一般曲线坐标系下波浪传播的数值模拟

Numerical simulation model of wave propagation in curvilinear coordinates

在曲线坐标系下,建立了缓变水深水域波浪传播的数值模拟模型.模型适宜于复杂变化的边界形状,克服了各种代数坐标变换的局限性.在建立模型时,将原始的椭圆型缓坡方程的近似型式——依赖时间变化的抛物型方程,作为控制方程,既克服了一般抛物近似方法的缺点,又便利了方程的求解;从开边界条件、不同反射特性的固壁边界条件相统一的表达式出发,对边界条件进行处理;用ADI法数值求解控制方程.对模型的验证表明,数值解与物模实验值吻合良好,模型对于具有复杂边界的工程实际有较强的适应性.

In the curvilinear coordinates, a numerical simulation model for wave propagation in water of slowly varying topography is presented. The model is suitable to complicated boundary shapes and overcomes the limitation of other models with algorithm transformation. In the model, the time-dependent parabolic equation, deduced from the original elliptic type of mild-slope equation, is used as the governing equation. The present governing equation not only avoids the drawback to common parabolic form of mild-slope equation but also is convenient for solution. Based on the general conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phase shift, the boundary conditions for the present model are treated. The alternative direction implicit method is used to solve the governing equation. The numerical results of the present model are in agreement with those of physical models. Systematical tests show that the present model can reasonably simulate the wave transformation, such as shoaling, refraction, diffraction and reflection. So the present model is able to be used in coastal engineering with complicated boundary shapes extensively.