任意水深变化Boussinesq型方程非线性波数值计算

首先从一个含有耗散项的高阶非线性和频散性波浪理论模型出发，建立了适用于任意底坡变化，相对水深h／Lo≤1的非线性波数学模型。应用全隐式交错网格和二阶精度中心差分法。得到离散方程组。进一步对其一阶导数项进行修正，达到与方程高阶项同量阶精度。精度检验表明本文计算结果与理论解和物理模型结果符合良好。

Numerical calculation of nonlinear wave using Boussinesq equation in water of arbitrarily varying depths

Based on a high order nonlinear and dispersive wave mode l with dissipative terms, a nonlinear nu merical model is developed. The control equations are discretized by using Alte rnating Direction Implicity Algorithm an d second order centering difference algo rithm. In order to improve the accuracy, the one-order differential terms in the equations are corrected to reach the sa me accuracy as high-order terms. The acc uracy tests show that the results of the numerical model are well consistent wit h those of the analytical solutions and physical models.