Boussinesq方程的高精度求解及其验证

High accuracy scheme for nonlinear Boussinesq equations and verification

本文采用高精度紧致差分格式提高浅水非线性的 Boussinesq方程的求解精度 ,在未增加求解难度的前提下 ,建立了高精度、低耗散及较好线性色散性的数学模型。通过验证 ,表明非线性项求解精度的提高 ,使模型能更好地描述复杂地形上波浪的非线性变形 ,并能合理地模拟工程实际问题中的波浪折射、绕射。

A high accuracy scheme was proposed by using the compact difference scheme for solving nonlinear Boussinesq equations in shallow water. A numerical model with high accuracy, lower dissipation and better linear dispersion property was established. The verification shows the improvement of accuracy, especially in calculating nonlinear terms, makes the model applicable to describe the nonlinear deformation of waves in sophisticated topography. Meanwhile the model reflects the physical phenomenon of wave refraction, diffraction, and reflection etc. in practical engineering reasonably.