The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general ...The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.展开更多
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equ...The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.展开更多
Hongxing reservoir was constructed on the floodplain of Hulan River in Heilongjiang. The geological problem of the reservoir is the seepage of the dam base and its related seepage stability. The leakage of the reservo...Hongxing reservoir was constructed on the floodplain of Hulan River in Heilongjiang. The geological problem of the reservoir is the seepage of the dam base and its related seepage stability. The leakage of the reservoir is caused by the water head differences between the upstream and downstream of the dam. Severe seepage could decrease the engineering benefits of the reservoir. Moreover,infiltration function of water will influence the safety of the dam. Through the analysis on the granule constitute and the formation of the dam base,the types of the seepage failure apt to happen were defined and the anti-infiltration and the permissible depression ratio were determined. Using the numerical simulation software GMS,the two-dimension numerical modeling has been carried out to analyze the seepage field of the reservoir. Through the two conditions modeling with concrete impervious wall and no concrete impervious wall,the largest flow rate,single-wide seepage discharge and the max infiltration gradient of the dam base were calculated. According to the permeable depression ratio of the dam base,the seepage stability of Hongxing reservoir dam base was analyzed.展开更多
The h-version adaptive finite element method for 3-D seepage problem ispresented in this paper. The adaptive system includes 4 modules; 3-D mesh generation, finite elementanalysis for 3-D seepage, mesh error estimatio...The h-version adaptive finite element method for 3-D seepage problem ispresented in this paper. The adaptive system includes 4 modules; 3-D mesh generation, finite elementanalysis for 3-D seepage, mesh error estimation and post-process. The effectiveness of this systemis verified by the given example.展开更多
Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering appl...Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications. A three-dimensional anisotropic heterogeneous steady random seepage model was developed on the basis of the finite element method. A statistical analysis of the distribution characteristics of soil parameters sampled from the main embankment of the Yangtze River in the Southern Jingzhou zone of China was conducted. The Kolomogorov-Smirnov test verified the statistical hypothesis that the permeability coefficient tensor has a Gaussian distribution. With the help of numerical analysis of the stochastic seepage field using the developed model, various statistical and random characteristics of the stochastic seepage field of the main embankment of the Yangtze River in the Southern Jingzhou zone of China were investigated. The model was also examined with statistical testing. Through the introduction of random variation of the upstream and downstream water levels into the model, the effects of the boundary randomness due to variation of the downstream and upstream water levels on the variation of simulated results presented with a vector series of the random seepage field were analyzed. Furthermore, the combined influence of the variation of the soil permeability coefficient and such seepage resistance measures as the cut-off wall and relief ditch on the hydraulic head distribution was analyzed and compared with the results obtained by determinate analysis. Meanwhile, sensitivities of the hydraulic gradient and downstream exit height to the variation of boundary water level were studied. The validity of the simulated results was verified by stochastic testing and measured data. The developed model provides more detail and a full stochastic algorithm to characterize and analyze three-dimensional stochastic seepage field problems.展开更多
The wave-induced seepage force is investigated on marine structures resting on or buried in the seabed.The bed is modelled as a poroelastic medium containing a nearly saturated water.The governing equations are solved...The wave-induced seepage force is investigated on marine structures resting on or buried in the seabed.The bed is modelled as a poroelastic medium containing a nearly saturated water.The governing equations are solved with Finite Element Method.For a pipeline buried in the seabed,agreement between the present numerical results and that of Cheng H.D.(1986)is quite satisfactory.展开更多
Based on the basic principle of the finite element method, the implicit composite element method for numerical simulation of seepage in underground engineering is proposed. In the simulation, the faults and drainage h...Based on the basic principle of the finite element method, the implicit composite element method for numerical simulation of seepage in underground engineering is proposed. In the simulation, the faults and drainage holes are set implicitly in the model elements without adding additional elements. Elements containing fault or drainage-hole data are termed composite elements. Then, their information data in model could be obtained. By determining the osmotic transmission matrix of the composite elements, the permeability coefficient matrix is then obtained. The method was applied to the numerical simulation of the seepage field around the underground powerhouse of the Ganhe Pumping Station in Yunnan, China, using a compiled three-dimensional finite element method calculation program. The rock mass around the site includes two faults. The seepage field in the rock mass was analyzed at different stages of the engineering project. The results show that, before the excavation of the underground caverns, the rock mass seepage is affected by the faults and the groundwater permeated down along the tangential fault plane. After the excavation of the caverns during the operation period, the groundwater is basically drained away and the underground caverns are mostly above the groundwater level. Thus, the calculation results of the engineering example verify the implicit composite method for the simulation of faults and drainage holes. This method can well meet the calculation demands of practical engineering.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11361035 and 11301258)the Natural Science Foundation of Inner Mongolia(Nos.2012MS0106 and 2012MS0108)
文摘The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.
文摘The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.
文摘Hongxing reservoir was constructed on the floodplain of Hulan River in Heilongjiang. The geological problem of the reservoir is the seepage of the dam base and its related seepage stability. The leakage of the reservoir is caused by the water head differences between the upstream and downstream of the dam. Severe seepage could decrease the engineering benefits of the reservoir. Moreover,infiltration function of water will influence the safety of the dam. Through the analysis on the granule constitute and the formation of the dam base,the types of the seepage failure apt to happen were defined and the anti-infiltration and the permissible depression ratio were determined. Using the numerical simulation software GMS,the two-dimension numerical modeling has been carried out to analyze the seepage field of the reservoir. Through the two conditions modeling with concrete impervious wall and no concrete impervious wall,the largest flow rate,single-wide seepage discharge and the max infiltration gradient of the dam base were calculated. According to the permeable depression ratio of the dam base,the seepage stability of Hongxing reservoir dam base was analyzed.
文摘The h-version adaptive finite element method for 3-D seepage problem ispresented in this paper. The adaptive system includes 4 modules; 3-D mesh generation, finite elementanalysis for 3-D seepage, mesh error estimation and post-process. The effectiveness of this systemis verified by the given example.
基金supported by the National Natural Science Foundation of China (Grant No. 50379046)the Doctoral Fund of the Ministry of Education of China (Grant No. A50221)
文摘Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications. A three-dimensional anisotropic heterogeneous steady random seepage model was developed on the basis of the finite element method. A statistical analysis of the distribution characteristics of soil parameters sampled from the main embankment of the Yangtze River in the Southern Jingzhou zone of China was conducted. The Kolomogorov-Smirnov test verified the statistical hypothesis that the permeability coefficient tensor has a Gaussian distribution. With the help of numerical analysis of the stochastic seepage field using the developed model, various statistical and random characteristics of the stochastic seepage field of the main embankment of the Yangtze River in the Southern Jingzhou zone of China were investigated. The model was also examined with statistical testing. Through the introduction of random variation of the upstream and downstream water levels into the model, the effects of the boundary randomness due to variation of the downstream and upstream water levels on the variation of simulated results presented with a vector series of the random seepage field were analyzed. Furthermore, the combined influence of the variation of the soil permeability coefficient and such seepage resistance measures as the cut-off wall and relief ditch on the hydraulic head distribution was analyzed and compared with the results obtained by determinate analysis. Meanwhile, sensitivities of the hydraulic gradient and downstream exit height to the variation of boundary water level were studied. The validity of the simulated results was verified by stochastic testing and measured data. The developed model provides more detail and a full stochastic algorithm to characterize and analyze three-dimensional stochastic seepage field problems.
文摘The wave-induced seepage force is investigated on marine structures resting on or buried in the seabed.The bed is modelled as a poroelastic medium containing a nearly saturated water.The governing equations are solved with Finite Element Method.For a pipeline buried in the seabed,agreement between the present numerical results and that of Cheng H.D.(1986)is quite satisfactory.
基金supported by the National Key Basic Research Program of China(Grant No.2015CB057904)the Major Program of the National Natural Science Foundation of China(Grant No.91215301)+1 种基金the National Natural Science Foundation of China(Grant Nos.51279136&51209164)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110015)
文摘Based on the basic principle of the finite element method, the implicit composite element method for numerical simulation of seepage in underground engineering is proposed. In the simulation, the faults and drainage holes are set implicitly in the model elements without adding additional elements. Elements containing fault or drainage-hole data are termed composite elements. Then, their information data in model could be obtained. By determining the osmotic transmission matrix of the composite elements, the permeability coefficient matrix is then obtained. The method was applied to the numerical simulation of the seepage field around the underground powerhouse of the Ganhe Pumping Station in Yunnan, China, using a compiled three-dimensional finite element method calculation program. The rock mass around the site includes two faults. The seepage field in the rock mass was analyzed at different stages of the engineering project. The results show that, before the excavation of the underground caverns, the rock mass seepage is affected by the faults and the groundwater permeated down along the tangential fault plane. After the excavation of the caverns during the operation period, the groundwater is basically drained away and the underground caverns are mostly above the groundwater level. Thus, the calculation results of the engineering example verify the implicit composite method for the simulation of faults and drainage holes. This method can well meet the calculation demands of practical engineering.
