High order well-balanced finite difference WENO interpolation-based schemes for shallow water equations
High order well-balanced finite difference WENO interpolation-based schemes for shallow water equations
复制标题
基于高阶良好平衡有限差分 WENO 插值的浅水方程格式
DOI：
10.1016/j.compfluid.2020.104476
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发表时间：
2020-04-15
影响因子：
2.8
通讯作者：
Gao, Zhen
中科院分区：
文献类型：
--
作者：
Li, Peng;Don, Wai Sun;Gao, Zhen
针对浅水方程，提出了基于高阶平衡有限差分加权非振荡插值格式的广义形式的数值框架。与传统的基于WENO重构的方案相比，该方案的构建过程更加灵活。加权紧化非线性格式和有限差分备选WENO格式是两种具体的情况。为了保持精确的c -性质，有限差分格式中源项的分裂技术[j]。邢和舒，J.计算机学报。有限体积WENO格式中的重构技术[j]。Phys. 214(2006)]被采纳。在数学上证明了该方案能保持精确的c -性质，并在数值上证明了该方案在固定水面上具有良好的平衡性。此外，利用局部特征投影进一步减轻了吉布斯振荡。所提出的一般高阶WENO方案不仅能实现高阶精度，而且能捕获本质上非振荡的高梯度/激波。同时，在粗网格上可以很好地解决小扰动问题。(C) 2020 Elsevier Ltd.版权所有。
A numerical framework of the generalized form of high order well-balanced finite difference weighted essentially non-oscillatory (WENO) interpolation-based schemes is proposed for the shallow water equations. It demonstrates more flexible construction process than the classical WENO reconstruction-based schemes. The weighted compact nonlinear schemes and finite difference alternative WENO schemes are two specific cases. To maintain the exact C-property, the splitting technique for the source term in the finite difference scheme [Xing and Shu, J. Comput. Phys. 208 (2005)] and the reconstruction technique in the finite volume WENO scheme [Xing and Shu, J. Comput. Phys. 214 (2006)] are adopted. The proposed scheme can be proved mathematically to maintain the exact C-property and demonstrates numerically that it is well-balanced by construction for the stationary water surface. Moreover, the local characteristic projections are employed to further mitigate the Gibbs oscillations. The proposed generic high order WENO schemes not only achieve high order accuracy but also capture the high gradients/shock waves essentially non-oscillatory. Meanwhile, the small perturbation problems can be resolved well on a coarse grid. (C) 2020 Elsevier Ltd. All rights reserved.