A well-balanced conservative high-order alternative finite difference WENO (A-WENO) method for the shallow water equations

IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Advances in Water Resources Pub Date : 2025-02-01 DOI:10.1016/j.advwatres.2025.104898
Ziyao Xu , Chi-Wang Shu
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Abstract

In this paper, we develop a well-balanced, conservative, high-order finite difference weighted essentially non-oscillatory (WENO) method for the shallow water equations. Our approach exactly preserves the moving-water equilibria of the shallow water equations with non-flat bottom topography. The proposed method consists of two key components. First, we reformulate the source term into a flux-gradient form and discretize it using the same numerical flux as that of the true flux gradient to achieve the well-balanced property. Second, we interpolate the equilibrium variables, which remain constant at steady state, to construct the numerical flux. To achieve high-order accuracy and avoid truncation errors when obtaining equilibrium variables, we build our scheme within the alternative finite difference WENO (A-WENO) framework, which operates on point values rather than cell averages. Special attention is given to ensure that the conservation property is not compromised when designing well-balanced discretizations for the source term. We carefully analyze potential causes of non-conservative schemes in the discretization and explain why the discretized source term in our method is both conservative and simple. Extensive numerical tests are presented to validate the performance of the proposed method.
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来源期刊
Advances in Water Resources
Advances in Water Resources 环境科学-水资源
CiteScore
9.40
自引率
6.40%
发文量
171
审稿时长
36 days
期刊介绍: Advances in Water Resources provides a forum for the presentation of fundamental scientific advances in the understanding of water resources systems. The scope of Advances in Water Resources includes any combination of theoretical, computational, and experimental approaches used to advance fundamental understanding of surface or subsurface water resources systems or the interaction of these systems with the atmosphere, geosphere, biosphere, and human societies. Manuscripts involving case studies that do not attempt to reach broader conclusions, research on engineering design, applied hydraulics, or water quality and treatment, as well as applications of existing knowledge that do not advance fundamental understanding of hydrological processes, are not appropriate for Advances in Water Resources. Examples of appropriate topical areas that will be considered include the following: • Surface and subsurface hydrology • Hydrometeorology • Environmental fluid dynamics • Ecohydrology and ecohydrodynamics • Multiphase transport phenomena in porous media • Fluid flow and species transport and reaction processes
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