缓坡方程的有限分析数值模式

基于时间关联的双曲型缓坡方程，采用九点有限分析法，建立近岸波浪传播变形的数值模式，在对时间关联的双曲型缓坡方程数值离散时，空间导数采用九点有限分析法，时间导数仍采用有限差分法，再采用质量集中方法得到本文的数值模式。为了验证本模式的数值精度和有效性，分别对Berkhoff(1972)实验和突堤地形进行数值模拟，结果表明本模式的模拟值与物理模型试验值、解析解及有限差分模式的模拟值吻合良好，表明本模式可以对近岸波浪传播过程中折射、绕射、反射、浅水变形、波浪破碎和弱非线性等因素的影响进行较好的预测。

Finite Analytical Numerical Mode for Mild Slope Equation

A numerical model for wave propagation is proposed, which is accomplished by nine point finite-analytic methods based on the time-dependent hyperbolic mild-slope wave equation. The space’s differential is introduced by nine point finite-analytic meth-od and the time’s differential is introduced by finite-difference method when the time-dependent hyperbolic mild-slope wave equation is dispersed, and the numerical model has been got by the lumped mass method. The Berkhoff(1972) experiment and a breakwater stand out are simulated for validating the precision and validity of my numerical model. The calculated results are in agreement with the experimental value, theoretical and finite-difference model’s solution, that indicate that my model is capable of giving good pre-dictions of wave refraction, diffraction, shoaling, breaking energy dissipation and weakly nonlinearity in the near shore zone.