There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle th...There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.展开更多
Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary condi...Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.展开更多
Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different a...Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different advance coefficients of DTMB 4119, 4382, and 4384 propellers were calculated.The pressure coefficient distribution of the DTMB 4119 propeller at different sections was also physically tested.Comparisons indicated good agreement between the results of experiments and the simulation.It showed that the periodic boundary condition can be used to rationally predict the open water performance of a propeller.By analyzing the three established modes for the computation, it was shown that using the spline curve method to divide the grids can meet the calculation's demands for precision better than using the rake cutting method.展开更多
The velocity structure of the residual current across an entire section of the Qiongzhou Strait(QS) in summer is presented for the fi rst time. Shipboard Acoustic Doppler Current Profi le measurements, from the mid-re...The velocity structure of the residual current across an entire section of the Qiongzhou Strait(QS) in summer is presented for the fi rst time. Shipboard Acoustic Doppler Current Profi le measurements, from the mid-region of the QS(110.18°E), were collected on 1–4 August 2010. The diurnal tidal currents had their maximum amplitudes between 4.24 and 20.24 m. Their amplitude along the major axis ranged from approximately 0.55 m/s in the middle part of the strait(20.15°N) to 0.84 m/s in the north part of the strait(20.20°N). Both anticlockwise and clockwise tidal current rotations exist in the QS. During the observation period(neap tide), a signifi cant westward residual current occupied almost the entire study section. Two velocity cores of westward current were observed at the northern part and near the deepest trough, although an eastward current appeared in the middle part of the transect. The deepest core was located near 62 m at 20.13°N, with a maximum velocity of-0.34 m/s. The shallower core was located at approximately 16 m at 20.20°N, with a maximum velocity of-0.33 m/s. The estimated total volume of water transported through the QS was-0.16 Sv. This value is an important boundary condition, applicable to numerical models studying coastal ocean circulation in the northwestern South China Sea.展开更多
An OGCM, LICOM2.0, was used to investigate the effects of different surface boundary conditions for sea surface salinity （SSS） on simulations of global mean salinity, SSS, and the Atlantic Meridional Overturning Cir...An OGCM, LICOM2.0, was used to investigate the effects of different surface boundary conditions for sea surface salinity （SSS） on simulations of global mean salinity, SSS, and the Atlantic Meridional Overturning Circulation （AMOC）. Four numerical experiments （CTRL, Expl, Exp2 and Exp3） were designed with the same forcing data-set, CORE.v2, and different surface boundary conditions for SSS~ A new surface salinity boundary condition that consists of both virtual and real salt fluxes was adopted in the fourth experiment （Exp3）. Compared with the other experiments, the new salinity boundary condition prohibited a monotonous increasing or decreasing global mean salinity trend. As a result, global salinity was approximately conserved in EXP3. In the default salinity boundary condition setting in LICOM2.0, a weak restoring salinity term plays an essential role in reducing the simulated SSS bias, tending to increase the global mean salinity. However, a strong restoring salinity term under the sea ice can reduce the global mean salinity. The authors also found that adopting simulated SSS in the virtual salt flux instead of constant reference salinity improved the simulation of AMOC, whose strength became closer to that observed.展开更多
An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different fr...An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.展开更多
This paper presents a review of the work on fluid/structure impact based on inviscid and imcompressible liquid and irrotational flow. The focus is on the velocity potential theory together with boundary element method...This paper presents a review of the work on fluid/structure impact based on inviscid and imcompressible liquid and irrotational flow. The focus is on the velocity potential theory together with boundary element method （BEM）. Fully nonlinear boundary conditions are imposed on the unknown free surface and the wetted surface of the moving body. The review includes （1） vertical and oblique water entry of a body at constant or a prescribed varying speed, as well as free fall motion, （2） liquid droplets or column impact as well as wave impact on a body, （3） similarity solution of an expanding body. It covers two dimensional （2D）, axisymmetric and three dimensional （3D） cases. Key techniques used in the numerical simulation are outlined, including mesh generation on the multivalued free surface, the stretched coordinate system for expanding domain, the auxiliary function method for decoupling the mutual dependence of the pressure and the body motion, and treatment for the jet or the thin liquid film developed during impact.展开更多
In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simula- tion for the skin friction and heat flux, a research was performed to improve the compress...In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simula- tion for the skin friction and heat flux, a research was performed to improve the compressible wall function boundary condition proposed by Nichols. Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation. Be- sides, the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately. Whereafter, the application study of the modified wall func- tion was carried out. The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux, and profiles of velocity, temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y＋〈400, and that the modifications to the original wall function can obviously improve the simulation precision. As for the application of separation flows, it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression comer that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall re- gion inside the separation flows, which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows, while for the region near separation and reattachment points, the wall function gives results with a rela- tively large error, because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real ve- locity profiles near the separation and reattachment points.展开更多
In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Sto...In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.展开更多
Soil moisture has a significant influence on water, energy, and carbon biogeochemical cycles. A numerical method for solving Richards＇ equation is usually used for simulating soil moisture. Selection of a lower bound...Soil moisture has a significant influence on water, energy, and carbon biogeochemical cycles. A numerical method for solving Richards＇ equation is usually used for simulating soil moisture. Selection of a lower boundary condition for Richards＇ equation will further affect the simulation results for soil moisture, water cycle, energy balance, and carbon biogeochemical processes. In this study, the soil water movement dynamic sub-model of a hydrologically based land surface model, the variable infiltration capacity （VIC） model, was modified using the finite difference method （FDM） to solve a mixed form of Richards＇ equation. In addition, the VIC model was coupled with a terrestrial biogeochemical model, the Carnegie Ames Stanford Approach model of carbon, nitrogen, and phosphorus （CASACNP model）. The no-flux boundary （NB） and free-drainage boundary （FB） were selected to investigate their impacts on simulations of the water, energy, and soil carbon cycles based on the coupling model. The NB and FB had different influences on the water, energy, and soil carbon simulations. The water and energy simulations were more sensitive, while the soil carbon simulation was less sensitive to FB than to NB. Free-drainage boundary could result in lower soil moisture, evaporation, runoff, and heterotrophic respiration and higher surface soil temperature, sensible heat flux, and soil carbon content. The impact of the lower boundary condition on simulation would be greater with an increase in soil permeability. In the silt loam soil case, evaporation, runoff, and soil respiration of FB were nearly 169, 13%, and 1% smaller, respectively, compared to those of NB.展开更多
In two dimensions, we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions. As shown by Ding et al. （2013）, when the parameter λ→∞ oo, the solutions to the compressible li...In two dimensions, we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions. As shown by Ding et al. （2013）, when the parameter λ→∞ oo, the solutions to the compressible liquid crystal system approximate that of the incompressible one. Furthermore, Ding et al. （2013） proved that the regular incompressible limit solution is global in time with small enough initial data. In this paper, we show that the solution to the compressible liquid crystal flow also exists for all time, provided that is sufficiently large and the initial data are almost incompressible.展开更多
文摘There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.
文摘Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.
基金Supported by the National Natural Science Foundation of China under Grant No.10702016
文摘Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different advance coefficients of DTMB 4119, 4382, and 4384 propellers were calculated.The pressure coefficient distribution of the DTMB 4119 propeller at different sections was also physically tested.Comparisons indicated good agreement between the results of experiments and the simulation.It showed that the periodic boundary condition can be used to rationally predict the open water performance of a propeller.By analyzing the three established modes for the computation, it was shown that using the spline curve method to divide the grids can meet the calculation's demands for precision better than using the rake cutting method.
基金Supported by the National Natural Science Foundation for Young Scientists of China(No.40806012)
文摘The velocity structure of the residual current across an entire section of the Qiongzhou Strait(QS) in summer is presented for the fi rst time. Shipboard Acoustic Doppler Current Profi le measurements, from the mid-region of the QS(110.18°E), were collected on 1–4 August 2010. The diurnal tidal currents had their maximum amplitudes between 4.24 and 20.24 m. Their amplitude along the major axis ranged from approximately 0.55 m/s in the middle part of the strait(20.15°N) to 0.84 m/s in the north part of the strait(20.20°N). Both anticlockwise and clockwise tidal current rotations exist in the QS. During the observation period(neap tide), a signifi cant westward residual current occupied almost the entire study section. Two velocity cores of westward current were observed at the northern part and near the deepest trough, although an eastward current appeared in the middle part of the transect. The deepest core was located near 62 m at 20.13°N, with a maximum velocity of-0.34 m/s. The shallower core was located at approximately 16 m at 20.20°N, with a maximum velocity of-0.33 m/s. The estimated total volume of water transported through the QS was-0.16 Sv. This value is an important boundary condition, applicable to numerical models studying coastal ocean circulation in the northwestern South China Sea.
基金partially supported by the National Basic Research Program of China[grant number 2013CB956204]the Strategic Priority Research Program of the Chinese Academy of Sciences[grant number XDA11010403],[grant number XDA11010304]the National Natural Science Foundation of China[grant number 41305028]
文摘An OGCM, LICOM2.0, was used to investigate the effects of different surface boundary conditions for sea surface salinity （SSS） on simulations of global mean salinity, SSS, and the Atlantic Meridional Overturning Circulation （AMOC）. Four numerical experiments （CTRL, Expl, Exp2 and Exp3） were designed with the same forcing data-set, CORE.v2, and different surface boundary conditions for SSS~ A new surface salinity boundary condition that consists of both virtual and real salt fluxes was adopted in the fourth experiment （Exp3）. Compared with the other experiments, the new salinity boundary condition prohibited a monotonous increasing or decreasing global mean salinity trend. As a result, global salinity was approximately conserved in EXP3. In the default salinity boundary condition setting in LICOM2.0, a weak restoring salinity term plays an essential role in reducing the simulated SSS bias, tending to increase the global mean salinity. However, a strong restoring salinity term under the sea ice can reduce the global mean salinity. The authors also found that adopting simulated SSS in the virtual salt flux instead of constant reference salinity improved the simulation of AMOC, whose strength became closer to that observed.
基金Project(41074085)supported by the National Natural Science Foundation of ChinaProject(NCET-12-0551)supported by the Funds for New Century Excellent Talents in University,ChinaProject supported by Shenghua Yuying Program of Central South University,China
文摘An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.
基金Foundation item： Supported by the National Natural Science Foundation of China （Grant Nos. 11302057, 11302056）, the Fundamental Research Funds for the Central Universities （Grant No. HEUCF140115） and the Research Funds for State Key Laboratory of Ocean Engineering in Shanghai Jiao Tong University （Grant No. 1310）.
文摘This paper presents a review of the work on fluid/structure impact based on inviscid and imcompressible liquid and irrotational flow. The focus is on the velocity potential theory together with boundary element method （BEM）. Fully nonlinear boundary conditions are imposed on the unknown free surface and the wetted surface of the moving body. The review includes （1） vertical and oblique water entry of a body at constant or a prescribed varying speed, as well as free fall motion, （2） liquid droplets or column impact as well as wave impact on a body, （3） similarity solution of an expanding body. It covers two dimensional （2D）, axisymmetric and three dimensional （3D） cases. Key techniques used in the numerical simulation are outlined, including mesh generation on the multivalued free surface, the stretched coordinate system for expanding domain, the auxiliary function method for decoupling the mutual dependence of the pressure and the body motion, and treatment for the jet or the thin liquid film developed during impact.
基金supported by the National Natural Science Foundation of China(Grant No.11202014)
文摘In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simula- tion for the skin friction and heat flux, a research was performed to improve the compressible wall function boundary condition proposed by Nichols. Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation. Be- sides, the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately. Whereafter, the application study of the modified wall func- tion was carried out. The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux, and profiles of velocity, temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y＋〈400, and that the modifications to the original wall function can obviously improve the simulation precision. As for the application of separation flows, it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression comer that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall re- gion inside the separation flows, which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows, while for the region near separation and reattachment points, the wall function gives results with a rela- tively large error, because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real ve- locity profiles near the separation and reattachment points.
基金supported by the National High-Tech Research and Development Program of China (No.2009AA01A135)the National Natural Science Foundation of China (Nos. 10926080, 10971165, 10871156)Xian Jiaotong University (No. XJJ2008033)
文摘In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.
基金supported by the National Science Foundation for Distinguished Young Scholars of China (No. 51309245)supported by the US Department of Energy and National Aeronautics and Space Administration
文摘Soil moisture has a significant influence on water, energy, and carbon biogeochemical cycles. A numerical method for solving Richards＇ equation is usually used for simulating soil moisture. Selection of a lower boundary condition for Richards＇ equation will further affect the simulation results for soil moisture, water cycle, energy balance, and carbon biogeochemical processes. In this study, the soil water movement dynamic sub-model of a hydrologically based land surface model, the variable infiltration capacity （VIC） model, was modified using the finite difference method （FDM） to solve a mixed form of Richards＇ equation. In addition, the VIC model was coupled with a terrestrial biogeochemical model, the Carnegie Ames Stanford Approach model of carbon, nitrogen, and phosphorus （CASACNP model）. The no-flux boundary （NB） and free-drainage boundary （FB） were selected to investigate their impacts on simulations of the water, energy, and soil carbon cycles based on the coupling model. The NB and FB had different influences on the water, energy, and soil carbon simulations. The water and energy simulations were more sensitive, while the soil carbon simulation was less sensitive to FB than to NB. Free-drainage boundary could result in lower soil moisture, evaporation, runoff, and heterotrophic respiration and higher surface soil temperature, sensible heat flux, and soil carbon content. The impact of the lower boundary condition on simulation would be greater with an increase in soil permeability. In the silt loam soil case, evaporation, runoff, and soil respiration of FB were nearly 169, 13%, and 1% smaller, respectively, compared to those of NB.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11001085,11071086 and 11128102)+2 种基金the University Special Research Foundation for PhD Program(Grant No.20104407110002)the PhD Programs Foundation of Ministry of Education of China(Grant No.20100172120026)the Fundamental Research Funds for the Central Universities(Grant No.2012ZZ0075)
文摘In two dimensions, we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions. As shown by Ding et al. （2013）, when the parameter λ→∞ oo, the solutions to the compressible liquid crystal system approximate that of the incompressible one. Furthermore, Ding et al. （2013） proved that the regular incompressible limit solution is global in time with small enough initial data. In this paper, we show that the solution to the compressible liquid crystal flow also exists for all time, provided that is sufficiently large and the initial data are almost incompressible.
