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A flux-splitting solver for shallow water equations with source terms. (English) Zbl 1033.76033
Summary: This paper introduces a stable flux-splitting solver for one-dimensional shallow water equations. This solver is specifically designed to satisfy a strengthened consistency condition for stationary solutions that ensures the stability and accuracy of the scheme. It applies to channels with variable depth and width, including terms modelling friction at bottom and vertical walls. Some numerical tests by comparison to both analytical solutions and experimental measurements show the good performances of the scheme.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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[1] Aves, Runge-Kutta solutions of a hyperbolic conservation law with source term, SIAM Journal on Scientific Computing 22 (1) pp 20– (2000) · Zbl 0966.65063
[2] Burguete, Efficient construction of high-resolution TVD conservative schemes for equations with source terms. Application to shallow water flows, International Journal for Numerical Methods in Fluids 37 pp 209– (2001) · Zbl 1003.76059
[3] LeVeque, A study of numerical methods for hyperbolic conservation laws with stiff source terms, Journal of Computational Physics 86 pp 187– (1990) · Zbl 0682.76053
[4] Zhou, The surface gradiente method for the treatment of source terms in the shallow-water equations, Journal of Computational Physics 168 pp 1– (2001) · Zbl 1074.86500
[5] Bermúdez, Upwind methods for hyperbolic conservation laws with source terms, Computers Fluids 23 (8) pp 1049– (1994) · Zbl 0816.76052
[6] Vázquez Cendon ME Estudio de esquemas descentrados para su aplicacion a las leyes de conservación hiperbólicas con términos fuente 1994
[7] Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics (1997) · Zbl 0888.76001
[8] Godlewski, Mathematiques et Applications (1991)
[9] Vijayasundaram G Resolution Numérique des équations d’Euler pour des écoulements transsoniques avec un schéma de Godunov en éléments finis 1982
[10] Godlewski, Numerical Approximation of Hyperbolic Systems of Conservation Laws (1996) · Zbl 0860.65075
[11] Bermudez, Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes, Computer Methods in Applied Mechanics and Engineering 155 pp 49– (1998) · Zbl 0961.76047
[12] Brufau P Simulación bidimensional de flujos hidrodinámicos transitorios en gemotrŕas irregulares 2000
[13] Maria Elena Vázquez Cendón, Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry, Journal of Computational Physics 148 pp 497– (1999) · Zbl 0931.76055
[14] Chacón, Modelling of compressible flows with highly oscillating initial data by homogenization, Applied Numerical Mathematics 26 pp 435– (1998) · Zbl 0936.76070
[15] Alcrudo, A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations, International Journal for Numerical Methods in Fluids 16 pp 489– (1993) · Zbl 0766.76067
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