The surface gradient method for the treatment of source terms in the shallow-water equations
The surface gradient method for the treatment of source terms in the shallow-water equations
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DOI：
10.1006/jcph.2000.6670
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发表时间：
2001-03
影响因子：
4.1
通讯作者：
J. Zhou;D. Causon;C. Mingham;D. Ingram
中科院分区：
文献类型：
--
作者：
J. Zhou;D. Causon;C. Mingham;D. Ingram
本文提出了一种新的求解浅水方程的Godunov型方法。与传统的基于保守变量的数据重建方法不同，本文选择水面线作为数据重建的基础。这提供了在单元界面处的保守变量的精确值，使得可以用黎曼解算器精确地计算通量。主要优点是：（1）对源项采用简单的中心离散;（2）对于齐次项，该格式并不比传统的方法复杂;（3）可以精确地预测水面高程的小扰动;（4）该方法一般适用于定常和非定常浅水问题。通过定常和非定常流动问题验证了格式的精度。数值预测和解析解之间已经取得了很好的一致性。结果表明，新方案是准确的，简单，有效的，和强大的。
A novel scheme has been developed for data reconstruction within a Godunov-type method for solving the shallow-water equations with source terms. In contrast to conventional data reconstruction methods based on conservative variables, the water surface level is chosen as the basis for data reconstruction. This provides accurate values of the conservative variables at cell interfaces so that the fluxes can be accurately calculated with a Riemann solver. The main advantages are: (1) a simple centered discretization is used for the source terms; (2) the scheme is no more complicated than the conventional method for the homogeneous terms; (3) small perturbations in the water surface elevation can be accurately predicted; and (4) the method is generally suitable for both steady and unsteady shallow-water problems. The accuracy of the scheme has been verified by recourse to both steady and unsteady flow problems. Excellent agreement has been obtained between the numerical predictions and analytical solutions. The results indicate that the new scheme is accurate, simple, efficient, and robust.