基于MUSTA格式的全非线性Boussinesq波浪传播数值模型

房克照; 王磊; 刘忠波; 邹志利; 尹晶

doi:10.6052/0459-1879-13-338

基于MUSTA格式的全非线性Boussinesq波浪传播数值模型

doi: 10.6052/0459-1879-13-338

1.
大连理工大学海岸及近海工程国家重点实验室, 辽宁大连116024
2. 国家海洋和环境监测中心, 辽宁大连116023

基金项目: 国家创新研究团队（51221961）和国家海洋局海域管理技术重点实验室（201206）资助项目.

详细信息

作者简介:
房克照，讲师，主要研究方向：海岸动力学.E-mail：kfang@dlut.edu.cn

中图分类号: O353.2
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- 被引次数: 0
出版历程
- 收稿日期: 2013-10-14
- 修回日期: 2014-03-10
- 刊出日期: 2014-09-18

A FULLY NONLINEAR BOUSSINESQ MODELFOR WAVE PROPAGATION BASED ON MUSTA SCHEME

1.
The State Key Laboratory of Coastal and O shore Engineering, Dalian University of Technology, Dalian 116024, China
2. State Oceanic Administration, Dalian 116023, China

Funds: The project was supported by the National Foundation for Creative Research Groups (51221961) and National Marine Environmental Monitoring Center (201206).

摘要

摘要: 建立了求解二维全非线性布氏（Boussinesq）水波方程的有限差分/有限体积混合数值格式. 针对守恒形式的控制方程，采用有限体积方法并结合 MUSTA格式计算数值通量，剩余项则采用有限差分方法求解，采用具有总变差减小（totalvariation diminishing， TVD）性质的三阶龙格-库塔法进行时间积分.该格式具备间断捕捉、程序实现简单、数值稳定性强、海岸动边界以及波浪破碎处理方便和可调参数少等优点.利用典型算例对数值模型进行了验证，计算结果与实验数据吻合较好.
- Boussinesq水波方程 /
- 数值模拟 /
- MUSTA /
- 全非线性 /
- 有限体积方法
Abstract: A hybrid finite-difference/finite-volume scheme is developed to solve the 2D fully nonlinear Boussinesq equations. Finite volume method, in conjunction with the MUSTA scheme, is used to evaluate the flux terms while finite difference method is used to approximate the rest terms in the conservative governing equations. The third order Runge-Kutta method with TVD property is adopted for time marching. The proposed model has the advantages of shock capturing, easy coding and strong stability preserving, and contains less adjustable parameters. Two typical numerical tests are conducted for model validation, and the calculated results are in good agreement with experimental data.
- Boussinesq equations /
- numerical simulation /
- MUSTA /
- fully nonlinear /
- finite volume method

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参考文献(27)

李孟国, 王正林, 蒋德才. 关于波浪Boussines方程的研究. 青岛海洋大学学报, 2002, 32(3): 345-354 (Li Mengguo, Wang Zhenglin, Jiang Decai. Study on the Boussinesq equations. Journal of Ocean University of Qindao, 2002, 32(3): 345-354 (in Chinese))

马小舟, 董国海, 滕斌. 基于Boussinesq方程的波浪模型. 力学学报, 2006, 38(6): 760-766 (Ma Xiaozhou, Dong Guohai, Teng Bin. A wave model based on the Boussinesq equations. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(6): 760-766 (in Chinese))

王大国, 邹志利, 唐春安. 港口非线性波浪耦合计算模型研究. 力学学报, 2007, 39(5): 587-594 (Wang Daguo, Zou Zhili, Tang Chunan. The coupled numerical model of non-linear wave harbour. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(5): 587-594 (in Chinese))

桂琴琴, 邹志利, 王大国. 箱形船体波浪和波浪压力的非线性时域模型. 工程力学, 2011, 28(2): 239-245 (Gui Qinqin, Zou Zhili, Tang Chunan. Time-domian model of nonlinear wave forces on a box-shaped ship. Engineering Mechanics, 2011, 28(2): 239-245 (in Chinese))

Liu SX, Sun ZB, Li JX. An unstructured fem model based on boussinesq equations and its application to the calculation of multidirectional wave run-up in a cylinder group. Applied Mathematical Modelling, 2012, 36(6): 4146-4164

Shi FY, Kirby JT, Harris JC, et al. A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation. Ocean Modelling, 2012(43-44): 36-51

Kirby JT, Wei G, Chen Q, et al.FUNWAVE1.0 Fully Nonlinear Boussinesq Wave Model Documentation and User'S Manual. Newwark:CACR, 1998

Lynett PJ.Nearshore wave modeling with high-order Boussinesq-type equations.Journal of Waterway, Port, Coastal, and Ocean Engineering , 2006, 132(1): 348-357

张明亮, 时锋, 郝子宁. 具有捕捉能力的一维溃坝波及孤立波爬坡数学模型. 水动力研究与进展, 2012, 27(6): 687-695 (Zhang Mingliang, Shi Feng, Hao Zining. One dimensional numerical model for dam break wave and solitary wave runup with shock capturing capacity. Chinese Journal of Hydrodynamics, 2012, 27(6): 687-695 (in Chinese))

Bradford SF, Sanders BF. Finite volume schemes for the Boussinesq equations. In: Proc. of Ocean Wave Measurement and Analysis. 2001, 953-962

Erduran KS, Llic S, Kutijia V. Hybrid-finite volume finite-difference scheme for the solution of Boussinesq equations. International Journal for Numerical Methods in Fluids, 2005, 49: 1213-1232

Cienfuegos R, Barthelemy E, Bonneton P. A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: boundary conditions and validation. International Journal for Numerical Methods in Fluids, 2007, 53: 1423-1455

Shiach JB, Mingham CG. A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations. Coastal Engineering, 2009, 59(1): 32-45

Orszaghova J, Borthwick AGL, Taylor PH. From the paddle to the beach-A Boussinesq shallow water numerical wave tank based on Madsen and Sorensen's equations. Journal of Computational Physics, 2011, 231: 328-344

Roeber V, Cheung KF, Kobayashi MH. Shock-capturing Boussinesq-type model for nearshore wave processes. Coastal Engineering, 2010, 57(4): 407-423

房克照, 邹志利, 孙家文等. 扩展型Boussinesq水波方程的混合求解格式. 水科学进展, 2013, 24(5): 699-705 (Fang Kezhao, Zou Zhili, Sun Jiawen, et al. A hybrid numerical scheme for the extended Boussinesq equations. Advances in Water Science, 2013, 24(5): 699-705 (in Chinese))

Roeber V, Cheung KF. Boussinesq-type model for energetic breaking waves in fringing reef environments. Coastal Engineering, 2012, 70: 1-20

Tonelli M, Petti M. Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone. Ocean Engineering , 2010, 37(4): 567-582

Toro EF. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer Verlag, 2009

Toro EF. MUSTA: A multi-stage numerical flux. Applied Numerical Mathematics, 2006, 56(10-11): 1464-1479

Toro EF. MUSTA fluxes for systems of conservation laws. Journal of Computational Physics, 2006, 216(2): 403-429

Guo WD, Lao JS, Lin GF. Finite-volume multi-stage schemes for shallow-water flow simulation. International Journal for Numerical Methods in Fluids, 2008, 57(2): 177-204

Wei G, Kirby JT, Grilli ST et al. A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. Journal of Fluid Mechanics, 1995, 294: 71-92

Zou ZL, Fang KZ. Alternative forms of the higher-order Boussinesq equations: Derivations and validations. Coastal Engineering, 2008, 55(6): 506-521

Yamamoto S, Kano S, Daiguji H. An efficient CFD approach for simulating unsteady hypersonic shock-shock interference flows. Comput. Fluids, 1998, 27(5-6): 571-580

Berkhoff JCW, Booy N, Radder AC. Verification of numerical wave propagation models for simple harmonic linear waves. Coastal Engineering, 1982, 6: 255-379

Swigle DT. Laboratory study of the three-dimensional turbulence and kinematic properties associated with a breaking solitary wave. [Master Thesis], Texas: Texas A&M University, 2009

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