Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directl...Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the effciency of the characteristic constrained interpolation profile （CIP） method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.展开更多
The contact angle is one of important parameters to simulate droplet spreading and impingement phenomena on the surface. In the most numerical research, it is assumed constant value and it is implemented as boundary c...The contact angle is one of important parameters to simulate droplet spreading and impingement phenomena on the surface. In the most numerical research, it is assumed constant value and it is implemented as boundary condition. However, contact angle is changed according to contact line velocity and time. Hence, for accurate simulation, dynamic contact angle which has various values as time elapsed is adopted. In the present study, the numerical analysis is performed on the droplet spreading phenomena considering dynamic contact angle function which is obtained from single droplet spreading experiment on the flat and bare surface. The CIP （cubic interpolated pseudo-particle） method by Yabe is used for analysis of interface between liquid and gas phases. The numerical results considering contact angle function which newly modeled as time and contact angle are compared with numerical results considering Hoffman＇s function and experimental data for range of Weber number which are 4.427 and 11.334. In contrast of numerical result considering Hoffman＇s function, the numerical result shows good agreement with experimental data as time elapsed in contact angle evolution, deformation of droplet spreading radius and height. Indeed, overall, the results display the increasing maximum spreading radius and the decreasing height as Weber numbers increased.展开更多
An enhanced numerical model for simulating two-dimensional incompressible viscous flow with distorted free surface is reported. The numerical simulation is carried out through the CIP （Constrained Interpolation Prof...An enhanced numerical model for simulating two-dimensional incompressible viscous flow with distorted free surface is reported. The numerical simulation is carried out through the CIP （Constrained Interpolation Profile）-based method, which is described in the paper. A more accurate interface capturing scheme, the VOF/WLIC scheme （VOF：Volume-of-Fluid;WLIC：weighed line interface calculation）, is adopted as the interface capturing method. To assess the developed algorithm and its versatility, a selection of test problems are examined, i.e. the square wave propagation, the Zalesak’s rigid body rotation, dam breaking problem with and without obstacles, wave sloshing in an excited wave tank and interaction between extreme waves and a floating body. Excellent agreements are obtained when numerical results are compared with available analytical, experimental, and other numerical results. These examples demonstrate that the use of the VOF/WLIC scheme in the free surface capturing makes better results and also the proposed CIP-based model is capable of predicting the freak wave-related phenomena.展开更多
A constrained interpolation profile CIP-based numerical tank is developed to simulate violent free surface flows.The numerical simulation is performed by the CIP-based Cartesian grid method,which is described in the p...A constrained interpolation profile CIP-based numerical tank is developed to simulate violent free surface flows.The numerical simulation is performed by the CIP-based Cartesian grid method,which is described in the present paper.The tangent of hyperbola for interface capturing（THINC） scheme is applied for capturing complex free surfaces.The new model is capable of simulating a flow with violently varied free surface.A series of computations are conducted to assess the developed algorithm and its versatility.These tests include the collapse of water column with and without an obstacle,sloshing in a fixed tank,the generation of regular waves in a tank,the generation of extreme waves in a tank.Excellent agreements are obtained when numerical results are compared with available analytical,experimental,and other numerical results.展开更多
利用自主研发的CIP-ZJU(Constrained Interpolation Profile Method in Zhejiang University)高精度数学模型研究强非线性自由表面流动问题.模型在直角坐标系统下建立,采用紧致插值曲线CIP方法作为流场的基本求解器,通过多相流的方式实...利用自主研发的CIP-ZJU(Constrained Interpolation Profile Method in Zhejiang University)高精度数学模型研究强非线性自由表面流动问题.模型在直角坐标系统下建立,采用紧致插值曲线CIP方法作为流场的基本求解器,通过多相流的方式实现固-液-气耦合同步求解,采用平衡格式的VOF(VOF/WLIC:Volume of Fluid/Weighted Line Interface Calculation)自由面捕捉方法改进了原模型,利用浸入边界方法处理运动物体.利用改进的CIP模型开展了不同类型的物体冲击液面引起的液滴飞溅现象的数值模拟,重点分析液滴飞溅过程中的自由液面变形、作用荷载和物体位置等.通过数值结果与实验结果的比较验证模型的可靠性.结果表明:平衡格式的VOF自由面捕捉方法能更精确地重构自由面,本文的数学模型可精确预测强非线性自由表面流动问题.展开更多
基于自主研发的紧致插值曲线CIP方法的数学模型,研究孤立波在大陆架上传播及冲击爬升海岸峭壁的数值模拟.在立面二维直角坐标下建立模型,采用高阶差分CIP方法作为流场的基本求解器,利用分步算法离散Navier-Stokes方程,通过多相流理论描...基于自主研发的紧致插值曲线CIP方法的数学模型,研究孤立波在大陆架上传播及冲击爬升海岸峭壁的数值模拟.在立面二维直角坐标下建立模型,采用高阶差分CIP方法作为流场的基本求解器,利用分步算法离散Navier-Stokes方程,通过多相流理论描述固-液-气之间的相互作用,采用流体体积法(volume of fluid,VOF)类型的具有高精度、紧致的系数权重双曲正切(tangent of hyperbola for interface capturing with slope weighting,THINC-SW)方法改进传统的数学模型,重构了自由面采用浸入边界法(immersed boundary method,IBM)计算固-液边界,避免按照地形边界建立贴边网格的问题.研究孤立波在峭壁前的波形演变及在峭壁上的爬坡高度,比较不同的大陆架水平长度和不同海岸峭壁坡度对孤立波爬高峰值的大小及出现时间的影响,分析孤立波冲击爬坡时的压力分布,为不同海岸地形采取相适应的波浪防护措施提供理论及数据支持.展开更多
In this study,the water entry of wedges in regular waves is numerically investigated by a two-dimensional in-house numerical code.The numerical model based on the viscous Navier−Stokes(N−S)equations employs a high-ord...In this study,the water entry of wedges in regular waves is numerically investigated by a two-dimensional in-house numerical code.The numerical model based on the viscous Navier−Stokes(N−S)equations employs a high-order different method—the constrained interpolation profile(CIP)method to discretize the convection term.A Volume of Fluid(VOF)-type method,the tangent of hyperbola for interface capturing/slope weighting(THINC/SW)is employed to capture the free surface/interface,and an immersed boundary method is adopted to treat the motion of wedges.The momentum source function derived from the Boussinesq equation is applied as an internal wavemaker to generate regular waves.The accuracy of the numerical model is validated in comparison with experimental results in the literature.The results of water entry in waves are provided in terms of the impact force of wedge,velocity and pressure distributions of fluid.Considerable attention is paid to the effects of wave parameters and the position of wedge impacting the water surface.It is found that the existence of waves significantly influences the velocity and pressure field of fluid and impact force on the wedges.展开更多
Hydroelastic behavior of an elastic wedge impacting on calm water surface was investigated. A partitioned approach by coupling finite difference method （FDM） and finite element method （FEM） was developed to analyz...Hydroelastic behavior of an elastic wedge impacting on calm water surface was investigated. A partitioned approach by coupling finite difference method （FDM） and finite element method （FEM） was developed to analyze the fluid structure interaction （FSI） problem. The FDM, in which the Constraint Interpolation Profile （CIP） method was applied, was used for solving the flow field in a fixed regular Cartesian grid system. Free surface was captured by the Tangent of Hyperbola for Interface Capturing with Slope Weighting （THINC/SW） scheme. The FEM was applied for calculating the structural deformation. A volume weighted method, which was based on the immersed boundary （IB） method, was adopted for coupling the FDM and the FEM together. An elastic wedge water entry problem was calculated by the coupled FDM-FEM method. Also a comparison between the current numerical results and the published results indicate that the coupled FDM-FEM method has reasonably good accuracy in predicting the impact force.展开更多
基金supported by National Natural Science Foundation of China (NSFC) projects (Grant Nos. 40875065 and 40805045)the research projects 2008R001 at Chinese Academy of Meteorological Sciences (CAMS) and 2008 LASWZI05 at the State Key Laboratory of Severe Weather, CAMS
文摘Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the effciency of the characteristic constrained interpolation profile （CIP） method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.
文摘The contact angle is one of important parameters to simulate droplet spreading and impingement phenomena on the surface. In the most numerical research, it is assumed constant value and it is implemented as boundary condition. However, contact angle is changed according to contact line velocity and time. Hence, for accurate simulation, dynamic contact angle which has various values as time elapsed is adopted. In the present study, the numerical analysis is performed on the droplet spreading phenomena considering dynamic contact angle function which is obtained from single droplet spreading experiment on the flat and bare surface. The CIP （cubic interpolated pseudo-particle） method by Yabe is used for analysis of interface between liquid and gas phases. The numerical results considering contact angle function which newly modeled as time and contact angle are compared with numerical results considering Hoffman＇s function and experimental data for range of Weber number which are 4.427 and 11.334. In contrast of numerical result considering Hoffman＇s function, the numerical result shows good agreement with experimental data as time elapsed in contact angle evolution, deformation of droplet spreading radius and height. Indeed, overall, the results display the increasing maximum spreading radius and the decreasing height as Weber numbers increased.
基金financially supported by the National Natural Science Foundation of China(Grant No.51209184)the Fundamental Research Funds for the Central Universities(Grant No.2012QNA4020)+1 种基金the Zhejiang Open Foundation of the Most Important Subjects,the Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province(Grant No.2013SS03)the Educational Commission of Zhejiang Province of China(Grant No.Y201225713)
文摘An enhanced numerical model for simulating two-dimensional incompressible viscous flow with distorted free surface is reported. The numerical simulation is carried out through the CIP （Constrained Interpolation Profile）-based method, which is described in the paper. A more accurate interface capturing scheme, the VOF/WLIC scheme （VOF：Volume-of-Fluid;WLIC：weighed line interface calculation）, is adopted as the interface capturing method. To assess the developed algorithm and its versatility, a selection of test problems are examined, i.e. the square wave propagation, the Zalesak’s rigid body rotation, dam breaking problem with and without obstacles, wave sloshing in an excited wave tank and interaction between extreme waves and a floating body. Excellent agreements are obtained when numerical results are compared with available analytical, experimental, and other numerical results. These examples demonstrate that the use of the VOF/WLIC scheme in the free surface capturing makes better results and also the proposed CIP-based model is capable of predicting the freak wave-related phenomena.
基金supported by the Fundamental Research Funds for the Central Universities
文摘A constrained interpolation profile CIP-based numerical tank is developed to simulate violent free surface flows.The numerical simulation is performed by the CIP-based Cartesian grid method,which is described in the present paper.The tangent of hyperbola for interface capturing（THINC） scheme is applied for capturing complex free surfaces.The new model is capable of simulating a flow with violently varied free surface.A series of computations are conducted to assess the developed algorithm and its versatility.These tests include the collapse of water column with and without an obstacle,sloshing in a fixed tank,the generation of regular waves in a tank,the generation of extreme waves in a tank.Excellent agreements are obtained when numerical results are compared with available analytical,experimental,and other numerical results.
文摘利用自主研发的CIP-ZJU(Constrained Interpolation Profile Method in Zhejiang University)高精度数学模型研究强非线性自由表面流动问题.模型在直角坐标系统下建立,采用紧致插值曲线CIP方法作为流场的基本求解器,通过多相流的方式实现固-液-气耦合同步求解,采用平衡格式的VOF(VOF/WLIC:Volume of Fluid/Weighted Line Interface Calculation)自由面捕捉方法改进了原模型,利用浸入边界方法处理运动物体.利用改进的CIP模型开展了不同类型的物体冲击液面引起的液滴飞溅现象的数值模拟,重点分析液滴飞溅过程中的自由液面变形、作用荷载和物体位置等.通过数值结果与实验结果的比较验证模型的可靠性.结果表明:平衡格式的VOF自由面捕捉方法能更精确地重构自由面,本文的数学模型可精确预测强非线性自由表面流动问题.
文摘基于自主研发的紧致插值曲线CIP方法的数学模型,研究孤立波在大陆架上传播及冲击爬升海岸峭壁的数值模拟.在立面二维直角坐标下建立模型,采用高阶差分CIP方法作为流场的基本求解器,利用分步算法离散Navier-Stokes方程,通过多相流理论描述固-液-气之间的相互作用,采用流体体积法(volume of fluid,VOF)类型的具有高精度、紧致的系数权重双曲正切(tangent of hyperbola for interface capturing with slope weighting,THINC-SW)方法改进传统的数学模型,重构了自由面采用浸入边界法(immersed boundary method,IBM)计算固-液边界,避免按照地形边界建立贴边网格的问题.研究孤立波在峭壁前的波形演变及在峭壁上的爬坡高度,比较不同的大陆架水平长度和不同海岸峭壁坡度对孤立波爬高峰值的大小及出现时间的影响,分析孤立波冲击爬坡时的压力分布,为不同海岸地形采取相适应的波浪防护措施提供理论及数据支持.
基金supported by Foundation of Zhejiang Institute of Hydraulic and Estuary(Grant No.Haian A18003)the Science and Technology Plan Projects of Zhejiang water(Grant No.RB1803)+1 种基金Zhejiang Provincial Natural Science Foundation(Grant Nos.LQ19E090004 and LQ16E090004)the Science and Technology Plan Projects of Zhejiang Province(Grant No.2018F10026)and Tang Scholar.
文摘In this study,the water entry of wedges in regular waves is numerically investigated by a two-dimensional in-house numerical code.The numerical model based on the viscous Navier−Stokes(N−S)equations employs a high-order different method—the constrained interpolation profile(CIP)method to discretize the convection term.A Volume of Fluid(VOF)-type method,the tangent of hyperbola for interface capturing/slope weighting(THINC/SW)is employed to capture the free surface/interface,and an immersed boundary method is adopted to treat the motion of wedges.The momentum source function derived from the Boussinesq equation is applied as an internal wavemaker to generate regular waves.The accuracy of the numerical model is validated in comparison with experimental results in the literature.The results of water entry in waves are provided in terms of the impact force of wedge,velocity and pressure distributions of fluid.Considerable attention is paid to the effects of wave parameters and the position of wedge impacting the water surface.It is found that the existence of waves significantly influences the velocity and pressure field of fluid and impact force on the wedges.
基金the support of Grants-in-Aid for Scientific Research (B), MEXT (No.24360358)
文摘Hydroelastic behavior of an elastic wedge impacting on calm water surface was investigated. A partitioned approach by coupling finite difference method （FDM） and finite element method （FEM） was developed to analyze the fluid structure interaction （FSI） problem. The FDM, in which the Constraint Interpolation Profile （CIP） method was applied, was used for solving the flow field in a fixed regular Cartesian grid system. Free surface was captured by the Tangent of Hyperbola for Interface Capturing with Slope Weighting （THINC/SW） scheme. The FEM was applied for calculating the structural deformation. A volume weighted method, which was based on the immersed boundary （IB） method, was adopted for coupling the FDM and the FEM together. An elastic wedge water entry problem was calculated by the coupled FDM-FEM method. Also a comparison between the current numerical results and the published results indicate that the coupled FDM-FEM method has reasonably good accuracy in predicting the impact force.
