Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data imm...Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data immersion method(BDIM)for compressible flows,which were solved using a fully self-programmed Fortran code.Results show that the predicted thrust spectrum aligns closely with the experimental measurements.In addition,it captures the thrust dipole directivity of the noise around the rotating propeller due to random pressure pulsations on the blades,as well as the flow structures simultaneously.Furthermore,the differences in the statistical characteristics,flow structures,and low-frequency broadband thrust spectra due to different turbulence levels were investigated.This analysis indicates that the interaction between the upstream,which is characterized by a lower turbulence level and a higher turbulent length of scale,and the rotating propeller results in a lower amplitude in force spectra and a slight increase in the scale of tip vortices.展开更多
In this paper, an identification method to estimate the unbalances is introduced, which is based on the boundary element method (BEM). By using the vibration response measured at some points on the flexible rotor the ...In this paper, an identification method to estimate the unbalances is introduced, which is based on the boundary element method (BEM). By using the vibration response measured at some points on the flexible rotor the unbalances can be identified conveniently. Therefore, the rotor can be balanced without test runs.展开更多
The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （B...The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.展开更多
In order to obtain a high-quality weld during the laser welding process, extracting the characteristic parameters of weld pool is an important issue for automated welding. In this paper, the type 304 austenitic stainl...In order to obtain a high-quality weld during the laser welding process, extracting the characteristic parameters of weld pool is an important issue for automated welding. In this paper, the type 304 austenitic stainless steel is welded by a 5 kW high-power fiber laser and a high-speed camera is employed to capture the topside images of weld pools. Then we propose a robust visual-detection approach for the molten pool based on the supervised descent method. It provides an elegant framework for representing the outline of a weld pool and is especially efficient for weld pool detection in the presence of strong uncertainties and disturbances. Finally, welding experimental results verified that the proposed approach can extract the weld pool boundary accurately, which will lay a solid foundation for controlling the weld quality of fiber laser welding process.展开更多
The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious o...The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious outside boundary of the physical domain of interest. In this study, the BKM is first used to calculate the free vibration of free and simply-upported thin plates. Compared with the analytical solution and ANSYS （a commercial FEM code） results, the present BKM is highly accurate and fast convergent.展开更多
To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced v...To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced velocities and gap spacing to observe flow-induced vibrations(FIVs).The immersed boundary–lattice Boltzmann flux solver(IB–LBFS)was applied as a numerical solution method,allowing for straightforward application on a simple Cartesian mesh.The accuracy and rationality of this method have been verified through comparisons with previous numerical results,including studies on flow past three stationary circular cylinders arranged in a similar pattern and vortex-induced vibrations of a single cylinder across different reduced velocities.When examining the FIVs of three cylinders,numerical simulations were carried out across a range of reduced velocities(3.0≤Ur≤13.0)and gap spacing(L=3D,4D,and 5D).The observed vibration response included several regimes:the desynchronization regime,the initial branch,and the lower branch.Notably,the transverse amplitude peaked,and a double vortex street formed in the wake when the reduced velocity reached the lower branch.This arrangement of three cylinders proved advantageous for energy capture as the upstream cylinder’s vibration response mirrored that of an isolated cylinder,while the response of each downstream cylinder was significantly enhanced.Compared to a single cylinder,the vibration and flow characteristics of this system are markedly more complex.The maximum transverse amplitudes of the downstream cylinders are nearly identical and exceed those observed in a single-cylinder set-up.Depending on the gap spacing,the flow pattern varied:it was in-phase for L=3D,antiphase for L=4D,and exhibited vortex shedding for L=5D.The wake configuration mainly featured double vortex streets for L=3D and evolved into two pairs of double vortex streets for L=5D.Consequently,it well illustrates the coupling mechanism that dynamics characteristics and wake vortex change with gap spacing and reduced velocities.展开更多
A method combining the immersed boundary technique and a multi- relaxation-time （MRT） lattice Boltzmann flux solver （LBFS） is presented for numerical simulation of incompressible flows over circular and elliptic c...A method combining the immersed boundary technique and a multi- relaxation-time （MRT） lattice Boltzmann flux solver （LBFS） is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations （LBEs）. The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.展开更多
A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first e...A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.展开更多
A scientific delineation of geographical boundaries reflects the cognitive level of scientific abstraction and systematic analysis of the spatial variation of geographical objects and is a basic scientific issue of ge...A scientific delineation of geographical boundaries reflects the cognitive level of scientific abstraction and systematic analysis of the spatial variation of geographical objects and is a basic scientific issue of geography. From the perspective of earth system science,this study first explicates the core issues(e.g., basic concepts, scientific contents, and basic properties) of geographical boundaries. Based on the principles of scientificity and systematicness, we then classify geographical boundaries in terms of intrinsic mechanisms, extrinsic appearance and scientific attributes. Furthermore, this paper analyzes the mathematical connotation and representation methods of geographical boundaries, discusses the characteristics of and differences between traditional and modern methods for geographical boundary delineation. Finally, we present a framework for a “geographical boundary model”with an integration of qualitative, quantitative, and positioning methods. Focusing on geographical boundary(a basic theoretical problem in geography), this study engaged in concept definition and method analysis, with the findings enriching the theory and methodology of geographical information science.展开更多
Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved ...Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.展开更多
The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mes...The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mesh,while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field.The boundary condition is implemented by introducing a force term into the momentum equation,and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process.Over the past decades,the diffuse-interface IBM has gained popularity and spawned many variants,effectively handling a wide range of flow problems from isothermal to thermal flows,from laminar to turbulent flows,and from complex geometries to fluidstructure interaction scenarios.This paper first outlines the basic principles of the diffuse-interface IBM,then highlights recent advancements achieved by the authors’research group,and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.展开更多
The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through...The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.展开更多
The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary....The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary.Therefore,this method has the merits of purely meshless,easy to program,high solution accuracy and so on.In this paper,we investigate the effectiveness of the BKM for solving Helmholtz-type problems under various conditions through a series of novel numerical experiments.The results demonstrate that the BKM is efficient and achieves high computational accuracy for problems with smooth or continuous boundary conditions.However,when applied to discontinuous boundary problems,the method exhibits significant numerical instability,potentially leading to substantial deviations in the computed results.Finally,three potential improvement strategies are proposed to mitigate this limitation.展开更多
This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic...This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic simulations and its high computational cost in broadband problems are examined.To improve efficiency,a Taylor series expansion is applied to decouple frequency-dependent terms in BEM.Additionally,the SecondOrder Arnoldi(SOAR)model order reduction method is integrated to reduce computational costs and enhance numerical stability.Furthermore,an isogeometric sensitivity boundary integral equation is formulated using the direct differentiation method,incorporating Cauchy principal value integrals and Hadamard finite part integrals to handle singularities.The proposed method improves the computational efficiency,and the acoustic sensitivity analysis provides theoretical support for further acoustic structure optimization.展开更多
Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the chall...Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the challenge of being computationally overpowered.This study proposes an efficient fracturing simulator to analyze fracture morphology during hydraulic fracturing processes in deep shale gas reservoirs.The simulator integrates the boundary element displacement discontinuity method and the finite volume method to model the fluid-solid coupling process by employing a pseudo-3D fracture model to calculate the fracture height.In particular,the Broyden iteration method was introduced to improve the computational efficiency and model robustness;it achieved a 46.6%reduction in computation time compared to the Newton-Raphson method.The influences of horizontal stress differences,natural fracture density,and natural fracture angle on the modified zone of the reservoir were simulated,and the following results were observed.(1)High stress difference reservoirs have smaller stimulated reservoir area than low stress difference reservoirs.(2)A higher natural fracture angle resulted in larger modification zones at low stress differences,while the effect of a natural fracture angle at high stress differences was not significant.(3)High-density and long natural fracture zones played a significant role in enhancing the stimulated reservoir area.These findings are critical for comprehending the impact of geological parameters on deep shale reservoirs.展开更多
A Discrete Boltzmann Method(DBM)with a Maxwell-type boundary condition is constructed to investigate the influence of rarefaction on laminar Shock Wave/Boundary Layer Interaction(SWBLI).Due to the complexity of compre...A Discrete Boltzmann Method(DBM)with a Maxwell-type boundary condition is constructed to investigate the influence of rarefaction on laminar Shock Wave/Boundary Layer Interaction(SWBLI).Due to the complexity of compressible flow,a Knudsen number vector Kn,whose components include the local Knudsen numbers such as Kn_(ρ)and Kn_(U),is introduced to characterize the local structures,where Kn_(ρ)and Kn_(U)are Knudsen numbers defined in terms of the density and velocity interfaces,respectively.Since first focusing on the steady state of SWBLI,the DBM considers up to the second-order Kn_(ρ)(rarefaction/non-equilibrium)effects.The model is validated using Mach number 2 SWBLI and the necessity of using DBM with sufficient physical accuracy is confirmed by the shock collision problem.Key findings include the following:the leading-edge shock wave increases the local density Knudsen number Kn_(ρ)and eventually leads to the failure of linear constitutive relations in the Navier-Stokes(N-S)model and surely also in the lower-order DBM;the non-equilibrium effect differences in regions behind the leading-edge shock wave are primarily correlated with Kn_(ρ),while in the separation region are primarily correlated with Kn_(U);the non-equilibrium quantities D_(2)and D_(4,2),as well as the viscous entropy production rate S_(NOMF)can be used to identify the separation zone.The findings clarify various effects and main mechanisms in different regions associated with SWBLI,which are concealed in N-S model.展开更多
The boundary dement method was improved for the 2D elastic composites with randomly distributed inclusions. This problem can be reduced to a boundary integral equation for a multi-connected domain. Further, considerin...The boundary dement method was improved for the 2D elastic composites with randomly distributed inclusions. This problem can be reduced to a boundary integral equation for a multi-connected domain. Further, considering the matrices of the tractions and displacements for each group of the identical inclusion were the same, an effective computational scheme was designed, since the orders of the resulting matrix equations can be greatly reduced. Numerical examples indicate that this boundary element method scheme is more effective than the conventional multi-domain boundary element method for such a problem. The present scheme can be used to investigate the effective mechanical properties of the fiber-reinforced composites.展开更多
A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in freque...A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in frequency domain and transformed into boundary integralequations. An appropriate fundamental solution for the Helmholtzequation with pure imaginary constant is found. The condition ofzero-stress is imposed on the free surface, and non-slip condition offluid particles is Imposed on the walls of the container. For rigidmotion models, the expressions for added mass and Added damping tothe structural motion equations are obtained. Some typical numericalexamples are Presented.展开更多
In this paper, an efficient multigrid fictitious boundary method （MFBM） coupled with the FEM solver package FEATFLOW was used for the detailed simulation of incompressible viscous flows around one or more moving NAC...In this paper, an efficient multigrid fictitious boundary method （MFBM） coupled with the FEM solver package FEATFLOW was used for the detailed simulation of incompressible viscous flows around one or more moving NACA0012 airfoils. The calculations were carded on a fixed multigrid finite element mesh on which fluid equations were satisfied everywhere, and the airfoils were allowed to move freely through the mesh. The MFBM was employed to treat interactions between the fluid and the airfoils The motion of the airfoils was modeled by Newton-Euler equations. Numerical results of experiments verify that this method provides an efficient way to simulate incompressible viscous flows around moving airfoils.展开更多
A new and computationally efficient version of the immersed boundary method,which is combined with the coarse-graining method,is introduced for modeling inextensible filaments immersed in low-Reynolds number flows.Thi...A new and computationally efficient version of the immersed boundary method,which is combined with the coarse-graining method,is introduced for modeling inextensible filaments immersed in low-Reynolds number flows.This is used to represent actin biopolymers,which are constituent elements of the cytoskeleton,a complex network-like structure that plays a fundamental role in shape morphology.An extension of the traditional immersed boundary method to include a stochastic stress tensor is also proposed in order to model the thermal fluctuations in the fluid at smaller scales.By way of validation,the response of a single,massless,inextensible semiflexible filament immersed in a thermally fluctuating fluid is obtained using the suggested numerical scheme and the resulting time-averaged contraction of the filament is compared to the theoretical value obtained from the worm-like chain model.展开更多
基金Supported by the National Key R&D Program of China(2022YFB3303500).
文摘Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data immersion method(BDIM)for compressible flows,which were solved using a fully self-programmed Fortran code.Results show that the predicted thrust spectrum aligns closely with the experimental measurements.In addition,it captures the thrust dipole directivity of the noise around the rotating propeller due to random pressure pulsations on the blades,as well as the flow structures simultaneously.Furthermore,the differences in the statistical characteristics,flow structures,and low-frequency broadband thrust spectra due to different turbulence levels were investigated.This analysis indicates that the interaction between the upstream,which is characterized by a lower turbulence level and a higher turbulent length of scale,and the rotating propeller results in a lower amplitude in force spectra and a slight increase in the scale of tip vortices.
文摘In this paper, an identification method to estimate the unbalances is introduced, which is based on the boundary element method (BEM). By using the vibration response measured at some points on the flexible rotor the unbalances can be identified conveniently. Therefore, the rotor can be balanced without test runs.
基金Project supported by the National Natural Science Foundation of China (Grant No 10871124)Innovation Program of Shanghai Municipal Education Commission (Grant No 09ZZ99)Shanghai Leading Academic Discipline Project (Grant No J50103)
文摘The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.
基金Project was supported by the National Key R&D Program of China(Grant No.2017YFB1104404)
文摘In order to obtain a high-quality weld during the laser welding process, extracting the characteristic parameters of weld pool is an important issue for automated welding. In this paper, the type 304 austenitic stainless steel is welded by a 5 kW high-power fiber laser and a high-speed camera is employed to capture the topside images of weld pools. Then we propose a robust visual-detection approach for the molten pool based on the supervised descent method. It provides an elegant framework for representing the outline of a weld pool and is especially efficient for weld pool detection in the presence of strong uncertainties and disturbances. Finally, welding experimental results verified that the proposed approach can extract the weld pool boundary accurately, which will lay a solid foundation for controlling the weld quality of fiber laser welding process.
基金supported by the National Natural Science Foundation of China(No.10672051).
文摘The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious outside boundary of the physical domain of interest. In this study, the BKM is first used to calculate the free vibration of free and simply-upported thin plates. Compared with the analytical solution and ANSYS （a commercial FEM code） results, the present BKM is highly accurate and fast convergent.
基金Supported by the National Natural Science Foundation of China(52201350,52201394,and 52271301)the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(Grant No.SML2022008).
文摘To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced velocities and gap spacing to observe flow-induced vibrations(FIVs).The immersed boundary–lattice Boltzmann flux solver(IB–LBFS)was applied as a numerical solution method,allowing for straightforward application on a simple Cartesian mesh.The accuracy and rationality of this method have been verified through comparisons with previous numerical results,including studies on flow past three stationary circular cylinders arranged in a similar pattern and vortex-induced vibrations of a single cylinder across different reduced velocities.When examining the FIVs of three cylinders,numerical simulations were carried out across a range of reduced velocities(3.0≤Ur≤13.0)and gap spacing(L=3D,4D,and 5D).The observed vibration response included several regimes:the desynchronization regime,the initial branch,and the lower branch.Notably,the transverse amplitude peaked,and a double vortex street formed in the wake when the reduced velocity reached the lower branch.This arrangement of three cylinders proved advantageous for energy capture as the upstream cylinder’s vibration response mirrored that of an isolated cylinder,while the response of each downstream cylinder was significantly enhanced.Compared to a single cylinder,the vibration and flow characteristics of this system are markedly more complex.The maximum transverse amplitudes of the downstream cylinders are nearly identical and exceed those observed in a single-cylinder set-up.Depending on the gap spacing,the flow pattern varied:it was in-phase for L=3D,antiphase for L=4D,and exhibited vortex shedding for L=5D.The wake configuration mainly featured double vortex streets for L=3D and evolved into two pairs of double vortex streets for L=5D.Consequently,it well illustrates the coupling mechanism that dynamics characteristics and wake vortex change with gap spacing and reduced velocities.
文摘A method combining the immersed boundary technique and a multi- relaxation-time （MRT） lattice Boltzmann flux solver （LBFS） is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations （LBEs）. The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.
基金the support from the National Natural Science Foundation of China(Grants 12022209,11972103,and 11825202)the Liaoning Revitalization Talents Program of China(Grant XLYC1807126)the Fundamental Research Funds for the Central Universities(Grant DUT21LAB124).
文摘A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.
基金National Natural Science Foundation of China,No.41930102。
文摘A scientific delineation of geographical boundaries reflects the cognitive level of scientific abstraction and systematic analysis of the spatial variation of geographical objects and is a basic scientific issue of geography. From the perspective of earth system science,this study first explicates the core issues(e.g., basic concepts, scientific contents, and basic properties) of geographical boundaries. Based on the principles of scientificity and systematicness, we then classify geographical boundaries in terms of intrinsic mechanisms, extrinsic appearance and scientific attributes. Furthermore, this paper analyzes the mathematical connotation and representation methods of geographical boundaries, discusses the characteristics of and differences between traditional and modern methods for geographical boundary delineation. Finally, we present a framework for a “geographical boundary model”with an integration of qualitative, quantitative, and positioning methods. Focusing on geographical boundary(a basic theoretical problem in geography), this study engaged in concept definition and method analysis, with the findings enriching the theory and methodology of geographical information science.
基金support of this work by the National Natural Science Foundation of China(No.51405096)the Fundamental Research Funds for the Central Universities(HEUCF210710).
文摘Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.
基金partially supported by the National Natural Science Foundation of China(Nos.92271103,12202191)。
文摘The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mesh,while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field.The boundary condition is implemented by introducing a force term into the momentum equation,and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process.Over the past decades,the diffuse-interface IBM has gained popularity and spawned many variants,effectively handling a wide range of flow problems from isothermal to thermal flows,from laminar to turbulent flows,and from complex geometries to fluidstructure interaction scenarios.This paper first outlines the basic principles of the diffuse-interface IBM,then highlights recent advancements achieved by the authors’research group,and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.
基金supported by the National Natural Science Foundation of China(Grant 12472113).
文摘The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.
基金Supported by the Key Scientific Research Plan of Colleges and Universities in Henan Province(23B140006)。
文摘The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary.Therefore,this method has the merits of purely meshless,easy to program,high solution accuracy and so on.In this paper,we investigate the effectiveness of the BKM for solving Helmholtz-type problems under various conditions through a series of novel numerical experiments.The results demonstrate that the BKM is efficient and achieves high computational accuracy for problems with smooth or continuous boundary conditions.However,when applied to discontinuous boundary problems,the method exhibits significant numerical instability,potentially leading to substantial deviations in the computed results.Finally,three potential improvement strategies are proposed to mitigate this limitation.
基金supported by the Shanxi Scholarship Council of China(Grant No.2023-036)the Natural Science Foundation of Shanxi Province(Grant No.202303021222020).
文摘This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic simulations and its high computational cost in broadband problems are examined.To improve efficiency,a Taylor series expansion is applied to decouple frequency-dependent terms in BEM.Additionally,the SecondOrder Arnoldi(SOAR)model order reduction method is integrated to reduce computational costs and enhance numerical stability.Furthermore,an isogeometric sensitivity boundary integral equation is formulated using the direct differentiation method,incorporating Cauchy principal value integrals and Hadamard finite part integrals to handle singularities.The proposed method improves the computational efficiency,and the acoustic sensitivity analysis provides theoretical support for further acoustic structure optimization.
文摘Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the challenge of being computationally overpowered.This study proposes an efficient fracturing simulator to analyze fracture morphology during hydraulic fracturing processes in deep shale gas reservoirs.The simulator integrates the boundary element displacement discontinuity method and the finite volume method to model the fluid-solid coupling process by employing a pseudo-3D fracture model to calculate the fracture height.In particular,the Broyden iteration method was introduced to improve the computational efficiency and model robustness;it achieved a 46.6%reduction in computation time compared to the Newton-Raphson method.The influences of horizontal stress differences,natural fracture density,and natural fracture angle on the modified zone of the reservoir were simulated,and the following results were observed.(1)High stress difference reservoirs have smaller stimulated reservoir area than low stress difference reservoirs.(2)A higher natural fracture angle resulted in larger modification zones at low stress differences,while the effect of a natural fracture angle at high stress differences was not significant.(3)High-density and long natural fracture zones played a significant role in enhancing the stimulated reservoir area.These findings are critical for comprehending the impact of geological parameters on deep shale reservoirs.
基金support from the National Key R&D Program of China(No.2020YFC2201100)the Foundation of National Key Laboratory of Shock Wave and Detonation Physics,China(No.JCKYS2023212003)+1 种基金the National Natural Science Foundation of China(No.12172061)the Opening Project of State Key Laboratory of Explosion Science and Safety Protection(Beijing Institute of Technology)(No.KFJJ25-02M).
文摘A Discrete Boltzmann Method(DBM)with a Maxwell-type boundary condition is constructed to investigate the influence of rarefaction on laminar Shock Wave/Boundary Layer Interaction(SWBLI).Due to the complexity of compressible flow,a Knudsen number vector Kn,whose components include the local Knudsen numbers such as Kn_(ρ)and Kn_(U),is introduced to characterize the local structures,where Kn_(ρ)and Kn_(U)are Knudsen numbers defined in terms of the density and velocity interfaces,respectively.Since first focusing on the steady state of SWBLI,the DBM considers up to the second-order Kn_(ρ)(rarefaction/non-equilibrium)effects.The model is validated using Mach number 2 SWBLI and the necessity of using DBM with sufficient physical accuracy is confirmed by the shock collision problem.Key findings include the following:the leading-edge shock wave increases the local density Knudsen number Kn_(ρ)and eventually leads to the failure of linear constitutive relations in the Navier-Stokes(N-S)model and surely also in the lower-order DBM;the non-equilibrium effect differences in regions behind the leading-edge shock wave are primarily correlated with Kn_(ρ),while in the separation region are primarily correlated with Kn_(U);the non-equilibrium quantities D_(2)and D_(4,2),as well as the viscous entropy production rate S_(NOMF)can be used to identify the separation zone.The findings clarify various effects and main mechanisms in different regions associated with SWBLI,which are concealed in N-S model.
文摘The boundary dement method was improved for the 2D elastic composites with randomly distributed inclusions. This problem can be reduced to a boundary integral equation for a multi-connected domain. Further, considering the matrices of the tractions and displacements for each group of the identical inclusion were the same, an effective computational scheme was designed, since the orders of the resulting matrix equations can be greatly reduced. Numerical examples indicate that this boundary element method scheme is more effective than the conventional multi-domain boundary element method for such a problem. The present scheme can be used to investigate the effective mechanical properties of the fiber-reinforced composites.
文摘A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in frequency domain and transformed into boundary integralequations. An appropriate fundamental solution for the Helmholtzequation with pure imaginary constant is found. The condition ofzero-stress is imposed on the free surface, and non-slip condition offluid particles is Imposed on the walls of the container. For rigidmotion models, the expressions for added mass and Added damping tothe structural motion equations are obtained. Some typical numericalexamples are Presented.
基金Supported by National 863 Plan Project of Ministry of Science and Technology of China under Grant No. 2006AA09Z354National Natural Science Foundation of China under Grant No. 10672101.
文摘In this paper, an efficient multigrid fictitious boundary method （MFBM） coupled with the FEM solver package FEATFLOW was used for the detailed simulation of incompressible viscous flows around one or more moving NACA0012 airfoils. The calculations were carded on a fixed multigrid finite element mesh on which fluid equations were satisfied everywhere, and the airfoils were allowed to move freely through the mesh. The MFBM was employed to treat interactions between the fluid and the airfoils The motion of the airfoils was modeled by Newton-Euler equations. Numerical results of experiments verify that this method provides an efficient way to simulate incompressible viscous flows around moving airfoils.
文摘A new and computationally efficient version of the immersed boundary method,which is combined with the coarse-graining method,is introduced for modeling inextensible filaments immersed in low-Reynolds number flows.This is used to represent actin biopolymers,which are constituent elements of the cytoskeleton,a complex network-like structure that plays a fundamental role in shape morphology.An extension of the traditional immersed boundary method to include a stochastic stress tensor is also proposed in order to model the thermal fluctuations in the fluid at smaller scales.By way of validation,the response of a single,massless,inextensible semiflexible filament immersed in a thermally fluctuating fluid is obtained using the suggested numerical scheme and the resulting time-averaged contraction of the filament is compared to the theoretical value obtained from the worm-like chain model.
