浅水非线性波的数值模拟

Numerical Simulation of Nonlinear Wave in Shallow Water

在交错网格上构造了求解非线性Boussinesq方程的紧致差分格式,此格式可以在只用到三个网格结点的情况下,达到空间四阶精度。利用这个格式,对浅水非线性波的传播过程进行数值模拟,并将此数值模型应用于求解线性、非线性波过双突堤的绕射问题,研究了非线性对水波绕射的影响。结果表明,由于非线性对流项的作用,使得非线性波较之线性波具有更强的散射性,因此在港口工程中,应该考虑非线性效应的影响。

The compact difference scheme for two dimensional Boussinesq equation is given on a staggered grid. This scheme could reach fourth-order accuracy in space by only using three grid points. Using the compact difference scheme, the propogation of nonlinear wave in shallow water has been simulated. The mathematical model of this paper has also been used to simulate the diffraction of the linear and nonlinear wave, and the effect of nonlinearity on wave diffraction was studied.