【摘要】 推导了含量阶为O(ε1/2)的瞬变非均匀流的Boussinesq水波方程,讨论了该量阶水流对流场速度和压力分布的影响,采用了Crank-Nicolson格式的预估-校正有限差分法对该方程进行了数值求解.把数值结果与无水流情况的实验结果进行了对比,验证了该方程和数值计算方法的有效性,与经典的Boussinesq方程和含量阶为O(1)的瞬变非均匀流的Boussinesq水波方程的计算结果进行了比较,考察了该方程的适用范围.更多还原

【Abstract】 The Boussinesq equations with the transient and non-uniform current of O(ε^1/2)are derived. The effects of currents on the distributions of velocities and pressure are discussed. The prediction-correction method of finite difference scheme is employed to solve the equations numerically. The numerical results are compared with the experimental data for the case of currents being equal to 0 and the agreements are good, which demonstrates the accuracy of the equations and the efficiency of the numerical methods. The numerical results are also compared with the numerical results of the classic Boussinesq equations and the Boussinesq equations with strong currents of O（1）, and the application range of the equations is also investigated.更多还原