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中文摘要：
针对海洋环境的波流混合作用问题，本文利用时域高阶边界元方法建立模拟波流混合作用的完全非线性数值水槽模型，其中自由水面满足完全非线性自由水面条件．采用混合欧拉一拉格朗日方法追踪流体瞬时水面，运用四阶Runga—Kutta方法更新下一时间步的波面和速度势．为了避免由于网格运动变形而引起数值不稳定问题，在每一时间步内对网格进行重新划分，通过采用二次形状函数计算新网格的物理量和几何量．与原Boussinesq模型结果对比吻合很好，验证了本模型的准确性．进一步研究了水流作用下波面的变化及水流对波浪非线性的影响，逆流使波浪非线性进一步增强，而顺流使波浪非线性减弱．
英文摘要：
Concerning the problem of wave-current interactions in an ocean environment, a fully nonlinear numerical flume model simulating wave-current interactions was developed based on the time-domain higher-order boundary element method. The fully nonlinear free water surface boundaries were satisfied. The mixed Eulerian-Lagrangian scheme was adopted to track the transient free surface with the fourth-order Runga-Kutta method for refreshing wave profile and velocity potential at the next time step. The meshes were divided again at each time step to avoid numerical instabilities caused by mesh motions. The physical and geometrical variables at the new positions were computed by using the quadratical shape function in the remeshing processes. The present numerical model was verified by comparison with published Boussinesq model results. The variations of wave profile under water flow action and the influence caused by water flow to wave nonlinearity were further studied. The findings show that wave nonlinearity is amplified and weakened by counter and fair currents, respectively.
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