应用非线性色散关系数值求解双曲型缓坡方程

摘要

Based on the original hyperbolic mild slope equation,a nonlineardispersion relation is introduced to take the nonlinear effect of waves into account.The improvement of the numerical scheme elevates the calculation speed and efficiency in solving the hyperbolic mild slope equation.The nonlinear dispersion relation and the improved numerical scheme are applied to the calculation of water waves over an elliptic shoal.The result is satisfactory.%在经典双曲型缓坡方程的基础上，通过引入非线性色散关系，使其能够有效地考虑波浪的非线性影响，数值格式的改进使方程的数值求解快速高效.将非线性色散关系和改进后的数值格式用于经典的椭圆形浅滩上的波浪变形计算，取得了比较满意的结果.