Adv. Appl. Math. Mech., 15 (2023), pp. 1515-1539.
Published online: 2023-10
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In this article, we develop a new well-balanced finite volume central weighted essentially non-oscillatory (CWENO) scheme for one- and two-dimensional shallow water equations over uneven bottom. The well-balanced property is of paramount importance in practical applications, where many studied phenomena can be regarded as small perturbations to the steady state. To achieve the well-balanced property, we construct numerical fluxes by means of a decomposition algorithm based on a novel equilibrium preserving reconstruction procedure and we avoid applying the traditional hydrostatic reconstruction technique accordingly. This decomposition algorithm also helps us realize a simple source term discretization. Both rigorous theoretical analysis and extensive numerical examples all verify that the proposed scheme maintains the well-balanced property exactly. Furthermore, extensive numerical results strongly suggest that the resulting scheme can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions at the same time.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0131}, url = {http://global-sci.org/intro/article_detail/aamm/22050.html} }In this article, we develop a new well-balanced finite volume central weighted essentially non-oscillatory (CWENO) scheme for one- and two-dimensional shallow water equations over uneven bottom. The well-balanced property is of paramount importance in practical applications, where many studied phenomena can be regarded as small perturbations to the steady state. To achieve the well-balanced property, we construct numerical fluxes by means of a decomposition algorithm based on a novel equilibrium preserving reconstruction procedure and we avoid applying the traditional hydrostatic reconstruction technique accordingly. This decomposition algorithm also helps us realize a simple source term discretization. Both rigorous theoretical analysis and extensive numerical examples all verify that the proposed scheme maintains the well-balanced property exactly. Furthermore, extensive numerical results strongly suggest that the resulting scheme can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions at the same time.