☆ 4.7 Article

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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2013)

期刊

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷 252, 期 -, 页码 62-74

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ELSEVIER

DOI: 10.1016/j.cam.2013.01.014

关键词

Central scheme; Well-balanced; C-property; Non-oscillatory; Shallow water equations

类别

Mathematics, Applied

资金

Programa de Apoyo a la Investigacion y Desarrollo of the Universidad Politecnica de Valencia [PAID-06-10, PAID-05-12]
Spanish Ministry of Education and Science [CGL2009-14220-C02-01, CGL2010-19591]

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Reagent

摘要

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. (C) 2013 Elsevier B.V. All rights reserved.

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