In this study, a computational model is established for solving wave propagation over a submerged dike based on RANS equations combined with Level-Set method. The fifth-order finite difference WENO scheme is used for spatial discretization, and a TVD third-order Runge-Kutta explicit time scheme is employed for time discretization in the model. The Level-Set method is used for tracking the free interface between the air and water phases, and a relaxation method is employed for wave generation and absorption. In order to validate the accuracy and applicability of the model, numerical investigation of the wave propagation over a submerged dike is conducted. The numerical results show a good agreement with experimental data. Further studies are carried out to investigate the influence of physical parameters, such as wave height, submerged depth, seaward and leeward slope gradients, on the process of wave propagation over a submerged dike. Results reveal that when the wave height is higher, submerged depth smaller, and seaward slope flatter, the effect of shoaling is more obvious; when leeward slope is flatter, the effect of shoaling on wave is slightly larger, but not obvious.
Key words
submerged dike /
Level-Set method /
wave propagation /
numerical investigation /
shoaling
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References
[1] BROCCHINI M, DRAGO M, IOVENITTI L. The Modelling of Short Waves in Shallow Waters. Comparison of Numerical Methods based on Boussinesq and Serre Equations[C]∥American Society of Civil Engineers. Proceedings of the 23rd International Conference on Coastal Engineering. Venice, Italy. October 4-9, 1992: 76-88.
[2] BEJI S, BATTJES J A. Numerical Simulation of Nonlinear Wave Propagation over a Bar[J]. Coastal Engineering, 1994, 23(1): 1-16.
[3] 孙 先, 杨文俊, 王国栋. 基于 坐标变换和水位函数法的立面二维水动力学模型[J]. 长江科学院院报, 2012, 29(7): 6-9, 26.
[4] KOBAYASHI N, OTTA A, ROY I. Wave Reflection and Run-up on Rough Slopes[J]. Journal of Waterway, Port, Coastal and Ocean Engineering, 1987, 113(3): 282-298.
[5] 陈善群, 廖 斌, 李海峰. 用最小二乘无网格有限差分方法求解二维浅水方程[J]. 长江科学院院报, 2012, 29(6): 36-39, 57.
[6] 李昌良, 谢媛媛. 不同结构形式潜堤上的随机波浪运动[J]. 海岸工程, 2008, 27(1): 1-9.
[7] 蒋昌波, 曹永港, 陈 杰, 等. 斜坡上梯形潜堤附近流动结构的数值研究[J]. 水动力学研究与进展A辑, 2009, 24(3): 286-295.
[8] JACOBSEN N G, FUHRMAN D R, FREDSØE J. A Wave Generation Toolbox for the Open-source CFD Library: OpenFOAM[J]. International Journal for Numerical Methods in Fluids, 2011, 70(9): 1073-1088.
[9] 刘忠波, 于德海, 孙昭晨. 潜堤上破碎波浪传播变形的数值模型及其验证[J]. 海洋通报, 2011, 30(6): 633-636.
[10] OSHER S,SETHIAN J A.Fronts Propagating with Curvature-dependent Speed:Algorithms based on Hamil-ton-Jacobi Formulations[J].Journal of Computational Physics, 1988, 79(1): 12-49.
[11] VAN DER VORST H A. Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems[J]. SIAM Journal on Scientific and Statistical Computing, 1992, 13(2): 631-644.
[12] WILCOX D C. Turbulence Modeling for CFD[M]. Los Angeles: DCW Industries Inc., 1994.
[13] JIANG G S, SHU C W. Efficient Implementation of Weighted ENO Schemes[J]. Journal of Computational Physics, 1996, 126(1): 202-228.
[14] SHU C W, OSHER S. Efficient Implementation of EssentiallyNon-oscillatoryShockCapturingSchemes[J].Journal of Computational Physics, 1988, 77(2): 439-471.
[15] MAYER S,GARAPON A,SØRENSEN L S.A Fractional StepMethodforUnsteadyFreeSurfaceFlowwithApplications to Non-linear Wave Dynamics[J].International
Journal for Numerical Methods in Fluids, 1998, 28(2): 293-315.
[16] BEJI S, BATTJES J A. Experimental Investigation of Wave Propagation over a Bar[J]. Coastal Engineering, 1993, 19(1/2): 151-162.
Funding
国家自然科学基金项目(51409001); 安徽省自然科学基金项目(1508085QE100); 安徽高校优秀青年人才支持计划项目(gxyq2017015)
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