研究了一类含弱非线性的改进型Boussinesq水波方程，在非交错网格下，利用有限差分法建立了混合四阶Adams-Bashforth-Moulton的预报校正格式的波浪数值模型。在数值模型中，关于空间一阶导数差分格式采用四阶精度、二阶导数差分格式采用二阶精度。针对波浪的一维、二维传播变形问题进行了数值计算，并通过与相关实验结果对比分析考察了该数值模型的适用性。

Based on the extended Boussinesq equation with weak nonlinearity, 2-D numerical model was established in nonstaggered grids by the finite difference method. The nonstaggered grids were used with the first-order spatial derivatives being discretized by the fourth-order and the second-order terms discertized by the second-order. For the time derivatives, a composite fourth-order accurate Adams-Bashforth Moulton scheme was used. Numerical simulation was done upon one-dimension and two-dimension wave propagations problem, and through the comparisons of numerical results with the related experimental data, the application of the extended Boussinesq equations were investigated.

刘忠波（1976－），男，山东临沭县人，博士，主要从事波浪理论和数值研究