In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e...In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.展开更多
Recent advancements in additive manufacturing(AM)have revolutionized the design and production of complex engineering microstructures.Despite these advancements,their mathematical modeling and computational analysis r...Recent advancements in additive manufacturing(AM)have revolutionized the design and production of complex engineering microstructures.Despite these advancements,their mathematical modeling and computational analysis remain significant challenges.This research aims to develop an effective computational method for analyzing the free vibration of functionally graded(FG)microplates under high temperatures while resting on a Pasternak foundation(PF).This formulation leverages a new thirdorder shear deformation theory(new TSDT)for improved accuracy without requiring shear correction factors.Additionally,the modified couple stress theory(MCST)is incorporated to account for sizedependent effects in microplates.The PF is characterized by two parameters including spring stiffness(k_(w))and shear layer stiffness(k_(s)).To validate the proposed method,the results obtained are compared with those of the existing literature.Furthermore,numerical examples explore the influence of various factors on the high-temperature free vibration of FG microplates.These factors include the length scale parameter(l),geometric dimensions,material properties,and the presence of the elastic foundation.The findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments.In addition,the findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments.In addition,the results of this research will have great potential in military and defense applications such as components of submarines,fighter aircraft,and missiles.展开更多
For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of ...For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.展开更多
A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines...A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.展开更多
The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite ...The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.展开更多
A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underex...A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.展开更多
A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations....A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.展开更多
A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface i...A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.展开更多
The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and ...The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.展开更多
The effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion induced by electromigration is analyzed by finite element method.The numerical results indicate that there ex...The effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion induced by electromigration is analyzed by finite element method.The numerical results indicate that there exists critical values of the linewidth hc,the electric fieldχc and the aspect ratioβc.When h>hc,χ<χc orβ<βc,the microcrack will evolve into a stable shape as it migrates along the interconnect line.When h≤hc,χ≥χc orβ≥βc,the microcrack will split into two smaller microcracks.The critical electric field,the critical aspect ratio and the splitting time have a stronger dependence on the linewidth when h≤6.In addition,the decrease of the linewidth,the increase of the electric field or the aspect ratio is beneficial to accelerate microcrack splitting,which may delay the open failure of the interconnect line.展开更多
Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on e...Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.展开更多
Propagation characteristics of surface acoustic waves（SAWs） in ZnO films/glass substrates are theoretically investigated by the three-dimensional（3D） finite element method. At first, for（11ˉ20） ZnO films/glass ...Propagation characteristics of surface acoustic waves（SAWs） in ZnO films/glass substrates are theoretically investigated by the three-dimensional（3D） finite element method. At first, for（11ˉ20） ZnO films/glass substrates, the simulation results confirm that the Rayleigh waves along the [0001] direction and Love waves along the [1ˉ100] direction are successfully excited in the multilayered structures. Next, the crystal orientations of the ZnO films are rotated, and the influences of ZnO films with different crystal orientations on SAW characterizations, including the phase velocity, electromechanical coupling coefficient, and temperature coefficient of frequency, are investigated. The results show that at appropriate h/λ, Rayleigh wave has a maximum k^2 of 2.4% in（90°, 56.5°, 0°） ZnO film/glass substrate structure; Love wave has a maximum k^2 of 3.81% in（56°, 90°, 0°） ZnO film/glass substrate structure. Meantime, for Rayleigh wave and Love wave devices, zero temperature coefficient of frequency（TCF） can be achieved at appropriate ratio of film thickness to SAW wavelength. These results show that SAW devices with higher k^2 or lower TCF can be fabricated by flexibly selecting the crystal orientations of ZnO films on glass substrates.展开更多
An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness...An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.展开更多
Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacita...Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacitance increases quasi-quadratically with the number of electrodes increasing.The quasi-quadratic dependence can be explained by a sequence of lumped capacitors connected in parallel.For a photomixer composed of 10 electrodes and 9 photoconductive gaps,the finger capacitance increases as the gap width increases at a small electrode width,and follows the reverse trend at a large electrode width.For a constant electrode width,the finger capacitance first decreases and then slightly increases as the gap broadens until the smallest finger capacitance is formed.We also investigate the finger capacitances at different electrode and gap configurations with the 8 μm × 8 μm photomixer commonly used in previous studies.These calculations lead to a better understanding of the finger capacitance affected by the finger parameters,and should lead to terahertz photomixer optimization.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
In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed...In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.展开更多
Two kinds of fabricated hollow-core photonic crystal fibres （HC-PCFs） arc studied using finite element method （FEM） because the structures of the fibres are special, Normalized transmission spectra and transverse ...Two kinds of fabricated hollow-core photonic crystal fibres （HC-PCFs） arc studied using finite element method （FEM） because the structures of the fibres are special, Normalized transmission spectra and transverse intensity distribution of the modes are calculated and measured. And the dispersion characteristics of these two kinds of HC- PCFs were analysed from 400 nm to 800 nm. Simulated and measured results show that the special structure could affect the properties of HC-PCFs, By comparing the simulated values with the measured results, it can be clarified that FEM is feasible and accurate for analysing photonic crystal fibres whose structures are irregular and complex.展开更多
This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the p...This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context.展开更多
In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.
文摘Recent advancements in additive manufacturing(AM)have revolutionized the design and production of complex engineering microstructures.Despite these advancements,their mathematical modeling and computational analysis remain significant challenges.This research aims to develop an effective computational method for analyzing the free vibration of functionally graded(FG)microplates under high temperatures while resting on a Pasternak foundation(PF).This formulation leverages a new thirdorder shear deformation theory(new TSDT)for improved accuracy without requiring shear correction factors.Additionally,the modified couple stress theory(MCST)is incorporated to account for sizedependent effects in microplates.The PF is characterized by two parameters including spring stiffness(k_(w))and shear layer stiffness(k_(s)).To validate the proposed method,the results obtained are compared with those of the existing literature.Furthermore,numerical examples explore the influence of various factors on the high-temperature free vibration of FG microplates.These factors include the length scale parameter(l),geometric dimensions,material properties,and the presence of the elastic foundation.The findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments.In addition,the findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments.In addition,the results of this research will have great potential in military and defense applications such as components of submarines,fighter aircraft,and missiles.
基金supported by National Natural Science Foundation of China(11771257)the Shandong Provincial Natural Science Foundation of China(ZR2023YQ002,ZR2023MA007,ZR2021MA004)。
文摘For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.
基金supported by the National Natural Science Foundation of China(11871312,12131014)the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。
文摘A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.
文摘The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.
文摘A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.
基金Supported by the National Natural Science Foundation of China(50976072,51106099,10902070)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50501)the Science Foundation for the Excellent Youth Scholar of Higher Education of Shanghai(slg09003)~~
文摘A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.
基金Project supported by the National Basic Research Program of China (973Project) (No.2002CB412709) and the National Natural Science Foundation of China (Nos.50278012,10272027,19832010)
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
基金supported by the Open Project of Key Laboratory of Aerospace EDLA,CASC(No.EDL19092208)。
文摘A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.
文摘The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.
基金supported by the Natural Science Foundation of Jiangsu Province of China (No. BK20141407)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion induced by electromigration is analyzed by finite element method.The numerical results indicate that there exists critical values of the linewidth hc,the electric fieldχc and the aspect ratioβc.When h>hc,χ<χc orβ<βc,the microcrack will evolve into a stable shape as it migrates along the interconnect line.When h≤hc,χ≥χc orβ≥βc,the microcrack will split into two smaller microcracks.The critical electric field,the critical aspect ratio and the splitting time have a stronger dependence on the linewidth when h≤6.In addition,the decrease of the linewidth,the increase of the electric field or the aspect ratio is beneficial to accelerate microcrack splitting,which may delay the open failure of the interconnect line.
基金Iranian Offshore Oil Company (IOOC) for financial support of this work
文摘Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.
基金supported by the National Natural Science Foundation of China(Grant No.11304160)the Natural Science Foundation of Jiangsu Provincial Higher Education Institutions,China(Grant No.13KJB140008)the Foundation of Nanjing University of Posts and Telecommunications,China(Grant No.NY213018)
文摘Propagation characteristics of surface acoustic waves（SAWs） in ZnO films/glass substrates are theoretically investigated by the three-dimensional（3D） finite element method. At first, for（11ˉ20） ZnO films/glass substrates, the simulation results confirm that the Rayleigh waves along the [0001] direction and Love waves along the [1ˉ100] direction are successfully excited in the multilayered structures. Next, the crystal orientations of the ZnO films are rotated, and the influences of ZnO films with different crystal orientations on SAW characterizations, including the phase velocity, electromechanical coupling coefficient, and temperature coefficient of frequency, are investigated. The results show that at appropriate h/λ, Rayleigh wave has a maximum k^2 of 2.4% in（90°, 56.5°, 0°） ZnO film/glass substrate structure; Love wave has a maximum k^2 of 3.81% in（56°, 90°, 0°） ZnO film/glass substrate structure. Meantime, for Rayleigh wave and Love wave devices, zero temperature coefficient of frequency（TCF） can be achieved at appropriate ratio of film thickness to SAW wavelength. These results show that SAW devices with higher k^2 or lower TCF can be fabricated by flexibly selecting the crystal orientations of ZnO films on glass substrates.
基金supported by the Innovation Training Project for Students in NUAA(No.2016C-X0010-129)the Key Laboratory of Aircraft Environment Control and Life Support(NUAA),Ministry of Industry and Information Technology
文摘An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2011AAxxx2008A)Hundred Talent Program of the Chinese Academy of Sciences (Grant No. J08-029)the Main Direction Program of Knowledge Innovation of the Chinese Academy of Sciences (Grant No. YYYJ-1123-4)
文摘Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacitance increases quasi-quadratically with the number of electrodes increasing.The quasi-quadratic dependence can be explained by a sequence of lumped capacitors connected in parallel.For a photomixer composed of 10 electrodes and 9 photoconductive gaps,the finger capacitance increases as the gap width increases at a small electrode width,and follows the reverse trend at a large electrode width.For a constant electrode width,the finger capacitance first decreases and then slightly increases as the gap broadens until the smallest finger capacitance is formed.We also investigate the finger capacitances at different electrode and gap configurations with the 8 μm × 8 μm photomixer commonly used in previous studies.These calculations lead to a better understanding of the finger capacitance affected by the finger parameters,and should lead to terahertz photomixer optimization.
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.
文摘In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.
基金Project supported by the State Key Development Program for Basic Research of China (Grant No 2003CB314905)the National High Technology Development Program of China (Grant No 2003AA311010)
文摘Two kinds of fabricated hollow-core photonic crystal fibres （HC-PCFs） arc studied using finite element method （FEM） because the structures of the fibres are special, Normalized transmission spectra and transverse intensity distribution of the modes are calculated and measured. And the dispersion characteristics of these two kinds of HC- PCFs were analysed from 400 nm to 800 nm. Simulated and measured results show that the special structure could affect the properties of HC-PCFs, By comparing the simulated values with the measured results, it can be clarified that FEM is feasible and accurate for analysing photonic crystal fibres whose structures are irregular and complex.
文摘This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
