Ceramic spheres,typically with a particle diameter of less than 0.8 mm,are frequently utilized as a critical proppant material in hydraulic fracturing for petroleum and natural gas extraction.Porous ceramic spheres wi...Ceramic spheres,typically with a particle diameter of less than 0.8 mm,are frequently utilized as a critical proppant material in hydraulic fracturing for petroleum and natural gas extraction.Porous ceramic spheres with artificial inherent pores are an important type of lightweight proppant,enabling their transport to distant fracture extremities and enhancing fracture conductivity.However,the focus frequently gravitates towards the low-density advantage,often overlooking the pore geometry impacts on compressive strength by traditional strength evaluation.This paper numerically bypasses such limitations by using a combined finite and discrete element method(FDEM)considering experimental results.The mesh size of the model undergoes validation,followed by the calibration of cohesive element parameters via the single particle compression test.The stimulation elucidates that proppants with a smaller pore size(40μm)manifest crack propagation evolution at a more rapid pace in comparison to their larger-pore counterparts,though the influence of pore diameter on overall strength is subtle.The inception of pores not only alters the trajectory of crack progression but also,with an increase in porosity,leads to a discernible decline in proppant compressive strength.Intriguingly,upon crossing a porosity threshold of 10%,the decrement in strength becomes more gradual.A denser congregation of pores accelerates crack propagation,undermining proppant robustness,suggesting that under analogous conditions,hollow proppants might not match the strength of their porous counterparts.This exploration elucidates the underlying mechanisms of proppant failure from a microstructural perspective,furnishing pivotal insights that may guide future refinements in the architectural design of porous proppant.展开更多
In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'...In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'' of the later. For this new stabilized formulation, a unified approach to convergence analysis is presented for a wide spectrum of finite element spaces. As long as the rotation space is appropriately enriched, the formulation is convergent for the finite element spaces of sufficiently high order. Optimal-order error estimates with constants independent of the plate thickness are proved for the various lower order methods of this kind.展开更多
Percussive drilling is gaining interest for both shallow and deep applications due to its potential for higher drilling rates in hard rocks.Therefore,for efficient rock breaking,the development of advanced percussive ...Percussive drilling is gaining interest for both shallow and deep applications due to its potential for higher drilling rates in hard rocks.Therefore,for efficient rock breaking,the development of advanced percussive drilling simulation tools has the potential to be transformative.Such tools must accurately capture the rock’s response to enable an effective analysis of the fragmentation process.Traditional continuum numerical methods,such as the finite element method(FEM),do not simulate discrete cracks or the contact interaction between rock fragments.The finite-discrete element method(FDEM)is a three-dimensional hybrid method that combines FEM with the discrete element method(DEM)that addresses these limitations.New FDEM simulation results of impacts on Kuru Grey granite show good agreement with published experimental data.The interpretation focuses on two significant processes in percussive drilling:crack propagation and chipping generation.FDEM successfully simulates the evolution of cracks,including radial,side,and inclined cracks,as well as crushed and cracked zones.The simulation also reproduces the coalescence of adjacent craters to generate more chippings.Additionally,the stress state,velocity field and discrete fractures simulated by FDEM provide detailed insights into the different fracture patterns for Kuru Grey granite,enhancing understanding of the fundamental underlying mechanisms.展开更多
The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh disto...The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.展开更多
In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,...In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.展开更多
In this paper,a new dynamic model for the flexible hub-beam system is proposed by using the principle of continuum medium mechanics and the finite element discretization method.In the proposed model,the coupling defor...In this paper,a new dynamic model for the flexible hub-beam system is proposed by using the principle of continuum medium mechanics and the finite element discretization method.In the proposed model,the coupling deformation of any element of the beam is only related with the nodal coordinates of this element.So this model is suitable to the rotating beam in an arbitrary shape.Numerical examples of slender beams in straight and irregular shapes are carried out to demonstrate the validation of the proposed model.Simulation results indicate that the proposed model can be used valid for dynamic description of flexible rotating beam in irregular shape, and for both low and high rotation speeds.展开更多
The discretization size is limited by the sampling theorem, and the limit is one half of the wavelength of the highest frequency of the problem. However, one half of the wavelength is an ideal value. In general, the d...The discretization size is limited by the sampling theorem, and the limit is one half of the wavelength of the highest frequency of the problem. However, one half of the wavelength is an ideal value. In general, the discretization size that can ensure the accuracy of the simulation is much smaller than this value in the traditional finite element method. The possible reason of this phenomenon is analyzed in this paper, and an efficient method is given to improve the simulation accuracy.展开更多
Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a d...Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.展开更多
We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization...We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization is based on difference methods, whereas the space discretization is done using finite element methods. The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. First, we define a fully discrete finite element approximation scheme for the semilinear parabolic control problem. Second, we derive the superconvergence properties for the control, the state and the adjoint state. Finally, we do some numerical experiments for illustrating our theoretical results.展开更多
A simulative analysis coupled with experiment on behaviors of a soil bed cut by a model bulldozer blade is carried out using the finite element/distinct element method（FE/DEM） facility built in the ELFEN package. Be...A simulative analysis coupled with experiment on behaviors of a soil bed cut by a model bulldozer blade is carried out using the finite element/distinct element method（FE/DEM） facility built in the ELFEN package. Before simulation, tensile/compression, triaxial compression and the soil specimens are examined through uniaxial direct shear tests to obtain model characteristics and relevant parameters, then soil cutting experiments are carried out via a mini-soil bin system with a soil bed of 60/120 mm in width and 10 mm in depth cut by a 1/9 scale model bulldozer blade moving with the velocity of 10 mm/s. The soil constitutive model includes the tensile elastic model for tensile breakage and the compressive elastoplastic relationship with Mohr-Coulomb criterion. The cutting length in simulation is set as 1/4 of that in the experiment divided into 1 869 triangular elements. The comparison between the simulated results and experimental ones shows that the used model is capable of analyzing soil dynamic behaviors qualitatively, and the predicted fracturing profiles in general conform to the experiment. Hence the feasibility for analyzing soil fracturing behaviors in tillage or other similar processes is validated.展开更多
On the basis of the three-dimensional(3D)random aggregate&mortar two-phase mesoscale finite element model,C++programming was used to identify the node position information of the interface between the aggregate an...On the basis of the three-dimensional(3D)random aggregate&mortar two-phase mesoscale finite element model,C++programming was used to identify the node position information of the interface between the aggregate and mortar elements.The nodes were discretized at this position and the zero-thickness cohesive elements were inserted.After that,the crack energy release rate fracture criterion based on the fracture mechanics theory was assigned to the failure criterion of the interface transition zone(ITZ)elements.Finally,the three-phase mesomechanical model based on the combined finite discrete element method(FDEM)was constructed.Based on this model,the meso-crack extension and macro-mechanical behaviour of coral aggregate concrete(CAC)under uniaxial compression were successfully simulated.The results demonstrated that the meso-mechanical model based on FDEM has excellent applicability to simulate the compressive properties of CAC.展开更多
Based on the elastic-plastic large deformation finite element formulation as well as the shell element combined discrete Kirchhoff theoretical plate element (DKT) with membrane square element, deep-drawing bending spr...Based on the elastic-plastic large deformation finite element formulation as well as the shell element combined discrete Kirchhoff theoretical plate element (DKT) with membrane square element, deep-drawing bending springback of typical U-pattern is studied. At the same time the springback values of the drawing of patterns' unloading and trimming about the satellite aerial reflecting surface are predicted and also compared with those of the practical punch. Above two springbacks all obtain satisfactory results, which provide a kind of effective quantitative pre-prediction of springback for the practical engineers.展开更多
To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d w...To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper approximations.As applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.展开更多
Loess is a special type of soil whose properties are significantly affected by water.However,the grout diffusion law for backfill grouting in loess shield tunnels remains unknown.Based on a visual model experimental d...Loess is a special type of soil whose properties are significantly affected by water.However,the grout diffusion law for backfill grouting in loess shield tunnels remains unknown.Based on a visual model experimental device,three experiments were conducted with 10%,20%,and 30%loess moisture.A finite discrete element method was used to verify the grout diffusion mode,and parameters such as the tunnel buried depth,grout viscosity,and elastic modulus were considered to analyse the grout diffusion law.Experiments and numerical simulations show that the screening diffusion of grout occurs at low loess moisture,whereas splitting diffusion occurs at high loess moisture.The farthest splitting diffusion distance decreases as the tunnel buried depth,grout viscosity,and elastic modulus increase.In addition,based on capillary theory and geotechnical strength criteria,screening diffusion and splitting diffusion models were established.This study investigated the grout diffusion law and grout diffusion model,providing a reference for the design and construction of loess shield tunnels.展开更多
A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algori...A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.展开更多
The Richards equation models the water flow in a partially saturated underground porous medium under the surface.When it rains on the surface,boundary conditions of Signorini type must be considered on this part of th...The Richards equation models the water flow in a partially saturated underground porous medium under the surface.When it rains on the surface,boundary conditions of Signorini type must be considered on this part of the boundary.The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler's scheme in time and finite elements in space.The convergence of this discretization leads to the well-posedness of the problem.展开更多
基金the financial support provided by Tianfu Yongxing Laboratory Organized Research Project Funding(No.2023CXXM01)the ARC linkage program(No.LP200100420).
文摘Ceramic spheres,typically with a particle diameter of less than 0.8 mm,are frequently utilized as a critical proppant material in hydraulic fracturing for petroleum and natural gas extraction.Porous ceramic spheres with artificial inherent pores are an important type of lightweight proppant,enabling their transport to distant fracture extremities and enhancing fracture conductivity.However,the focus frequently gravitates towards the low-density advantage,often overlooking the pore geometry impacts on compressive strength by traditional strength evaluation.This paper numerically bypasses such limitations by using a combined finite and discrete element method(FDEM)considering experimental results.The mesh size of the model undergoes validation,followed by the calibration of cohesive element parameters via the single particle compression test.The stimulation elucidates that proppants with a smaller pore size(40μm)manifest crack propagation evolution at a more rapid pace in comparison to their larger-pore counterparts,though the influence of pore diameter on overall strength is subtle.The inception of pores not only alters the trajectory of crack progression but also,with an increase in porosity,leads to a discernible decline in proppant compressive strength.Intriguingly,upon crossing a porosity threshold of 10%,the decrement in strength becomes more gradual.A denser congregation of pores accelerates crack propagation,undermining proppant robustness,suggesting that under analogous conditions,hollow proppants might not match the strength of their porous counterparts.This exploration elucidates the underlying mechanisms of proppant failure from a microstructural perspective,furnishing pivotal insights that may guide future refinements in the architectural design of porous proppant.
文摘In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'' of the later. For this new stabilized formulation, a unified approach to convergence analysis is presented for a wide spectrum of finite element spaces. As long as the rotation space is appropriately enriched, the formulation is convergent for the finite element spaces of sufficiently high order. Optimal-order error estimates with constants independent of the plate thickness are proved for the various lower order methods of this kind.
文摘Percussive drilling is gaining interest for both shallow and deep applications due to its potential for higher drilling rates in hard rocks.Therefore,for efficient rock breaking,the development of advanced percussive drilling simulation tools has the potential to be transformative.Such tools must accurately capture the rock’s response to enable an effective analysis of the fragmentation process.Traditional continuum numerical methods,such as the finite element method(FEM),do not simulate discrete cracks or the contact interaction between rock fragments.The finite-discrete element method(FDEM)is a three-dimensional hybrid method that combines FEM with the discrete element method(DEM)that addresses these limitations.New FDEM simulation results of impacts on Kuru Grey granite show good agreement with published experimental data.The interpretation focuses on two significant processes in percussive drilling:crack propagation and chipping generation.FDEM successfully simulates the evolution of cracks,including radial,side,and inclined cracks,as well as crushed and cracked zones.The simulation also reproduces the coalescence of adjacent craters to generate more chippings.Additionally,the stress state,velocity field and discrete fractures simulated by FDEM provide detailed insights into the different fracture patterns for Kuru Grey granite,enhancing understanding of the fundamental underlying mechanisms.
基金supported by the National Natural Science Foundation of China(11001037,11102037,11290143)the Fundamental Research Funds for the Central Universities(DUT13LK07)
文摘The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.
基金partially supported by the National Natural Science Foundation of China(Grant No.12261070)the Ningxia Key Research and Development Project of China(Grant No.2022BSB03048)+2 种基金partially supported by the Simons(Grant No.633724)and by Fundacion Seneca grant 21760/IV/22partially supported by the Spanish national research project PID2019-108336GB-I00by Fundacion Séneca grant 21728/EE/22.Este trabajo es resultado de las estancias(21760/IV/22)y(21728/EE/22)financiadas por la Fundacion Séneca-Agencia de Ciencia y Tecnologia de la Region de Murcia con cargo al Programa Regional de Movilidad,Colaboracion Internacional e Intercambio de Conocimiento"Jimenez de la Espada".(Plan de Actuacion 2022).
文摘In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.
基金the National Natural Science Foundationof China(Nos.10772113,10772112)
文摘In this paper,a new dynamic model for the flexible hub-beam system is proposed by using the principle of continuum medium mechanics and the finite element discretization method.In the proposed model,the coupling deformation of any element of the beam is only related with the nodal coordinates of this element.So this model is suitable to the rotating beam in an arbitrary shape.Numerical examples of slender beams in straight and irregular shapes are carried out to demonstrate the validation of the proposed model.Simulation results indicate that the proposed model can be used valid for dynamic description of flexible rotating beam in irregular shape, and for both low and high rotation speeds.
文摘The discretization size is limited by the sampling theorem, and the limit is one half of the wavelength of the highest frequency of the problem. However, one half of the wavelength is an ideal value. In general, the discretization size that can ensure the accuracy of the simulation is much smaller than this value in the traditional finite element method. The possible reason of this phenomenon is analyzed in this paper, and an efficient method is given to improve the simulation accuracy.
基金Projects(52004143,51774194)supported by the National Natural Science Foundation of ChinaProject(2020M670781)supported by the China Postdoctoral Science Foundation+2 种基金Project(SKLGDUEK2021)supported by the State Key Laboratory for GeoMechanics and Deep Underground Engineering,ChinaProject(U1806208)supported by the NSFC-Shandong Joint Fund,ChinaProject(2018GSF117023)supported by the Key Research and Development Program of Shandong Province,China。
文摘Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11271145）, the Foundation for Talent Introduction of Guangdong Provincial University, the Specialized Research Fund for the Doctoral Program of Higher Education （20114407110009）, and the Project of Department of Education of Guangdong Province （2012KJCX0036）.
文摘We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization is based on difference methods, whereas the space discretization is done using finite element methods. The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. First, we define a fully discrete finite element approximation scheme for the semilinear parabolic control problem. Second, we derive the superconvergence properties for the control, the state and the adjoint state. Finally, we do some numerical experiments for illustrating our theoretical results.
基金This project is supported by National Natural Science Foundation of China (No. 10372113)Royal Society-NSFC China-UK Joint Project (No. 16468).
文摘A simulative analysis coupled with experiment on behaviors of a soil bed cut by a model bulldozer blade is carried out using the finite element/distinct element method（FE/DEM） facility built in the ELFEN package. Before simulation, tensile/compression, triaxial compression and the soil specimens are examined through uniaxial direct shear tests to obtain model characteristics and relevant parameters, then soil cutting experiments are carried out via a mini-soil bin system with a soil bed of 60/120 mm in width and 10 mm in depth cut by a 1/9 scale model bulldozer blade moving with the velocity of 10 mm/s. The soil constitutive model includes the tensile elastic model for tensile breakage and the compressive elastoplastic relationship with Mohr-Coulomb criterion. The cutting length in simulation is set as 1/4 of that in the experiment divided into 1 869 triangular elements. The comparison between the simulated results and experimental ones shows that the used model is capable of analyzing soil dynamic behaviors qualitatively, and the predicted fracturing profiles in general conform to the experiment. Hence the feasibility for analyzing soil fracturing behaviors in tillage or other similar processes is validated.
基金supported by the Key Projects of the National Science Foundation of China(Nos.52178190,52078250,11832013)
文摘On the basis of the three-dimensional(3D)random aggregate&mortar two-phase mesoscale finite element model,C++programming was used to identify the node position information of the interface between the aggregate and mortar elements.The nodes were discretized at this position and the zero-thickness cohesive elements were inserted.After that,the crack energy release rate fracture criterion based on the fracture mechanics theory was assigned to the failure criterion of the interface transition zone(ITZ)elements.Finally,the three-phase mesomechanical model based on the combined finite discrete element method(FDEM)was constructed.Based on this model,the meso-crack extension and macro-mechanical behaviour of coral aggregate concrete(CAC)under uniaxial compression were successfully simulated.The results demonstrated that the meso-mechanical model based on FDEM has excellent applicability to simulate the compressive properties of CAC.
基金This project is supported by National Natural Science Foundation of China (No.19832020)Provincial Natural Science Foundation of Jilin (No.20000519)
文摘Based on the elastic-plastic large deformation finite element formulation as well as the shell element combined discrete Kirchhoff theoretical plate element (DKT) with membrane square element, deep-drawing bending springback of typical U-pattern is studied. At the same time the springback values of the drawing of patterns' unloading and trimming about the satellite aerial reflecting surface are predicted and also compared with those of the practical punch. Above two springbacks all obtain satisfactory results, which provide a kind of effective quantitative pre-prediction of springback for the practical engineers.
基金supported by National Natural Science Foundation of China(Grant Nos.10971059,11071265 and 11171232)the Funds for Creative Research Groups of China(Grant No.11021101)+2 种基金the National Basic Research Program of China(Grant No.2011CB309703)the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciencesthe Program for Innovation Research in Central University of Finance and Economics
文摘To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper approximations.As applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.
基金supported by the National Natural Science Foundation of China(Grant Nos.51878060,and 52108360)the Fundamental Research Funds for the Central Universities,CHD(Grant No.300102213206).
文摘Loess is a special type of soil whose properties are significantly affected by water.However,the grout diffusion law for backfill grouting in loess shield tunnels remains unknown.Based on a visual model experimental device,three experiments were conducted with 10%,20%,and 30%loess moisture.A finite discrete element method was used to verify the grout diffusion mode,and parameters such as the tunnel buried depth,grout viscosity,and elastic modulus were considered to analyse the grout diffusion law.Experiments and numerical simulations show that the screening diffusion of grout occurs at low loess moisture,whereas splitting diffusion occurs at high loess moisture.The farthest splitting diffusion distance decreases as the tunnel buried depth,grout viscosity,and elastic modulus increase.In addition,based on capillary theory and geotechnical strength criteria,screening diffusion and splitting diffusion models were established.This study investigated the grout diffusion law and grout diffusion model,providing a reference for the design and construction of loess shield tunnels.
基金This research is supported by the National Natural Science Foundation of China(10471011).
文摘A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.
文摘The Richards equation models the water flow in a partially saturated underground porous medium under the surface.When it rains on the surface,boundary conditions of Signorini type must be considered on this part of the boundary.The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler's scheme in time and finite elements in space.The convergence of this discretization leads to the well-posedness of the problem.
