On the accuracy of finite-difference solutions for nonlinear water waves
On the accuracy of finite-difference solutions for nonlinear water waves
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DOI：
10.1007/s10665-006-9108-4
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发表时间：
2007-06
影响因子：
1.3
通讯作者：
H. Bingham;Haiwen Zhang
中科院分区：
文献类型：
--
作者：
H. Bingham;Haiwen Zhang
本文考虑了非线性水波精确势流问题的低阶和高阶有限差分离散的相对精度和效率。该方法是Li和Fleming(Coastal Eng 30：235-238,1997)方法的推广，允许任意阶有限差分格式和可变网格间距。时间积分采用四阶龙格-库塔格式。对该方法的线性精度、稳定性和收敛特性进行了分析，发现在均匀网格上，具有拉伸垂直网格的高阶格式优于二阶格式。与高精度周期解的比较表明，这些结论适用于非线性问题，高阶格式的优势随着非线性的增加和精度容差的增加而增强。建议在垂直格式和四阶格式中采用非均匀网格间距的组合，以达到工程上的最佳效果。
This paper considers the relative accuracy and efficiency of low- and high-order finite-difference discretisations of the exact potential-flow problem for nonlinear water waves. The method developed is an extension of that employed by Li and Fleming (Coastal Engng 30: 235–238, 1997) to allow arbitrary-order finite-difference schemes and a variable grid spacing. Time-integration is performed using a fourth-order Runge–Kutta scheme. The linear accuracy, stability and convergence properties of the method are analysed and high-order schemes with a stretched vertical grid are found to be advantageous relative to second-order schemes on an even grid. Comparison with highly accurate periodic solutions shows that these conclusions carry over to nonlinear problems and that the advantages of high-order schemes improve with both increasing nonlinearity and increasing accuracy tolerance. The combination of non-uniform grid spacing in the vertical and fourth-order schemes is suggested as optimal for engineering purposes.