| 扩展型Boussinesq水波方程的混合求解格式 |
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| 引用本文： | 房克照,邹志利,孙家文,刘忠波.扩展型Boussinesq水波方程的混合求解格式[J].水科学进展,2013,24(5):699-705. |
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| 作者姓名： | 房克照 邹志利 孙家文 刘忠波 |
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| 作者单位： | 1.大连理工大学海岸和近海工程国家重点实验室, 辽宁大连 116024; |
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| 基金项目： | 国家自然科学基金资助项目(51009018);国家海洋局海域管理技术重点实验室资助项目(201206) |
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| 摘 要： | 为高效求解扩展型Boussinesq水波方程,建立了基于有限差分和有限体积方法的混合数值格式。将一维控制方程写为守恒形式,方程中通量部分采用有限体积方法求解,剩余部分采用有限差分方法求解。其中,有限体积方法采用Godunov类高分辨率格式,并结合HLL(Harten-Lax and van Leer)式黎曼问题近似解求界面数值通量,黎曼问题界面左右变量通过高精度状态插值方法(MUSCL)构筑。有限差分方法则采用具有二阶精度的中心差分公式进行。采用具有TVD(Total Variation Diminishing)性质的三阶龙格-库塔多步积分法进行时间积分。对数值模式进行了验证,数值结果同解析解或实验数据吻合良好。
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| 关 键 词： | Boussinesq水波方程 数值模拟 总变差减小 有限差分方法 有限体积方法 |
| 收稿时间： | 2012-11-08 |
A hybrid numerical scheme for extended Boussinesq equations |
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| FANG Kezhao,ZOU Zhili,SUN Jiawen,LIU Zhongbo.A hybrid numerical scheme for extended Boussinesq equations[J].Advances in Water Science,2013,24(5):699-705. |
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| Authors: | FANG Kezhao ZOU Zhili SUN Jiawen LIU Zhongbo |
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| Institution: | 1.State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China;2.National Marine Environmental Monitoring Center, State Oceanic Administration, Dalian 116023, China |
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| Abstract: | To efficiently solve the extended Boussinesq equations, a hybrid finite-difference and finite-volume scheme is developed. The one-dimensional governing equations are kept in conservation form. The flux term is discretized using the finite volume method, while the remaining terms are discretized using the finite difference method. A Godunov-type high resolution scheme, in conjunction with the Harten-Lax and van Leer (HLL) Riemann solver and the higher accuracy MUSCL (Monotone Upwind Schemes for Scalar Conservation Laws) method for variable reconstruction, is adopted to compute the interface flux. High order central difference formulas are used to discretize the remaining terms. The third order Runge-Kutta method with total variation diminishing (TVD) property is adopted for time marching. Numerical tests are conducted for model validation, and the computed results agree well with experimental data. |
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| Keywords: | Boussinesq equations numerical simulation total variation diminishing finite difference method finite volume method |
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