立面二维波浪变形的数值模拟

【作者】 滕爱国；

【导师】 邱大洪； 沈永明；

【作者基本信息】 大连理工大学 ， 港口、海岸及近海工程， 2000， 硕士

【摘要】 本文针对立面二维紊动波浪场的特点——二维、紊动性、具有自由表面，建立了求解不规则地形情况下立面二维带自由表面紊动波浪场的数学模型，该模型的特点是： 第一．从完整的N—S方程出发，采用张长高教授修正的k—ε模型来封闭雷诺方程，作为紊动波浪场的控制方程。该模型在离散动量方程的对流项时，计算内点采用三阶迎风格式，在边界点处应用一阶迎风格式和二阶中心格式组合的偏心差分格式。在计算程式上，采用了性能较好的压力迭代方法。 第二．采用VOF方法跟踪自由表面，在差分方法上应用施主与受主单元模型求解流体体积函数F的输运方程，计算表明该方法能够很好的模拟出各种地形下波浪表面的形状。 第三．在差分离散方法的基础上，采用通度概念，对不规则边界进行处理。在近壁区范围内，采用壁函数技术解决壁面效应问题。 依据本文所建立的数学模型，对深水平底情况下的线性波的传播、潜堤上椭余波的变形和波浪在斜坡上的变形进行了数值模拟，分别与理论值和实测资料进行了比较，吻合良好。更多还原

【Abstract】 Based on the Naviertokes equation, a numerical model to predict vertical two-dimensional turbulent wave field has been developed in the present thesis. The key technology introduced and implemented is as following: 1. A modified k?t turbulence model was derived to deal with the closure problem by using the Renolds-Stress formula proposed by Zhang Changgao. The finitefference method is used to approximate the predicting equations, in which the convective term of inner points is discretized by using third order upwind difference scheme and a linear combination of one order upwind difference scheme and centered difference scheme is applied to discretize the convective term of boundary points. 2. The modified VOF method is adopted to deal with free surface. The governing equation for the Volume of Fluid is solved by Donorcceptor method. The calculation results show that it can predict the surface transformation of wave over the irregular landform very well. 3. A partial cell parameter is introduced to treat irregular boundary, which is based on the finite ifference method. For the grid nodes immediately adjacent to the wall boundary, the viscosity sublayer is treated by wall function approximation. The transmittal of linear waves over flat bottom, the transformation of Cnoidal waves over a submerged bar and the transformation of regular waves over a slope are simulated by the model. The results are compared with theoretical and experimental values respectively. It shows that the calculation results agree reasonably with the theoretical and experimental values.更多还原