改进型Boussinesq方程高精度紧致差分显格式

采用一种高精度的紧致差分显格式对改进型Boussinesq方程进行数值求解;采用具有TVD性质的三阶Runge-Kutta方法进行预报,用三次样条函数进行校正,时间精度可达到四阶;在空间离散上采用六阶精度的三点紧致显格式进行计算;运用以上数值格式对Beji和Nadaoka改进型Boussinesq方程进行了求解,求解证明:高精度的数值结果和已知的试验结果吻合良好.作为验证算例,同时对波浪在台阶上的传播进行了模拟,从效果对比上可以看出,所得结果明显比Kittitanasuan的计算结果更靠近试验值.

A highly accurate compact explicit difference scheme for extended Boussinesq equations

A highly accurate compact explicit difference scheme for solving the extended Boussinesq equations is presented.A three-stage explicit Runge-Kutta method with TVD property is used for prediction and a cubic spline method is adopted for correction,thus the accuracy of time integration gets to the fourth order.For spatial integration,a three-point explicit compact difference scheme with sixth-order accuracy is employed.The extended Boussinesq equations derived by Beji and Nadaoka are solved by the proposed scheme.The numerical results agree well with experimental data.As a validation sample,the wave propagation on the rectangular step is simulated by the present scheme.The numerical results of the present scheme are in better agreement with experimental data than those of Kittitanasuan.