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BOUSSINESQ MODELLING OF NEARSHORE WAVES UNDER BODY FITTED COORDINATE

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Journal of Hydrodynamics 2012年第2期24卷 235-243页

作者： fang ke-zhao ZOU Zhi-li LIU Zhong-bo YIN Ji-wei State key Laboratory of Coastal and Offshore Engineering Dalian University of Technology Dalian 116024China key Laboratory of Coastal Disaster and Defence Ministry of Eduoation Hohai University Nanjing 210098China E-mail： kfang@***

A set of nonlinear Boussinesq equations with fully nonlinearity property is solved numerically in generalized coordinates,to develop a Boussinesq-type wave model in dealing with irregular computation boundaries in complex nearshore regions and to facilitate the grid refinements in *** governing equations expressed in contravariant components of velocity vectors under curvilinear coordinates are derived and a high order finite difference scheme on a staggered grid is employed for the numerical *** developed model is used to simulate nearshore wave propagations under curvilinear coordinates,the numerical results are compared against analytical or experimental data with a good agreement.

关键词： Boussinesq equation waves body fitted coordinate

Effect of the Coefficient on the Performance of A Two-Layer Boussinesq- Type Model

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China Ocean Engineering 2021年第1期35卷 36-47页

作者： SUN Jia-wen LIU Zhong-bo WANG Xing-gang fang ke-zhao DU Xin-yuan WANG Ping State Environmental Protection key Laboratory of Marine Ecosystem Restoration National Marine Environmental Monitoring CenterDalian 116023China Transportation Engineering College Dalian Maritime UniversityDalian 116026China Nanjing Hydraulic Research Institute Nanjing 210029China State key Laboratory of Coastal and Offshore Engineering Dalian University of TechnologyDalian 116024China Liaoning natural resources Affairs Service Center Shenyang 110032China

The coefficients embodied in a Boussinesq-type model are very important since they are determined to optimize the linear and nonlinear *** most conventional Boussinesq-type models,these coefficients are assigned the specific *** for the multi-layer Boussinesq-type models with the inclusion of the vertical velocity,however,the effect of the different values of these coefficients on linear and nonlinear performances has never been investigated *** present study focuses on a two-layer Boussinesq-type model with the highest spatial derivatives being 2 and theoretically and numerically examines the effect of the coefficient on model *** analysis show that different values for(0.13≤α≤0.25)do not have great effects on the high accuracy of the linear shoaling,linear phase celerity and even third-order nonlinearity for water depth range of 0

关键词： two-layer Boussinesq-type model dispersion nonlinear properties shoaling amplitude

Simulation of Horizontal-Two-Dimension Focused Waves Using A Two-Layer Boussinesq-Type Model

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China Ocean Engineering 2023年第5期37卷 725-737页

作者： ZOU Wen-feng WANG Ping LIU Zhong-bo fang ke-zhao SUN Jia-wen ZHANG Ning-chuan key Laboratory of coastal and offshore engineering Dalian University of TechnologyDalian 116024China State Environmental Protection key Laboratory of Marine Ecosystem Restoration National Marine Environmental Monitoring CenterDalian 116023China Dalian Maritime University College of Transportation EngineeringDalian 116024China

Accurate simulation of the horizontal-two-dimension(H2D)focused wave group in deep water requires high accuracy of a numerical *** two-layer Boussinesq-type model(Liu and fang,2016;Liu et al.,2018)with the highest spatial derivative of 2 has high accuracy in both linear and nonlinear *** on the further development of the velocity equations(Liu et al.,2023),the H2D numerical model for water waves is established with the prediction-correction-iteration model in the finite difference method,and a composite fourth-order Adams-Bashforth-Moulton scheme is used for time *** wave generation method proposed by Hsiao et al.(2005)is applied and calibrated in this H2D *** numerical calculations lead to the following three main conclusions:First,compared with the analytical solution of Stokes linear waves,the calculated velocity profiles show higher accuracy by using the improved velocity ***,the simulations of the focused multidirectional wave group are carried out,and good agreements are found,demonstrating that the present H2D numerical model shows high accuracy in simulating focused multidirectional wave groups,and the effectiveness of the improved velocity formulas is also ***,the velocity profiles throughout the computational domain at the time of maximum wave crest are ***,the FFT method is used to obtain the amplitude with different frequencies for several locations,and the changes of the wavelet energy spectrum at different locations are presented for several cases.

关键词： focused wave horizontal-two-dimension model finite difference method nonlinear property

应用二阶完全非线性Boussinesq方程模拟破碎波浪

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水科学进展 2012年第1期23卷 96-103页

作者：房克照邹志利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 河海大学海岸灾害及防护教育部重点实验室江苏南京210098

建立了基于高阶Boussinesq水波方程的一维波浪破碎数值模型。基于一组具有二阶完全非线性特征的Bouss-inesq水波方程,建立了交错网格下的高精度差分格式,推导了适用于该组方程的永形波解析解,其和松弛造波技术相结合实现了数值波浪水槽... 详细信息

建立了基于高阶Boussinesq水波方程的一维波浪破碎数值模型。基于一组具有二阶完全非线性特征的Bouss-inesq水波方程,建立了交错网格下的高精度差分格式,推导了适用于该组方程的永形波解析解,其和松弛造波技术相结合实现了数值波浪水槽中(强)非线性波浪的无反射入射。通过模拟封闭容器内水体晃动问题对数值格式进行了验证,通过模拟孤立波在斜坡海岸上的浅化过程说明了将方程从弱非线性发展到完全非线性的必要性。采用涡粘方法处理波浪破碎,利用物理模型实验数据,分析了模型中各波浪破碎参数对数值结果的影响并对参数进行了率定。应用该模型对规则波在斜坡海岸上的传播、变浅以及破碎过程进行了数值模拟研究,数值结果同实验数据吻合良好,验证了模型的有效性。

关键词： Boussinesq水波方程非线性波浪破碎有限差分法交错网格

Modelling of 2-D extended Boussinesq equations using a hybrid numerical scheme

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Journal of Hydrodynamics 2014年第2期26卷 187-198页

作者：房克照张哲邹志利刘忠波孙家文 State key Laboratory of Coastal and Offshore Engineering Dalian University of Technology National Marine Environment Monitoring Center State Oceanic Administration

In this paper, a hybrid finite-difference and finite-volume numerical scheme is developed to solve the 2-D Boussinesq equations. The governing equations are the extended version of Madsen and Sorensen＇s formulations. The governing equations are firstly rearranged into a conservative form. The finite volume method with the HLLC Riemann solver is used to discretize the flux term while the remaining terms are discretized by using the finite difference method. The fourth order MUSCL-TVD scheme is employed to reconstruct the variables at the left and right states of the cell interface. The time marching is performed by using the explicit second-order MUSCL-Hancock scheme with the adaptive time step. The developed model is validated against various experimental measurements for wave propagation, breaking and runup on three dimensional bathymetries.

关键词： hybrid scheme Boussinesq equations TVD Riemann solver

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双层Boussinesq水波方程（英文）

船舶力学 2015年第9期19卷 1072-1084页

作者：刘忠波房克照吕林大连海事大学交通运输管理学院辽宁大连116026 长沙理工大学水沙科学与水灾害防治湖南省重点实验室长沙410076 大连理工大学海岸和近海工程国家重点实验室辽宁大连116023

从Laplace方程出发,推导了一组适应于波浪在非平整地形上传播的双层Boussinesq水波方程,方程以双层水深积分平均速度表达且具有二阶全非线性特征。通过在动量方程中引入高阶色散项和非线性项进一步提高了方程的色散性和非线性性能。常... 详细信息

从Laplace方程出发,推导了一组适应于波浪在非平整地形上传播的双层Boussinesq水波方程,方程以双层水深积分平均速度表达且具有二阶全非线性特征。通过在动量方程中引入高阶色散项和非线性项进一步提高了方程的色散性和非线性性能。常水深情况下,分析了方程的色散关系和二阶波幅传递函数,并与Stokes解析解进行了比较。结果表明,在0.3%误差下方程可适用水深达kh≈6,在此水深范围内二阶波幅传递函数误差在10%以内。在非交错网格下,建立了基于有限差分方法和混合4阶Adams-Bashforth-Moulton时间积分格式的一维数值模型,模拟了波浪在潜堤上的传播变形,并与实验结果进行了对比,吻合程度较好。

关键词：双层Boussinesq方程色散性非线性

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波浪在渗透海床上传播的数学模型及其验证

大连理工大学学报 2013年第3期53卷 417-422页

作者：刘忠波孙昭晨房克照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

通过引入考虑可渗海床影响的阻力方程,将一组高阶Boussinesq水波方程拓展到可适用渗透海床的情况.在不同厚度介质情况下对新方程进行了理论分析,并将结果与解析解比较,讨论了方程的相速度及衰减率的精确度.在非交错网格下离散该方程,建... 详细信息

通过引入考虑可渗海床影响的阻力方程,将一组高阶Boussinesq水波方程拓展到可适用渗透海床的情况.在不同厚度介质情况下对新方程进行了理论分析,并将结果与解析解比较,讨论了方程的相速度及衰减率的精确度.在非交错网格下离散该方程,建立了基于高精度有限差分方法和预报-校正时间积分格式的一维数值模型.其中,在预报中采用三阶Adams-Bashforth格式,校正中则采用四阶Adams-Moulton格式.利用所建立数值模型,对渗透潜堤地形上的波浪传播变形进行了模拟,将数值计算结果与相关试验结果进行了比较分析,证明试验结果与数值结果吻合较好,说明这种改进方法是可行、有效的.

关键词： Boussinesq方程渗透色散性波浪

Highly mass activity electrocatalysts with ultralow Pt loading on carbon black for hydrogen evolution reaction

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International Journal of Minerals,Metallurgy and Materials 2025年第1期32卷 182-190页

作者： Shaorou ke Yajing zhao Xin Min Yanghong Li Ruiyu Mi Yangai Liu Xiaowen Wu Minghao fang zhaohui Huang Engineering Research Center of Ministry of Education for Geological Carbon Storage and Low Carbon Utilization of Resources Beijing Key Laboratory of Materials Utilization of Nonmetallic Minerals and Solid WastersNational Laboratory of Mineral MaterialsSchool of Materials Science and TechnologyChina University of Geosciences(Beijing)Beijing 100083China

Pt-based nanocatalysts offer excellent prospects for various ***,the low loading of Pt with excellent performance for efficient and stable nanocatalysts still presents a considerable *** this study,nanocatalysts with ultralow Pt content,excellent performance,and carbon black as support were prepared through in-situ ***~2-nm particles uniformly and stably dispersed on carbon black because of the strong s-p-d orbital hybridizations between carbon black and Pt,which suppressed the agglomeration of Pt *** unique structure is beneficial for the hydrogen evolution *** catalysts exhibited remarkable catalytic activity for hydrogen evolution reaction,exhibiting a potential of 100 mV at 100 mA·cm^(-2),which is comparable to those of commercial Pt/C *** activity(1.61 A/mg)was four times that of a commercial Pt/C catalyst(0.37 A/mg).The ultralow Pt loading(6.84wt%)paves the way for the development of next-generation electrocatalysts.

关键词： hydrogen evolution reaction ultralow platinum in-situ synthesis ultrasound

适合渗透海床波浪运动的三维Boussinesq型方程

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船舶力学 2024年第5期28卷 697-704页

作者：刘忠波韩沛秀房克照刘勇大连海事大学交通运输工程学院辽宁大连116026 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 中国海洋大学工程学院山东青岛266000

为考虑孔隙介质对波浪传播变形带来的衰减效应,在渗透介质流体的控制方程中引入线性阻力、非线性阻力和惯性力。自由表面采用精确的运动学和动力学边界条件,水底边界条件采用精确的动力学边界条件,自由水体和渗透介质水体之间满足垂向... 详细信息

为考虑孔隙介质对波浪传播变形带来的衰减效应,在渗透介质流体的控制方程中引入线性阻力、非线性阻力和惯性力。自由表面采用精确的运动学和动力学边界条件,水底边界条件采用精确的动力学边界条件,自由水体和渗透介质水体之间满足垂向速度连续、水平速度满足动量相等条件。首先推导最高空间导数为3的以两组计算速度表达的适合单层渗透海床波浪运动的三维Boussinesq型水波方程。其次,对新给出的方程进行傅里叶分析,并将方程的相速度及衰减率与Stokes线性波的解析解进行比较。在1%误差下,相对水深h_(2)/h_(1)=0.1~10,方程的解析解在无因次水深h_(1)/Lkes线性波的解析解都有较好的吻合,这超过了历史文献中任一个Boussinesq型水波方程的适用范围。进而建立立面二维水槽数值模型,并利用预报-校正-迭代的有限差分方法对数值模型进行求解,在变量对时间的导数求解中选择混合四阶AdamsBashforth-Moulton格式。最后,利用数值模拟再现波浪在渗透地形上的传播变形,并与相关试验结果进行比较,二者吻合程度较高。

关键词：渗透地形衰减率相速度数值模型