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（英文）
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摘要
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(Multitransmitting 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。
Wave propagation in a three-dimensional nonlinear numerical wave tank(NWT) is studied 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 desingularized boundary integral equation method(DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme(ABM4) and mixed Eulerian-Lagrangian(MEL) method are used for the timestepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied 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.
Wave propagation in a three-dimensional nonlinear numerical wave tank(NWT) is studied 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 desingularized boundary integral equation method(DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme(ABM4) and mixed Eulerian-Lagrangian(MEL) method are used for the timestepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied 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.
引文
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[4]Zhang X T,Khoo B C,Lou J.Wave propagation in a fully nonlinear numerical wave tank:a desingularized method[J].Ocean Engineering,2006,33:2310-2331.
[5]Zhang X T,Khoo B C,Lou J.Application of desingularized approach to water wave propagation over three-dimensional topography[J].Ocean Engineering,2007,34:1449-1458.
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[9]Xu G,Duan W Y.Time-domain simulation of wave-structure interaction based on multi-transmitting formula coupled with damping zone method for radiation boundary condition[J].Applied Ocean Research,2013;42:136-143.
[10]Duan W Y,Zhang T Y.Non-reflecting simulation for fully-nonlinear irregular wave radiation[C]//Proceedings of the 24th International Workshop on Water Wave and Floating Bodies.Bodies,Russia,2009.
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[12]Xu G.Time-domain simulation of second-order hydrodynamic force on floating bodies in irregular waves[D].Harbin:College of Shipbuilding Engineering,Harbin Engineering University,2010.(in Chinese)
[2]Boo S Y.Linear and nonlinear irregular waves and forces in a numerical wave tank[J].Ocean Engineering,2002,29:475-493.
[3]Wang C Z,Wu G X.Time domain analysis of second-order wave diffraction by an array of vertical cylinders[J].Journal of Fluids and Structures,2007,23(4):605-631.
[4]Zhang X T,Khoo B C,Lou J.Wave propagation in a fully nonlinear numerical wave tank:a desingularized method[J].Ocean Engineering,2006,33:2310-2331.
[5]Zhang X T,Khoo B C,Lou J.Application of desingularized approach to water wave propagation over three-dimensional topography[J].Ocean Engineering,2007,34:1449-1458.
[6]Koo W C,Kim M H.Fully nonlinear wave-body interactions with surface-piercing bodies[J].Ocean Engineering,2007,34:1000-1012.
[7]Liao Z P.Extrapolation non reflecting boundary conditions[J].Wave Motion,1996,24:117-138.
[8]Xu G,Duan W Y.Time domain simulation for water wave radiation by floating structures(Part A)[J].Journal of Marine Science and Application,2008;7:226-235.
[9]Xu G,Duan W Y.Time-domain simulation of wave-structure interaction based on multi-transmitting formula coupled with damping zone method for radiation boundary condition[J].Applied Ocean Research,2013;42:136-143.
[10]Duan W Y,Zhang T Y.Non-reflecting simulation for fully-nonlinear irregular wave radiation[C]//Proceedings of the 24th International Workshop on Water Wave and Floating Bodies.Bodies,Russia,2009.
[11]Cao Y,Schultz W W,Beck R F.Three dimensional desingularized boundary integral methods for potential problems[J].International Journal for Numerical Methods in Fluids,1991,12:785-803.
[12]Xu G.Time-domain simulation of second-order hydrodynamic force on floating bodies in irregular waves[D].Harbin:College of Shipbuilding Engineering,Harbin Engineering University,2010.(in Chinese)