A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes

• Autores: M. T. Capilla, A. Balaguer Beser
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 252, Nº 1, 2013, págs. 62-74
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.01.014
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• Resumen

  • This 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 with a natural continuous extension is applied for time discretization. A Gaussian quadrature rule is used to evaluate time integrals and a three-degree polynomial which calculates point-values from cell averages or flux values by avoiding the increase in the number of solution extrema at the interior of each cell is used as a reconstruction operator. That polynomial also guarantees that the number of extrema does not exceed the initial number of extrema and thus it avoids spurious numerical oscillations in the computed solution.

    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. The well-balanced property of the resulting scheme has also been investigated.