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零净质量射流的数值模拟 被引量:6
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作者 石清 李桦 《空气动力学学报》 EI CSCD 北大核心 2011年第1期114-117,共4页
对零净质量射流致动器的流场和有零净质量射流时翼型的绕流流场进行了数值模拟,分析了动网格与几何守恒率、边界条件、湍流模型对零净质量射流致动器流场计算的影响,分析了零净质量射流的速度幅值和驱动频率对翼型增升效果的影响。研究... 对零净质量射流致动器的流场和有零净质量射流时翼型的绕流流场进行了数值模拟,分析了动网格与几何守恒率、边界条件、湍流模型对零净质量射流致动器流场计算的影响,分析了零净质量射流的速度幅值和驱动频率对翼型增升效果的影响。研究结果表明,在复杂计算中可以对能动部件的边界作赋值处理;随着射流速度幅值的增加,翼型的平均升力系数和阻力系数都要增加;射流频率对升力的影响呈非线性。 展开更多
关键词 零净质量射流 动网格 数值边界条件 湍流模型 非定常流动
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Application of the double absorbing boundary condition in seismic modeling 被引量:1
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作者 刘洋 李向阳 陈双全 《Applied Geophysics》 SCIE CSCD 2015年第1期111-119,123,共10页
We apply the newly proposed double absorbing boundary condition(DABC)(Hagstrom et al., 2014) to solve the boundary reflection problem in seismic finite-difference(FD) modeling. In the DABC scheme, the local high... We apply the newly proposed double absorbing boundary condition(DABC)(Hagstrom et al., 2014) to solve the boundary reflection problem in seismic finite-difference(FD) modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer(PML), the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML. 展开更多
关键词 Double absorbing boundary condition numerical modeling finite-difference method artificial boundary condition
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A truncated implicit high-order finite-difference scheme combined with boundary conditions 被引量:2
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作者 常锁亮 刘洋 《Applied Geophysics》 SCIE CSCD 2013年第1期53-62,118,共11页
In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods (IFDM) for the first and second-order derivatives on normal grids and first- order derivatives on staggered gri... In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods (IFDM) for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition (ABC) to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme. 展开更多
关键词 Implicit finite difference symmetric boundary condition high-order accuracy TRUNCATION absorbing boundary condition staggered grid numerical modeling
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Numerical Simulation of the Flow around Two-dimensional Partially Cavitating Hydrofoils 被引量:2
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作者 Fahri Celik Yasemin Arikan Ozden Sakir Bal 《Journal of Marine Science and Application》 2014年第3期245-254,共10页
In the present study, a new approach is applied to the cavity prediction for two-dimensional (2D) hydrofoils by the potential based boundary element method (BEM). The boundary element method is treated with the so... In the present study, a new approach is applied to the cavity prediction for two-dimensional (2D) hydrofoils by the potential based boundary element method (BEM). The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by usethe of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code (FLUENT). Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others. 展开更多
关键词 boundary element method (BEM):sheet cavitation CFD HYDROFOIL cavity closure model 2D hydrofoils
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An Alternative Method to Study Wave Scattering by Semi-infinite Inertial Surfaces
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作者 R.Gayen Ranita Roy 《Journal of Marine Science and Application》 2013年第1期31-37,共7页
A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The disconti... A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green's second identity to the potential functions and appropriate Green's functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results. 展开更多
关键词 Fredholm integral equations inertial surface reflection coefficient water wave scattering boundary value problem
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Navier’s slip condition on time dependent Darcy-Forchheimer nanofluid using spectral relaxation method
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作者 Younghae DO G. K. RAMESH +1 位作者 G. S. ROOPA M. SANKAR 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第7期2000-2010,共11页
In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice o... In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice of cooling liquid is also an important component of the analysis to achieve better outputs. In this paper, we numerically investigate Darcy-Forchheimer nanoliquid flows past an unsteady stretching surface by incorporating various effects, such as the Brownian and thermophoresis effects, Navier’s slip condition and convective thermal boundary conditions. To solve the governing equations, using suitable similarity transformations, the nonlinear ordinary differential equations are derived and the resulting coupled momentum and energy equations are numerically solved using the spectral relaxation method. Through the systematically numerical investigation, the important physical parameters of the present model are analyzed. We find that the presence of unsteadiness parameter has significant effects on velocity, temperature, concentration fields, the associated heat and mass transport rates. Also, an increase in inertia coefficient and porosity parameter causes an increase in the velocity at the boundary. 展开更多
关键词 Darcy-Forchheimer flow nanoliquid Navier’s slip convective condition numerical solution
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The Application of a Numerical Model to Coastal Surface Water Waves
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作者 ZOUHuazhi LIHuajun LIUXiaodong LIUAixia 《Journal of Ocean University of China》 SCIE CAS 2005年第2期177-184,共8页
Based on the Navier-Stokes Equations (NSE), numerical simulation with fine grids is conducted to simulate the coastal surface wave changes, including wave generation, propagation, transformation and interactions betwe... Based on the Navier-Stokes Equations (NSE), numerical simulation with fine grids is conducted to simulate the coastal surface wave changes, including wave generation, propagation, transformation and interactions between waves and structures. This numerical model has been tested for the generation of the desired incident waves, including both regular and random waves. Some numerical results of this model are compared with available experimental data. In order to apply this model to actual cases, boundary conditions are considered in detail for different shoreline types (beach or breakwater, slope or vertical wall, etc. ). Finally, the utility of the model to a real coastal area is shown by applying it to a fishing port located in Shidao, Rongcheng, Shandong Province, P.R. China. 展开更多
关键词 wave propagation wave generation numerical simulation Navier-StokesEquations boundary condition
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Numerical Homogenization of the Elliptic Problem with Rapidly Varying Tensor or Boundary Condition
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作者 Jack Urombo Ephraim Makoni 《Journal of Mathematics and System Science》 2014年第6期421-432,共12页
Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this pap... Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems. 展开更多
关键词 2. Homogenization Elliptic equation
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Changes in Coupled Vibration Frequencies and Modes of Wall-Cavity Systems Induced by Stiffness Variation in the Structure
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作者 Soraya Mendes de Souza Lineu Jose Pedroso Paulo Marcelo Vieira Ribeiro 《Journal of Civil Engineering and Architecture》 2013年第9期1111-1117,共7页
Problems of fluid structure interactions are governed by a set of fundamental parameters. This work aims at showing through simple examples the changes in natural vibration frequencies and mode shapes for wall-cavity ... Problems of fluid structure interactions are governed by a set of fundamental parameters. This work aims at showing through simple examples the changes in natural vibration frequencies and mode shapes for wall-cavity systems when the structural rigidity is modified. Numerical results are constructed using ANSYS software with triangular finite elements for both the fluid (2D acoustic elements) and the solid (plane stress) domains. These former results are compared to proposed analytical expressions, showing an alternative benchmark tool for the analyst. Very rigid wall structures imply in frequencies and mode shapes almost identical to those achieved for an acoustic cavity with Neumann boundary condition at the interface. In this case, the wall behaves as rigid and fluid-structure system mode shapes are similar to those achieved for the uncoupled reservoir case. 展开更多
关键词 Fluid-structure finite element vibration modes acoustic cavities.
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边坡动力响应规律研究 被引量:114
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作者 祁生文 伍法权 孙进忠 《中国科学(E辑)》 CSCD 北大核心 2003年第B12期28-40,共13页
通过大量动力数值分析对边坡动力响应规律进行研究,发现了边坡动力响应的位移、速度、加速度三量放大系数等值线在边坡剖面上分布的节律性特点.对于一定的岩土体材料,当边坡高度在一定范围内时,边坡动力响应的位移、速度、加速度三量在... 通过大量动力数值分析对边坡动力响应规律进行研究,发现了边坡动力响应的位移、速度、加速度三量放大系数等值线在边坡剖面上分布的节律性特点.对于一定的岩土体材料,当边坡高度在一定范围内时,边坡动力响应的位移、速度、加速度三量在铅直方向会出现放大作用,而当边坡高度超过这个范围时,边坡动力响应的三量分布会出现铅直方向的节律性特点.边坡边缘部位对振动的反应幅值较之内部存在放大现象,随着水平深度的进一步增加,位移、速度、加速度三量在水平方向也出现节律性的变化.边坡坡度的变化对位移、速度、加速度放大系数等值线图的分布形式有明显影响,坡度决定了三量分布的等值线方向和极值区的走向.边坡的动力响应图像可以用两个指标刻画,一个是等值线的走向,一个是平行坡面方向的极值个数. 展开更多
关键词 边坡动力响应规律 动力数值分析 位移 速度 加速度 等值线 岩土体材料 节律性特点 单面坡 双面坡 边坡数值模型边界条件
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Numerical study of the flowing sequence of a pouring liquid 被引量:1
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作者 SUN ZhongGuo LIANG YangYang XI Guang 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2011年第8期1514-1519,共6页
Liquid flows in a particular sequence when it is poured out from an open-top receptacle. Since the sequence is hard to catch by experiment, a numerical simulation was performed in this pouring process with the moving ... Liquid flows in a particular sequence when it is poured out from an open-top receptacle. Since the sequence is hard to catch by experiment, a numerical simulation was performed in this pouring process with the moving particle semi-implicit (MPS) method. A modified solid-liquid boundary condition was verified and employed with a new definition of static liquid layers. The whole system was discretized by a set of particles and the liquid particles were marked and tracked in the pouring process. The flowing sequence of the liquid can be calculated by restoring the liquid particles back to their initial positions before it is poured. The mass transfer property is found to depend on the position of the rotation axis and the rotation speed, as well as the viscosity of the liquid. The mechanism of the flowing sequence results from a temporal vortex and its motion during the process. The character vortex is generated by the rotation of the container. The results reveal a principle for a versatile pouring process and may contribute to the applications in flowing control in many fields. 展开更多
关键词 meshless method particle method flowing sequence pouring liquid flow control
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A numerical study of a turbulent mixing layer and its generated noise 被引量:4
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作者 LI Dong GUO Li +1 位作者 ZHANG Xing HE GuoWei 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2013年第6期1157-1164,共8页
A direct numerical simulation of a turbulent mixing layer with the Reynolds number 500 and the convective Mach number 0.6 is performed and the results obtained are used to study the turbulent flow field and its genera... A direct numerical simulation of a turbulent mixing layer with the Reynolds number 500 and the convective Mach number 0.6 is performed and the results obtained are used to study the turbulent flow field and its generated noise.In the present simulation,the numerical techniques of absorbing buffer zones,artificial convection velocity and spatial filtering are used to achieve nonreflecting boundary conditions.The self-similarity is used to validate the present numerical simulations.The large-scale coherent structures are plotted together with the acoustic waves,which demonstrates the directivity of acoustic waves.The Lighthill's source and space-time correlations are further investigated.The main contributions to mixing noise are identified in terms of large-scale coherent structures,Lighthill's source and space-time correlations. 展开更多
关键词 direct numerical simulation mixing layer space-time correlation noise
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Recent advances in regional air-sea coupled models 被引量:6
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作者 PENG ShiQiu LIU DuanLing +1 位作者 SUN ZhaoBo LI YiNeng 《Science China Earth Sciences》 SCIE EI CAS 2012年第9期1391-1405,共15页
In this paper,we first briefly review the history of air-sea coupled models,and then introduce the current status and recent advances of regional air-sea coupled models.In particular,we discuss the core technical and ... In this paper,we first briefly review the history of air-sea coupled models,and then introduce the current status and recent advances of regional air-sea coupled models.In particular,we discuss the core technical and scientific issues involved in the development of regional coupled models,including the coupling technique,lateral boundary conditions,the coupling with sea waves(ices),and data assimilation.Furthermore,we introduce the application of regional coupled models in numerical simulation and dynamical downscaling.Finally,we discuss the existing problems and future directions in the development of regional air-sea coupled models. 展开更多
关键词 regional air-sea coupled models lateral boundary conditions data assimilation COUPLER dynamical downscaling
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Assessment of alternative scale-providing variables in a Reynolds-stress model using high-order methods 被引量:2
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作者 Xiang Fu Shengye Wang Xiaogang Deng 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第12期67-81,共15页
This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes(RANS)equations,which are coupled with the turbulence model equations.Three alternative scale-providing variab... This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes(RANS)equations,which are coupled with the turbulence model equations.Three alternative scale-providing variables for the specific dissipation rate(o)are implemented in the framework of the Reynolds stress model(RSM)for improving its robustness.Specifically,g(=1/√ω)has natural boundary conditions and reduced spatial gradients,and a new numerical constraint is imposed on itω(=lnω)can preserve positivity and also has reduced spatial gradients;the eddy viscosity v,also has natural boundary conditions and its equation is improved in this work.The solution polynomials of the mean-flow and turbulence-model equations are both reconstructed by the weighted compact nonlinear scheme(WCNS).Moreover,several numerical techniques are introduced to improve the numerical stability of the equation system.A range of canonical as well as industrial turbulent flows are simulated to assess the accuracy and robustness of the scale-transformed models.Numerical results show that the scale-transformed models have significantly improved robustness compared to the w model and still keep the characteristics of RSM.Therefore,the high-order discretization of the RANS and RSM equations,which number 12 in total,can be successfully achieved. 展开更多
关键词 Reynolds stress model Weighted compact nonlinear scheme Scale-providing variable ROBUSTNESS
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Simulation of Unsteady Flows with Fluctuating Inflow or Outflow Boundary Conditions
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作者 Jianjun Liu Guanghui ZhongInstitute of Engineering Thermophysics, Chinese Academy of Sciences, P.O. Box 2706, Beijing 100080, China 《Journal of Thermal Science》 SCIE EI CAS CSCD 2003年第2期162-166,共5页
This paper describes the numerical simulation of unsteady flows due to incoming wakes and/or varying back pressure,The solution method is based upon the one-step finite-volume TVD Lax-Wendroff scheme.Dual time-step ap... This paper describes the numerical simulation of unsteady flows due to incoming wakes and/or varying back pressure,The solution method is based upon the one-step finite-volume TVD Lax-Wendroff scheme.Dual time-step approach and multigrid algorithm are adopted to improve the computational efficiency of the baseline scheme.Numerical results for the transonic unsteady flow in a channel bump and the unsteady flow in a flat plate cascade and the VKI cascade are presented. 展开更多
关键词 numerical simulation unsteady flow fluctuating boundary conditions.
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Scaled boundary isogeometric analysis for 2D elastostatics 被引量:6
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作者 LIN Gao ZHANG Yong +1 位作者 HU ZhiQiang ZHONG Hong 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2014年第2期286-300,共15页
A new numerical method,scaled boundary isogeometric analysis(SBIGA)combining the concept of the scaled boundary finite element method(SBFEM)and the isogeometric analysis(IGA),is proposed in this study for 2D elastosta... A new numerical method,scaled boundary isogeometric analysis(SBIGA)combining the concept of the scaled boundary finite element method(SBFEM)and the isogeometric analysis(IGA),is proposed in this study for 2D elastostatic problems with both homogenous and inhomogeneous essential boundary conditions.Scaled boundary isogeometric transformation is established at a specified scaling center with boundary isogeometric representation identical to the design model imported from CAD system,which can be automatically refined without communication with the original system and keeping geometry invariability.The field variable,that is,displacement,is constructed by the same basis as boundary isogeometric description keeping analytical features in radial direction.A Lagrange multiplier scheme is suggested to impose the inhomogeneous essential boundary conditions.The new proposed method holds the semi-analytical feature inherited from SBFEM,that is,discretization only on boundaries rather than the entire domain,and isogeometric boundary geometry from IGA,which further increases the accuracy of the solution.Numerical examples,including circular cavity in full plane,Timoshenko beam with inhomogenous boundary conditions and infinite plate with circular hole subjected to remotely tension,demonstrate that SBIGA can be applied efficiently to elastostatic problems with various boundary conditions,and powerful in accuracy of solution and less degrees of freedom(DOF)can be achieved in SBIGA than other methods. 展开更多
关键词 scaled boundary isogeometric analysis SBFEM IGA ELASTOSTATICS inhomogeneous essential boundary condition
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Numerical Modeling of the Solidification Phase Change in a Pipe and Evaluation of the Effect of Boundary Conditions 被引量:1
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作者 A.Jalali A.F.Najafi 《Journal of Thermal Science》 SCIE EI CAS CSCD 2010年第5期419-424,共6页
A numerical solution to a two-dimensional model of flow and transient heat transfer involving solidification in a pipe has been established.Where the temperature of pipe wall is below the freezing point of fluid,phase... A numerical solution to a two-dimensional model of flow and transient heat transfer involving solidification in a pipe has been established.Where the temperature of pipe wall is below the freezing point of fluid,phase change of flowing fluid and the influence of different boundary condition,such as pipe wall temperature,initial temperature and inlet velocity has been taken into account.Also it has been investigated to elicit proper non-dimensional numbers to show the solidification proceeding results.Additionally comparing the two acceptable inlet conditions,show distinctions between velocity inlet and pressure inlet boundary condition in such problems,which affect the whole freezing process. 展开更多
关键词 Phase change SOLIDIFICATION Heat transfer
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Numerical simulation of cavitating flow around a slender body with slip boundary condition
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作者 Hao Liu DanDan Li +3 位作者 YaHui Xue PengYu Lu YiPeng Shi HuiLing Duan 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2016年第2期85-90,共6页
In this paper, we perform a numerical simulation of the cavitating flow around an underwater hemispherical-head slender body running at a high speed. For the first time, the slip boundary condition is introduced into ... In this paper, we perform a numerical simulation of the cavitating flow around an underwater hemispherical-head slender body running at a high speed. For the first time, the slip boundary condition is introduced into this problem, and we find that the slip boundary condition has a big influence on the cavitation in the flow-separation zone. By simulating the cavitating flow under different cavitation numbers, we demonstrate that the slip boundary condition can effectively reduce the intensity of cavitation, as represented by the length of cavitation bubbles. The present paper provides a new method for utilization of new surface materials to control the cavitation on the underwater moving objects. 展开更多
关键词 cavitating flow slender body slip boundary condition
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A numerical study of the effect of the marginal sea on coastal upwelling in a non-linear inertial model
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作者 CHAO JiPing KANG YanYan LI JianPing 《Science China Earth Sciences》 SCIE EI CAS 2014年第11期2587-2596,共10页
Inertia theory and the finite element method are used to investigate the effect of marginal seas on coastal upwelling. In contrast to much previous research on wind-driven upwelling, this paper does not consider local... Inertia theory and the finite element method are used to investigate the effect of marginal seas on coastal upwelling. In contrast to much previous research on wind-driven upwelling, this paper does not consider localized wind effects, but focuses instead on temperature stratification, the slope of the continental shelf, and the background flow field. Finite element method, which is both faster and more robust than finite difference method in solving problems with complex boundary conditions, was developed to solve the partial differential equations that govern coastal upwelling. Our results demonstrate that the environment of the marginal sea plays an important role in coastal upwelling. First, the background flow at the outer boundary is the main driving force of upwelling. As the background flow strengthens, the overall velocity of cross-shelf flow increases and the horizontal scale of the upwelling front widens, and this is accompanied by the movement of the upwelling front further offshore. Second, temperature stratification determines the direction of cross-shelf flows, with strong stratification favoring a narrow and intense upwelling zone. Third, the slope of the continental shelf plays an important role in controlling the intensity of upwelling and the height that upwelling may reach: the steeper the slope, the lower height of the upwelling. An additional phenomenon that should be noted is upwelling separation, which occurs even without a local wind force in the nonlinear model. 展开更多
关键词 coastal upwelling inertia theory Finite Element Method (FEM)
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Mathematical Modelling and Experimental Investigation of Gas Flow in Minichannels and Microchannels
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作者 Jan Vimmr Hynek Klterka +2 位作者 Marek Hajzman Martin Luxa Rudolf Dvork 《Journal of Thermal Science》 SCIE EI CAS CSCD 2010年第4期289-294,共6页
The first part of this study is focused on the numerical modelling and experimental investigation of transonic flow through a 2D model of the male rotor-housing gap in a dry screw compressor.Numerical simulations of t... The first part of this study is focused on the numerical modelling and experimental investigation of transonic flow through a 2D model of the male rotor-housing gap in a dry screw compressor.Numerical simulations of the clearance flow are performed with the help of the in-house compressible Navier-Stokes solver.Experimental measurements based on the Schlieren method in Toepler configuration are carried out.The objective of the second part of the study is to derive the analytical solution of gas microflow development in a gap between two parallel plates.The microflow is assumed to be laminar,incompressible and the velocity slip boundary conditions are considered at the walls.The constant velocity profile is prescribed at the inlet.For the mathematical description of the problem,the Oseen equation is used.The analytical results are compared with the numerical ones obtained using the developed incompressible Navier-Stokes solver including the slip flow boundary conditions. 展开更多
关键词 clearance gap transonic flow compressible Navier-Stokes solver mieroflow development Oseen flow model analytical solution incompressible Navier-Stokes solver
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