Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations. For time discretization, a three-stage explicit Runge-Kutta method with TVD property is used at pr...Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations. For time discretization, a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage, a cubic spline function is adopted at correcting stage, which made the time discretization accuracy up to fourth order; For spatial discretization, a three-point explicit compact difference scheme with arbitrary 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 the experimental data. At the same time, the comparisons of the two numerical results between the present scheme and low accuracy difference method are made, which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations. As a valid sample, the wave propagation on the rectangular step is formulated by the present scheme, the modelled results are in better agreement with the experimental data than those of Kittitanasuan.展开更多
The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechan...The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics （English Edition）, 2007, 28（7）, 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.展开更多
基金The project was financially supported by the National Natural Science Foundation of China (Grant No50479053)
文摘Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations. For time discretization, a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage, a cubic spline function is adopted at correcting stage, which made the time discretization accuracy up to fourth order; For spatial discretization, a three-point explicit compact difference scheme with arbitrary 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 the experimental data. At the same time, the comparisons of the two numerical results between the present scheme and low accuracy difference method are made, which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations. As a valid sample, the wave propagation on the rectangular step is formulated by the present scheme, the modelled results are in better agreement with the experimental data than those of Kittitanasuan.
基金Supported by the National Natural Science Foundation of China (Nos.50876114 and 10602043)the Program for New Century Excellent Talents in University,and the Scientific Research Key Project Fund of Ministry of Education (No.106142)
文摘The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics （English Edition）, 2007, 28（7）, 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.
