Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow pheno...Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.展开更多
In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique ...In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.展开更多
Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations...Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.展开更多
The extended finite element method(XFEM) is a numerical method for modeling discontinuities within a classical finite element framework. Based on the algorithm of XFEM, the major factors such as integral domain factor...The extended finite element method(XFEM) is a numerical method for modeling discontinuities within a classical finite element framework. Based on the algorithm of XFEM, the major factors such as integral domain factor and mesh density which all influence the calculation accuracy of stress intensity factor(SIF) are discussed,and the proper parameters to calculate the SIF are given. The results from the case analysis demonstrate that the crack path is the most sensitive to the crack growth increment size, and the crack path is not mesh-sensitive. A reanalysis method for the XFEM has been introduced. The example presented shows that there is a significantly reduced computational cost for each iteration of crack growth achieved by using the reanalysis method and the reanalysis approach has increasing benefits as the mesh density increases or the value of crack growth increments size decreases.展开更多
This paper applies the stochastic finite element method to analyse the statistics of stresses in earth dams and assess the safety and reliability of the dams. Formulations of the stochastic finite element method are b...This paper applies the stochastic finite element method to analyse the statistics of stresses in earth dams and assess the safety and reliability of the dams. Formulations of the stochastic finite element method are briefly reviewed and the procedure for assessing dam's strength and stability is described. As an example, a detailed analysis for an actual dam Nululin dam is performed. A practical method for studying built-dams based on the prototype observation data is described.展开更多
A new finite element level set method is developed to simulate the interface motion.The normal velocity of the moving interface can depend on both the local geometry,such as the curvature,and the external force such a...A new finite element level set method is developed to simulate the interface motion.The normal velocity of the moving interface can depend on both the local geometry,such as the curvature,and the external force such as that due to the flux from both sides of the interface of a material whose concentration is governed by a diffusion equation.The key idea of the method is to use an interface-fitted finite element mesh.Such an approximation of the interface allows an accurate calculation of the solution to the diffusion equation.The interface-fitted mesh is constructed from a base mesh,a uniform finite element mesh,at each time step to explicitly locate the interface and separate regions defined by the interface.Several new level set techniques are developed in the framework of finite element methods.These include a simple finite element method for approximating the curvature,a new method for the extension of normal velocity,and a finite element least-squares method for the reinitialization of level set functions.Application of the method to the classical solidification problem captures the dendrites.The method is also applied to the molecular solvation to determine optimal solute-solvent interfaces of solvation systems.展开更多
The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal st...The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal stability analysis and error estimate for these two algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms.展开更多
A concurrent multiscale method is developed for simulating quasi-static crack propagation in which the failure processes occur in only a small portion of the structure. For this purpose, a multiscale model is adopted ...A concurrent multiscale method is developed for simulating quasi-static crack propagation in which the failure processes occur in only a small portion of the structure. For this purpose, a multiscale model is adopted and both scales are discretized with finite-element meshes. The extended finite element method is employed to take into account the propagation of discontinuities on the fine-scale subregions. At the same time, for the other subregions, the coarse-scale mesh is employed and is resolved by using the extended multiscale finite element method. Several representative numerical examples are given to verify the validity of the method.展开更多
This article analyzes the relationship between the water level and the water-tube tilting in Shuangyang lake,based on the differential deformation features reflected by the NS and EW components of the water-tube tiltm...This article analyzes the relationship between the water level and the water-tube tilting in Shuangyang lake,based on the differential deformation features reflected by the NS and EW components of the water-tube tiltmeter.The results show a good spatiotemporal consistency between the variation of water level and the NS tilt component,which is considered to be affected by the magnitude and duration of the water level variation in Shuangyang Lake.The article uses Landsat remote sensing image data to extract the water boundary of Shuan-gyang Lake,and takes advantage of the finite element numerical simulation method to build three-dimensional models for different geological structural conditions of the Shuangyang seismostation.The simulation results show that when the underground medium is granite,the effect of water level variation on the vertical displacement of the surface is non-directional.With a 50-m soil layer in Model 2,the simulated NS tilt variation is equivalent to the actual observed water-tube tiltmeter NS component when the water level variation is 0.44 m and 0.8m.When the variation of water level reaches 2.0m,the simulation result of the NS component is 79.6 ms,which is slightly larger than the observed result of 60.32 ms.However,the simulation results show that the variation of the EW component is significantly smaller than that of the NS one.Due to the fact that the Shuan-gyang lake is long in the NS direction and short in the EW direction,the existence of the soil layer tends to generate ground deformation along the NS direction in the vicinity of the lake after the increase of water level,thereby resulting in the difference of the ground deformation in the two directions.展开更多
In this article we detail the methodology developed to construct an efficient interface description technique—the robust conservative level set(RCLS)—to simulate multiphase flows on mixed-element unstructured meshes...In this article we detail the methodology developed to construct an efficient interface description technique—the robust conservative level set(RCLS)—to simulate multiphase flows on mixed-element unstructured meshes while conserving mass to machine accuracy.The approach is tailored specifically for industry as the three-dimensional unstructured approach allows for the treatment of very complex geometries.In addition,special care has been taken to optimise the trade-off between accuracy and computational cost while maintaining the robustness of the numerical method.This was achieved by solving the transport equations for the liquid volume fraction using a WENO scheme for polyhedral meshes and by adding a flux-limiter algorithm.The performance of the resulting method has been compared against established multiphase numerical methods and its ability to capture the physics of multiphase flows is demonstrated on a range of relevant test cases.Finally,the RCLS method has been applied to the simulation of the primary breakup of a flat liquid sheet of kerosene in co-flowing high-pressure gas.This quasi-DNS/LES computation was performed at relevant aero-engine conditions on a three-dimensional mixed-element unstructured mesh.The numerical results have been validated qualitatively against theoretical predictions and experimental data.In particular,the expected breakup regime was observed in the simulation results.Finally,the computation reproduced faithfully the breakup length predicted by a correlation based on experimental data.This constitutes a first step towards a quantitative validation.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
高位滑坡对建筑集群的冲击破坏时常导致严重的人员伤亡,基于光滑粒子流体动力学-离散元法-有限元法(smoothed particle hydrodynamics-discrete element method-finite element method,SPH-DEM-FEM)耦合的数值模型,开展了高位滑坡对框...高位滑坡对建筑集群的冲击破坏时常导致严重的人员伤亡,基于光滑粒子流体动力学-离散元法-有限元法(smoothed particle hydrodynamics-discrete element method-finite element method,SPH-DEM-FEM)耦合的数值模型,开展了高位滑坡对框架结构建筑群的冲击过程、建筑结构破坏机理、冲击力时程与框架柱关键点应力和弯矩等动力机制研究。研究结果表明:SPH-DEM-FEM耦合数值方法能够有效地模拟碎石土滑坡中土(SPH)石(DEM)混合物的抛射弹跳、爬高绕流冲击运动过程。考虑了常规建筑垂直、平行于滑坡流向的三排建筑组合布局,位于滑坡近端的纵向排列建筑表现为连续性倾倒破坏,横向排列的建筑则呈现整体倾倒破坏;因前排建筑群对滑坡冲击能量的耗散及滑坡自身摩擦耗能,位于滑坡后端建筑表现为引流面墙体和前排柱发生局部破坏,结构保持稳定,损毁程度依次为上游无建筑缓冲耗能的建筑>有横向排列的建筑>有纵向排列的建筑;纵向、横向排列的建筑冲击力衰减幅度分别31%、21%。横向框架建筑整体倾倒的损毁机制表现为框架柱的直接剪断或节点塑形铰链失效;纵向框架建筑连续性倾倒的损毁机制表现为前排框架柱的失效引起后排框架柱轴向压力和极限弯矩增加,持续冲击荷载超过其极限弯矩致使后排框架柱发生弯曲破坏,最终结构倾倒。系统能量在动能、内能和摩擦耗能间转化,其中摩擦耗能占65.5%,结构耗能占23.6%,动能快速下降与内能急剧增加是建筑破坏的关键特征。展开更多
An interface capturing approach based on a level set function for simulating transient two-phase viscous incompressible flows is applied in this paper. A narrow-band signed distance function is adopted to indicate the...An interface capturing approach based on a level set function for simulating transient two-phase viscous incompressible flows is applied in this paper. A narrow-band signed distance function is adopted to indicate the phase fields and the interface. The multiphase flow is numerically solved by three stages with finite element method （FEM）： （1） solving a two-fluid Navier-Stokes （N-S） equations over the whole domain, （2） transporting the level set function with the obtained velocity field, （3） the level set function correction through a renormalization with continuous penalization which preserves the thickness of the interface. In this paper, the 3-D water colunm collapse with an obstacle is simulated, which yielded good agreement with the experimental data.展开更多
The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) descr...The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.展开更多
基金King Mongkut’s University of Technology North Bangkok (KMUTNB)the Office of the Higher Education Commission (OHEC)the National Metal and Materials Technology Center (MTEC) for supporting this research work
文摘Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.
文摘In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.
基金Project supported by the National Natural Science Foundation of China(No.11001061)the Science and Technology Foundation of Guizhou Province of China(No.[2008]2123)
文摘Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.
基金the National Basic Research Program(973) of China(No.2011CB013505)the National Natural Science Foundation of China(No.51279100)
文摘The extended finite element method(XFEM) is a numerical method for modeling discontinuities within a classical finite element framework. Based on the algorithm of XFEM, the major factors such as integral domain factor and mesh density which all influence the calculation accuracy of stress intensity factor(SIF) are discussed,and the proper parameters to calculate the SIF are given. The results from the case analysis demonstrate that the crack path is the most sensitive to the crack growth increment size, and the crack path is not mesh-sensitive. A reanalysis method for the XFEM has been introduced. The example presented shows that there is a significantly reduced computational cost for each iteration of crack growth achieved by using the reanalysis method and the reanalysis approach has increasing benefits as the mesh density increases or the value of crack growth increments size decreases.
文摘This paper applies the stochastic finite element method to analyse the statistics of stresses in earth dams and assess the safety and reliability of the dams. Formulations of the stochastic finite element method are briefly reviewed and the procedure for assessing dam's strength and stability is described. As an example, a detailed analysis for an actual dam Nululin dam is performed. A practical method for studying built-dams based on the prototype observation data is described.
基金supported by the US National Science Foundation(NSF)through the grant DMS-0451466 and DMS-0811259by the US Department of Energy through the grant DE-FG02-05ER25707+2 种基金supported by the NSF Center for Theoretical Biological Physics(CTBP)under the NSF grant PHY-0822283the grant Award Number R01GM096188 from the National Institute of General Medical Sciences(NIGMS)the National Institutes of Health(NIH).
文摘A new finite element level set method is developed to simulate the interface motion.The normal velocity of the moving interface can depend on both the local geometry,such as the curvature,and the external force such as that due to the flux from both sides of the interface of a material whose concentration is governed by a diffusion equation.The key idea of the method is to use an interface-fitted finite element mesh.Such an approximation of the interface allows an accurate calculation of the solution to the diffusion equation.The interface-fitted mesh is constructed from a base mesh,a uniform finite element mesh,at each time step to explicitly locate the interface and separate regions defined by the interface.Several new level set techniques are developed in the framework of finite element methods.These include a simple finite element method for approximating the curvature,a new method for the extension of normal velocity,and a finite element least-squares method for the reinitialization of level set functions.Application of the method to the classical solidification problem captures the dendrites.The method is also applied to the molecular solvation to determine optimal solute-solvent interfaces of solvation systems.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271298, 11271313, 61163027）, the Key Project of Chinese Ministry of Education （Grant No. 212197）, the Natural Science Foundation of Xinjiang Province （Grant No. 2013211B01）, and the Doctoral Foundation of Xinjiang University （Grant No. BS120102）.
文摘The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal stability analysis and error estimate for these two algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms.
基金Project supported by the National Natural Science Foundation of China(Nos.11232003,11072051,11272003 and 91315302)the 111 Project(No.B08014)+2 种基金the National Basic Research Program of China(Nos.2010CB832704 and 2011CB013401)Program for New Century Excellent Talents in University(No.NCET-13-0088)Ph.D.Programs Foundation of Ministry of Education of China(No.20130041110050)
文摘A concurrent multiscale method is developed for simulating quasi-static crack propagation in which the failure processes occur in only a small portion of the structure. For this purpose, a multiscale model is adopted and both scales are discretized with finite-element meshes. The extended finite element method is employed to take into account the propagation of discontinuities on the fine-scale subregions. At the same time, for the other subregions, the coarse-scale mesh is employed and is resolved by using the extended multiscale finite element method. Several representative numerical examples are given to verify the validity of the method.
基金sponsored by National Key Research and Development Program of China(2018YFC0807000)The Spark Program of Earthquake Technology of CEA(XH20070Y)The Earthquake Tracking Task of CEA(2021010221).
文摘This article analyzes the relationship between the water level and the water-tube tilting in Shuangyang lake,based on the differential deformation features reflected by the NS and EW components of the water-tube tiltmeter.The results show a good spatiotemporal consistency between the variation of water level and the NS tilt component,which is considered to be affected by the magnitude and duration of the water level variation in Shuangyang Lake.The article uses Landsat remote sensing image data to extract the water boundary of Shuan-gyang Lake,and takes advantage of the finite element numerical simulation method to build three-dimensional models for different geological structural conditions of the Shuangyang seismostation.The simulation results show that when the underground medium is granite,the effect of water level variation on the vertical displacement of the surface is non-directional.With a 50-m soil layer in Model 2,the simulated NS tilt variation is equivalent to the actual observed water-tube tiltmeter NS component when the water level variation is 0.44 m and 0.8m.When the variation of water level reaches 2.0m,the simulation result of the NS component is 79.6 ms,which is slightly larger than the observed result of 60.32 ms.However,the simulation results show that the variation of the EW component is significantly smaller than that of the NS one.Due to the fact that the Shuan-gyang lake is long in the NS direction and short in the EW direction,the existence of the soil layer tends to generate ground deformation along the NS direction in the vicinity of the lake after the increase of water level,thereby resulting in the difference of the ground deformation in the two directions.
文摘In this article we detail the methodology developed to construct an efficient interface description technique—the robust conservative level set(RCLS)—to simulate multiphase flows on mixed-element unstructured meshes while conserving mass to machine accuracy.The approach is tailored specifically for industry as the three-dimensional unstructured approach allows for the treatment of very complex geometries.In addition,special care has been taken to optimise the trade-off between accuracy and computational cost while maintaining the robustness of the numerical method.This was achieved by solving the transport equations for the liquid volume fraction using a WENO scheme for polyhedral meshes and by adding a flux-limiter algorithm.The performance of the resulting method has been compared against established multiphase numerical methods and its ability to capture the physics of multiphase flows is demonstrated on a range of relevant test cases.Finally,the RCLS method has been applied to the simulation of the primary breakup of a flat liquid sheet of kerosene in co-flowing high-pressure gas.This quasi-DNS/LES computation was performed at relevant aero-engine conditions on a three-dimensional mixed-element unstructured mesh.The numerical results have been validated qualitatively against theoretical predictions and experimental data.In particular,the expected breakup regime was observed in the simulation results.Finally,the computation reproduced faithfully the breakup length predicted by a correlation based on experimental data.This constitutes a first step towards a quantitative validation.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
文摘高位滑坡对建筑集群的冲击破坏时常导致严重的人员伤亡,基于光滑粒子流体动力学-离散元法-有限元法(smoothed particle hydrodynamics-discrete element method-finite element method,SPH-DEM-FEM)耦合的数值模型,开展了高位滑坡对框架结构建筑群的冲击过程、建筑结构破坏机理、冲击力时程与框架柱关键点应力和弯矩等动力机制研究。研究结果表明:SPH-DEM-FEM耦合数值方法能够有效地模拟碎石土滑坡中土(SPH)石(DEM)混合物的抛射弹跳、爬高绕流冲击运动过程。考虑了常规建筑垂直、平行于滑坡流向的三排建筑组合布局,位于滑坡近端的纵向排列建筑表现为连续性倾倒破坏,横向排列的建筑则呈现整体倾倒破坏;因前排建筑群对滑坡冲击能量的耗散及滑坡自身摩擦耗能,位于滑坡后端建筑表现为引流面墙体和前排柱发生局部破坏,结构保持稳定,损毁程度依次为上游无建筑缓冲耗能的建筑>有横向排列的建筑>有纵向排列的建筑;纵向、横向排列的建筑冲击力衰减幅度分别31%、21%。横向框架建筑整体倾倒的损毁机制表现为框架柱的直接剪断或节点塑形铰链失效;纵向框架建筑连续性倾倒的损毁机制表现为前排框架柱的失效引起后排框架柱轴向压力和极限弯矩增加,持续冲击荷载超过其极限弯矩致使后排框架柱发生弯曲破坏,最终结构倾倒。系统能量在动能、内能和摩擦耗能间转化,其中摩擦耗能占65.5%,结构耗能占23.6%,动能快速下降与内能急剧增加是建筑破坏的关键特征。
基金supported by the National Natural Science Foundation of China(Grant Nos.51379125,51411130131 and 11432009)The National Key Basic Research Development Program of China(973 Program,Grant No.2013CB036103)
文摘An interface capturing approach based on a level set function for simulating transient two-phase viscous incompressible flows is applied in this paper. A narrow-band signed distance function is adopted to indicate the phase fields and the interface. The multiphase flow is numerically solved by three stages with finite element method （FEM）： （1） solving a two-fluid Navier-Stokes （N-S） equations over the whole domain, （2） transporting the level set function with the obtained velocity field, （3） the level set function correction through a renormalization with continuous penalization which preserves the thickness of the interface. In this paper, the 3-D water colunm collapse with an obstacle is simulated, which yielded good agreement with the experimental data.
基金supported by the National Natural Science Foundation of China (Grant No. 11002029)
文摘The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.
