicada; Escuela Técnica Superior de Ingeniería del Diseño; Dpto. de Ingeniería Cartográfica Geodesia y Fotogrametría; Escuela Técnica Superior de Ingeniería Geodésica, Cartográfica y Topográfica; Instituto Universitario de Seguridad Industrial, Radiofísica y Medioambiental; Grupo de Cartografía Geoambiental y Teledetección; Ministerio de Ciencia e Innovación; Universitat Politècnica de València[EN] We present a well-balanced high-resolution non-oscillatory central finite volume scheme for solving the shallow water equations with a non-flat bottom topology. Time integration is obtained following a Runge¿Kutta procedure, coupled with its natural continuous extension. We use a central scheme with a point value reconstruction algorithm based on average or flux values, which satisfies the monotonicity preserving property. We apply a special treatment for the source term spatial integration, which preserves the time and space accuracy and it results in a well-balanced scheme. Several one-dimensional test cases are used to verify the behaviour and non-oscillatory properties of our scheme.
- PublicationA high-order numerical method for sediment transport problems simulation and its comparison with laboratory experiments(John Wiley & Sons, 2021-11) Capilla Romá, Maria Teresa; Balaguer Beser, Ángel Antonio; Nácher-Rodríguez, Beatriz; Vallés Morán, Francisco José; Dpto. de Ingeniería Hidráulica y Medio Ambiente; Dpto. de Matemática Aplicada; Escuela Técnica Superior de Ingeniería del Diseño; Dpto. de Ingeniería Cartográfica Geodesia y Fotogrametría; Escuela Técnica Superior de Ingeniería Geodésica, Cartográfica y Topográfica; Instituto Universitario de Ingeniería del Agua y del Medio Ambiente; Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos; Instituto Universitario de Seguridad Industrial, Radiofísica y Medioambiental; Grupo de Cartografía Geoambiental y Teledetección; GENERALITAT VALENCIANA[EN] This article describes a high-order well-balanced central finite volume scheme for solving the coupled Exner-shallow water equations in one dimensional channels with rectangular section and variable width. Such numerical method may solve the proposed bedload sediment transport problem without the need to diagonalize the Jacobian matrix of flow. The numerical scheme uses a Runge¿Kutta method with a fourth-order continuous natural extension for time discretization. The source term approximation is designed to verify the exact conservation property. Comparison of the numerical results for two accuracy tests have proved the stability and accuracy of the scheme. The results of the laboratory tests have also been used to calibrate different expressions of the solid transport discharge in the computer code. Two experimental tests have been carried out to study the erosive phenomenon and the consequent sediment transport: one test consisting of a triangular dune, and other caused by the effect of channel contraction.
- PublicationA new reconstruction procedure in central schemes for hyperbolic conservation laws(Wiley: 12 months, 2011-07-01) Balaguer Beser, Ángel Antonio; Dpto. de Matemática Aplicada; Dpto. de Ingeniería Cartográfica Geodesia y Fotogrametría; Escuela Técnica Superior de Ingeniería Geodésica, Cartográfica y Topográfica; Grupo de Cartografía Geoambiental y Teledetección; Ministerio de Ciencia e Innovación; Universitat Politècnica de ValènciaThis paper presents a new point value reconstruction algorithm based on average values or flux values for central Runge-Kutta schemes in the resolution of hyperbolic conservation laws. This reconstruction employs a fourth-order accurate approximation of point values of the solution at the two extrema and at the mid-point of each cell. These point values are modified in order to enforce monotonicity and shape preserving properties. This correction has been applied essentially in the cells close to the maxima and minima of the solution and in these cases, it has been proven that the reconstruction is fourth-order accurate. In the cells with a maximum or minimum of the solution, a correction has also been applied to such point values with the aim of ensuring that the resulting numerical solution has a non-oscillatory behavior. Several standard one- and two-dimensional test cases are used to verify high-order accuracy, non-oscillatory behavior and high-resolution properties for smooth and discontinuous solutions, and also in their componentwise extension to the Euler gas dynamics equations. © 2011 John Wiley & Sons, Ltd.
- PublicationA new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes(Elsevier, 2013-11) Capilla Romá, Maria Teresa; Balaguer Beser, Ángel Antonio; Dpto. de Matemática Aplicada; Escuela Técnica Superior de Ingeniería del Diseño; Dpto. de Ingeniería Cartográfica Geodesia y Fotogrametría; Escuela Técnica Superior de Ingeniería Geodésica, Cartográfica y Topográfica; Instituto Universitario de Seguridad Industrial, Radiofísica y Medioambiental; Grupo de Cartografía Geoambiental y Teledetección; Ministerio de Ciencia e Innovación; Universitat Politècnica de ValènciaThis paper is concerned with the development of high-order well-balanced central schemes to solve the shallow water equations in two spatial dimensions. A Runge Kutta scheme is applied for time discretization. A Gaussian quadrature rule is used to evaluate time integrals and a three-degree polynomial which calculates point-values or flux values. A new procedure has been defined to evaluate the flux integrals and to approach the 2D source term integrals in order to verify the exact C-property, using the water surface elevation instead of the water depth as a variable. Numerical experiments have confirmed the high-resolution properties of our numerical scheme in 2D test problems.