In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me...In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.展开更多
An alternating direction implicit (ADI) Galerkin method with moving finite element spaces is formulated for a class of second order hyperbolic equations in two space variables. A priori H 1 error estimate is derived.
In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant...In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.展开更多
The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reyn...The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.展开更多
Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the fl...Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body＇s inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.展开更多
The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and ana...The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.展开更多
A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characte...A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.展开更多
This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elemen...This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations.展开更多
The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and an...The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.展开更多
Fluxgate current sensors(FGCSs)are increasingly employed in power systems due to their high-precision characteristics,yet their measurement flexibility remains constrained by conventional closed-core designs.To addres...Fluxgate current sensors(FGCSs)are increasingly employed in power systems due to their high-precision characteristics,yet their measurement flexibility remains constrained by conventional closed-core designs.To address this limitation,we proposed a split-core sensor structure comprising four magnetic core strips,which achieved non-intrusive current measurement while maintaining detection accuracy.An analytical model of the induced electromotive force was established based on the probe’s geometric configuration,followed by finite element simulations to optimize key parameters including core radius,core width,excitation coil turns,and sensing coil configuration.A complete prototype integrating the measurement probe,excitation circuit,and signal processing circuitry was developed and experimentally validated.The experimental results show a sensitivity of 0.1099 V/A,a hysteresis error of 0.559%,and a repeatability error of 1.574%over a measurement range of±10 A.After polynomial fitting-based error compensation,the nonlinearity error was reduced to 0.208%,achieving performance comparable to closed-core sensors.This work provided a practical solution for applications demanding both high measurement accuracy and installation flexibility.展开更多
This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity...This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.展开更多
An especial snake SiC pipe was designed for collecting losing heat from furnaces. The three-dimensions thermal, fluid and thermal stress coupled field of heat exchanger was analyzed by using the commercial engineering...An especial snake SiC pipe was designed for collecting losing heat from furnaces. The three-dimensions thermal, fluid and thermal stress coupled field of heat exchanger was analyzed by using the commercial engineering computer package ANSYS. The structural and operational parameters of heat exchanger, the junction between standpipe and snake pipe, the diameter of snake pipe, ratio of thickness to diameter of pipe, velocity of inlet air were optimized for thermal stress. The computed results show that the large thermal stress exits in the SiC, and the stand pipe should be ellipse for the least thermal stress; the optimal ratio of thickness to diameter of pipe is 6, the velocity of inlet air is 25 m/s. The most thermal stress is in inverse proportion to diameter of pipe and velocity of inlet air.展开更多
Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces sever...Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces several forms of topographic effects: direct effect on gravity, secondary indirect effect on gravity and indirect effects on the (quasi-) geoid, respectively. To strike a balance between computation accuracy and numerical efficiency, the global integration region of topographic effects is usually divided into near zone and far zone. We focus on the computation of near-zone topographic effects, which are functions of actual topographic masses and condensed masses. Since there have already been mature formulas for gravitational attraction and potential of actual topographic masses using rectangular prism model, we put forward surface element model for condensed masses. Afterwards, the formulas for near-zone direct and indirect effects are obtained easily by combining the rectangular prism model and surface element model. To overcome the planar approximation errors involved with the new formulas for near-zone topographic effects, the Earth’s curvature can be taken into account. It is recommended to apply the formulas based on the rectangular prism and surface element considering the Earth’s curvature to calculate near-zone topographic effects for high-accuracy demand to determine geoid and quasi-geoid.展开更多
A finite element based numerical method is employed to analyze the wave radiation by multiple or a group of cylinders in the time domain. The nonlinear free surface and body surface boundary conditions are satisfied b...A finite element based numerical method is employed to analyze the wave radiation by multiple or a group of cylinders in the time domain. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a Finite Element Method （FEM）. The matrix equation of the FEM is solved through iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional （3-D） mesh required is generated based on a two-dimensional （2-D） hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including the cases of two cylinders and four cylinders and a group of eighteen cylinders are obtained to show the joint influences of cylinders on the first- and second- order waves and forces, including the effects of spacing ratios and wave frequency on the second order waves and the mean force, in particular.展开更多
基金heprojectissupportedbyNNSFofChina (No .1 9972 0 39) .
文摘In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.
基金the National Natural Sciences Foundation of China
文摘An alternating direction implicit (ADI) Galerkin method with moving finite element spaces is formulated for a class of second order hyperbolic equations in two space variables. A priori H 1 error estimate is derived.
基金supported by the National Natural Science Foundation of China (60533060, 10672032, 10726067)Science Foundation of Dalian University of Technology (SFDUT07001)
文摘In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.
文摘The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.
文摘Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body＇s inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.
文摘The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.
文摘A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.
文摘This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations.
文摘The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.
基金supported by Yunnan Fundamental Research Projects(No.202301AT070181)Yunnan Fundamental Research Projects(No.202401CF070126)+1 种基金Xingdian Talent Support Program of Yunnan Province(No.KKRD202203070)Yunnan High level Science and Technology Talents and Innovation Team Selection Special Project(No.202405AS350001).
文摘Fluxgate current sensors(FGCSs)are increasingly employed in power systems due to their high-precision characteristics,yet their measurement flexibility remains constrained by conventional closed-core designs.To address this limitation,we proposed a split-core sensor structure comprising four magnetic core strips,which achieved non-intrusive current measurement while maintaining detection accuracy.An analytical model of the induced electromotive force was established based on the probe’s geometric configuration,followed by finite element simulations to optimize key parameters including core radius,core width,excitation coil turns,and sensing coil configuration.A complete prototype integrating the measurement probe,excitation circuit,and signal processing circuitry was developed and experimentally validated.The experimental results show a sensitivity of 0.1099 V/A,a hysteresis error of 0.559%,and a repeatability error of 1.574%over a measurement range of±10 A.After polynomial fitting-based error compensation,the nonlinearity error was reduced to 0.208%,achieving performance comparable to closed-core sensors.This work provided a practical solution for applications demanding both high measurement accuracy and installation flexibility.
基金The project supported by the National Natural Science Foundation of China(10132010 and 10472089)
文摘This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.
文摘An especial snake SiC pipe was designed for collecting losing heat from furnaces. The three-dimensions thermal, fluid and thermal stress coupled field of heat exchanger was analyzed by using the commercial engineering computer package ANSYS. The structural and operational parameters of heat exchanger, the junction between standpipe and snake pipe, the diameter of snake pipe, ratio of thickness to diameter of pipe, velocity of inlet air were optimized for thermal stress. The computed results show that the large thermal stress exits in the SiC, and the stand pipe should be ellipse for the least thermal stress; the optimal ratio of thickness to diameter of pipe is 6, the velocity of inlet air is 25 m/s. The most thermal stress is in inverse proportion to diameter of pipe and velocity of inlet air.
基金The National Natural Science Foundation of China (41674025,41674082)The Independent Research Foundation of State Key Laboratory of Geo-information Engineering (SKLGIE2018-ZZ-10).
文摘Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces several forms of topographic effects: direct effect on gravity, secondary indirect effect on gravity and indirect effects on the (quasi-) geoid, respectively. To strike a balance between computation accuracy and numerical efficiency, the global integration region of topographic effects is usually divided into near zone and far zone. We focus on the computation of near-zone topographic effects, which are functions of actual topographic masses and condensed masses. Since there have already been mature formulas for gravitational attraction and potential of actual topographic masses using rectangular prism model, we put forward surface element model for condensed masses. Afterwards, the formulas for near-zone direct and indirect effects are obtained easily by combining the rectangular prism model and surface element model. To overcome the planar approximation errors involved with the new formulas for near-zone topographic effects, the Earth’s curvature can be taken into account. It is recommended to apply the formulas based on the rectangular prism and surface element considering the Earth’s curvature to calculate near-zone topographic effects for high-accuracy demand to determine geoid and quasi-geoid.
基金supported by the Fundamental Research Funds for the Central Universities and NPRP 08-691-2-289 grantfrom Qatar National Research Fund (QNRF)
文摘A finite element based numerical method is employed to analyze the wave radiation by multiple or a group of cylinders in the time domain. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a Finite Element Method （FEM）. The matrix equation of the FEM is solved through iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional （3-D） mesh required is generated based on a two-dimensional （2-D） hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including the cases of two cylinders and four cylinders and a group of eighteen cylinders are obtained to show the joint influences of cylinders on the first- and second- order waves and forces, including the effects of spacing ratios and wave frequency on the second order waves and the mean force, in particular.
