基于多次透射公式和无奇异边界元法模拟全非线性数值波浪水池

摘要

Wave propagation in a three-dimensional nonlinear numerical wave tank (NWT) is stud-ied based on the fully nonlinear velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved by using the indirect desingular-ized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bash-forth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is ap-plied to eliminate the possible saw-tooth instabilities. An effective Multi-transmitting Formula method for radiation condition is employed to transmit wave out of computational region. The numerical results are compared with analytical solutions. The results show that MTF method can be used for simulating fully nonlinear wave propagation.%文章基于势流理论对全非线性的三维数值水池进行了模拟,其控制方程由无奇异边界积分方程法(Desingularized Boundary Integral Equation Method,DBIEM)进行离散求解,在求解全非线性的自由面微分方程时,文中采用混合欧拉—拉格朗日法(Mixed Eulerian-Lagrangian,MEL)和四阶Adams-Bashforth-Moulton(ABM4)预报—修正方法,为了避免结果发散即增强数值稳定性,文中采用B样条法来光顺波面.同时,在远方辐射控制面上采用多次透射公式方法(Multi-transmitting Formula,MTF)来进行消波,文中得到的结果与理论解进行了比较,结果表明该方法可用来有效模拟全非线性的数值波浪水池.