An explicit,time-dependent variable grid finite difference method is introduced and analyzed for approximating the solution of a scalar conservation law in two dimension. The scheme is stable,and the numerical solutio...An explicit,time-dependent variable grid finite difference method is introduced and analyzed for approximating the solution of a scalar conservation law in two dimension. The scheme is stable,and the numerical solution is proved to converges to the relevant physical solution.展开更多
In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with t...In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance.展开更多
The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the ...The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.展开更多
Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and ...Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.展开更多
Boundary procedure is an important phenomenon in numerical simulation. To reduce or eliminate the spurious reflections significantly which is occurred in boundary is a challenging and vital approach. The appropriate a...Boundary procedure is an important phenomenon in numerical simulation. To reduce or eliminate the spurious reflections significantly which is occurred in boundary is a challenging and vital approach. The appropriate artificial numerical boundaries can be applied to eliminate the effect of unnecessary spurious reflections in case of the numerical simulations of wave propagation phenomena problems. Typically, to reduce the artificial reflections, the absorbing boundary conditions are necessary. In this paper, we overview and investigate the appropriate typical absorbing boundary conditions and analyzed the boundary effect of two dimensional wave equation numerically. Reflections over the wide-ranging incident angles are complicated to eliminate, but the absorbing boundary conditions that we have applied are computationally cost efficient, easy to apply and able to reduce reflections significantly. For numerical solution, finite difference method is applied to develop numerical scheme using 2D wave equation. Using the developed numerical scheme, we obtain the numerical solution of the governing equation as an initial boundary value problem and realize the qualitative behavior of the solution in infinite space. The finite difference numerical scheme has been investigated by developing MATLAB programming language code. Numerical results have been discussed and analyzed with presenting different qualitative behavior of the numerical scheme. The accuracy and efficiency of the numerical scheme has been illustrated. The stability analysis was discussed and verified stability condition. Using the numerical scheme and absorbing boundary conditions, the boundary effects and absorption of spurious reflection of boundary have been demonstrated.展开更多
The acoustic tools widely used in borehole well logging and being developed in borehole acoustic reflection imaging do not have the function of azimuthal measurement due to a symmetric source, so they can not be used ...The acoustic tools widely used in borehole well logging and being developed in borehole acoustic reflection imaging do not have the function of azimuthal measurement due to a symmetric source, so they can not be used to evaluate the azimuthal character of borehole formation. In this paper, a 3D finite difference method was used to simulate the acoustic fields in a fluid-filled borehole generated by a traditional monopole source and a phased arc array. Acoustic waveforms were presented for both cases. The analysis of the simulated waveforms showed that different from the monopole source, the acoustic energy generated by the phased arc array transmitter mainly radiated to the borehole in a narrow azimuthal range, which was the key technique to implement azimuthal acoustic well logging. Similar to the monopole source, the waveforms generated by the phased arc array in the fluid-filled borehole also contain compressional （P） waves and shear （S） waves refracted along the borehole, which is the theoretical foundation of phased arc array acoustic well logging.展开更多
The Ginzbury-Landau theory for bainitic transformation was devised, which contains two first-order phase transformations, one being reconstructive represented by the diffusional proeutectoidal precipitation of ferrite...The Ginzbury-Landau theory for bainitic transformation was devised, which contains two first-order phase transformations, one being reconstructive represented by the diffusional proeutectoidal precipitation of ferrite, and the other the displacive transformation. It provides a coupled mechanism for the formation of bainite. With the numerical simulation results, a diffusion-induced nucleation and a diffusion-accompanied growth of displacive transformation were suggested. This theory can be helpful to over- throw the thermodynamic difficulty of displacive transformation above the Ms temperature, and also helpful to understand the Bs temperature, the partial supersaturation, the single variation of bainitic carbides, and the incomplete-reaction phenomenon of bainitic transformation, etc..展开更多
A number of phenomena and processes in geosciences can be summarized by second order partial differential equations. The major numerical methods for their solution include the classical finite difference method and th...A number of phenomena and processes in geosciences can be summarized by second order partial differential equations. The major numerical methods for their solution include the classical finite difference method and the finite element method newly developed in the last two or three decades. Since 1977 the author has proved that for the Laplace and Poisson equations, these two methods are identical and are different only in the process of formulation. For transient problems, such as heat conduction in the earth and the groundwater and oil-gas unsteady flow in porous media, there are some differences in resulting linear algebraic euqations. In general, two methods give similar results, but when the time step is decreased to some extent, the resulting algebraic equation will be consistent with the anti-heat conduction equation rather than the original heat conduction equation. This is the reason why unrealistic potentials are produced by the finite element method. Such a problem can be overcome by using the lumped mass procedure, but it makes the two methods identical again.To improve the traditional finite difference method, it is quite desirable to introduce the common practice of the finite element method to define the parameters in elements rather than on nodes.展开更多
This study carries out a complete analysis of time-space solution of hy- drodynamics of pentagonal/decagonal quasicrystals. The behaviors of wave propagation for phonons and diffusion for phasons and coupling between ...This study carries out a complete analysis of time-space solution of hy- drodynamics of pentagonal/decagonal quasicrystals. The behaviors of wave propagation for phonons and diffusion for phasons and coupling between phonon-phason fields are explored explicitly. Comprehensive discussion on physical time-space variations of all hydrodynamic field variables of the alloy quasicrystals is given. The computational spec- imen is simple, convenient in testing computational results, and provides a possibility that is easy to test experimentally. The quantitative results of mass density, viscosity ve- locities, phonon displacements, phason displacements, phonon stresses, phason stresses, viscosity stresses, and their time-space variations help us understand the motion of solid quasicrystals in a hydrodynamic condition （long-wavelength and low-frequency）. The analysis presented in this paper can be used for octagonal and dodecagonal quasicrys- tals and is easily extended to other two-dimensional quasicrystals and three-dimensional icosahedral quasicrystals. Some problems explored by the computational results are also discussed.展开更多
This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified HoekeBrown failure criterion.Although th...This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified HoekeBrown failure criterion.Although this criterion is considered a reference value for empirical and numerical calculations,some limitations of its basic simplifications have not been clarified yet.This research compares the analytical results obtained from the novel discontinuity layout optimization(DLO)method and the numerical solutions from the finite difference method(FDM).The limitations of the analytical solution are considered by comparing different DLO failure modes,thus allowing for the first time a critical evaluation of its scope and conditioning for implementation.Errors of up to 40%in the bearing capacity and unrealistic failure modes are the main issues in the analytical solution.The main aspects of the DLO method are also analyzed with an emphasis on the linearization of the rock failure criterion and the accuracy resulting from the discretization size.The analysis demonstrates DLO as a very efficient and accurate tool to address the pile tip bearing capacity,presenting considerable advantages over other methods.展开更多
A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function w...A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.展开更多
In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform...In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform and finite differences, are used in different subdomains. Our aim of this approach is to combine the flexibility of differential transform and the efficiency of finite differences. An explicit hybrid method for the transient response of inhomogeneous nonlinear partial differential equations is presented;applying finite difference scheme on the fixed grid size is used to approximate the space discretisation, whereas the differential transform method is used for time operator. Comparison of the efficiency of the different approaches is a very important aspect of this study. In our test cases, the hybrid approach is faster than the corresponding highly optimized finite difference method in two dimensional computations. We compared our hybrid approach’s results with the exact and/or numerical solutions of PDE which obtained from Adomian Decomposition Method. Results show that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations and get remarkable results in predicting the solutions of nonlinear initial value problems.展开更多
This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kut...This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kutta method and it's datum results are discussed. This paper solves ODES of general form using variable mesh-length, linearizing the nonlinear terms by finite analysis method, fuilding an iteration sequence, and amending the nonlinear terms by iteration . The conditions of convergent operation of iteration solution is checked. The movement orbit and velocity of the pellets are calculated. Analysis of research results and it's application examples are illustrated.展开更多
In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using ...In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using the finite element scheme.The mass conservation and current density continuous equation with the penalty scheme was applied 10 improve the stability.According to the phase-field model coupled with the energy law preserving method,the GMAW model was discretized and a metal transfer process with a pulse current was simulated.It was found that the numerical solution agrees well with the data of the metal transfer process obtained by high-speed photography.Compared with the numerical solution of the volume of fuid model,which was widely studied in the GMAW system based on the finite element method Euler scheme,the energy law preserving method can provide better accuracy in predicting the shape evolution of the droplet and with a greater computing efficiency.展开更多
For compressible two-phase displacement problem,the modified upwind finite difference fractionalsteps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplicationof differen...For compressible two-phase displacement problem,the modified upwind finite difference fractionalsteps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplicationof difference operators,decomposition of high order difference operators,the theory of prior estimates and tech-niques are used.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.Thismethod has already been applied to the numerical simulation of seawater intrusion and migration-accumulationof oil resources.展开更多
The numerical simulation and analysis of natural gas hydrates with heat and mass transfer are essential for identifying and predicting reservoir states during dissociation and seepage processes.In specific cases,the t...The numerical simulation and analysis of natural gas hydrates with heat and mass transfer are essential for identifying and predicting reservoir states during dissociation and seepage processes.In specific cases,the transported substance may undergo phase transitions between solid,liquid,or gas states during dissociation and hydration processes.To effectively predict hydrate dissociation performance influenced by multi-field coupling processes,this study proposes a novel bond-based peridynamic coupled finite difference model that accounts for gas-liquid two-phase seepage behavior.The developed peridynamic(PD)model simulates hydrate dissociation reactions accompanied by gas-liquid seepage,mass transfer,and heat transfer phenomena.The formulation demonstrates strong agreement with established analytical solutions for one-dimensional problems and finite element transient solutions for two-dimensional problems in the literature,validating the accuracy and reliability of the newly constructed model.This research presents an innovative approach to simulate heat transport and multiphase flow phenomena associated with hydrate dissociation.展开更多
波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风...波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。展开更多
文摘An explicit,time-dependent variable grid finite difference method is introduced and analyzed for approximating the solution of a scalar conservation law in two dimension. The scheme is stable,and the numerical solution is proved to converges to the relevant physical solution.
基金This work was parially supported by the Natural Science Foundation of Beijing Munisipality(Grant No.1212007)by the Science Foundations of China University of Petroleum,Beijing(Grant Nos.2462020YXZZ004 and 2462020XKJS02).
文摘In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11304074,61475042,and 11274088)the Natural Science Foundation of Hebei Province,China(Grant Nos.A2015202320 and GCC2014048)the Key Subject Construction Project of Hebei Province University,China
文摘The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.
基金supported by the National Natural Science Foundation of China(No.42372287 and No.U24A20178)the Fundamental Research Funds for the Central Universities CHD(No.2024SHEEAR002)+3 种基金the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shaanxi Province(No.2020024)the China Postdoctoral Science Foundation(GZC20232955,2024M753472,and 2024MD763937)the Science-Technology Foundation for Young Scientists of Gansu Province,China(No.24JRRA097)the Study of biodiversity survey and limiting factor analysis of Yinkentala(2023ZL01).
文摘Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.
文摘Boundary procedure is an important phenomenon in numerical simulation. To reduce or eliminate the spurious reflections significantly which is occurred in boundary is a challenging and vital approach. The appropriate artificial numerical boundaries can be applied to eliminate the effect of unnecessary spurious reflections in case of the numerical simulations of wave propagation phenomena problems. Typically, to reduce the artificial reflections, the absorbing boundary conditions are necessary. In this paper, we overview and investigate the appropriate typical absorbing boundary conditions and analyzed the boundary effect of two dimensional wave equation numerically. Reflections over the wide-ranging incident angles are complicated to eliminate, but the absorbing boundary conditions that we have applied are computationally cost efficient, easy to apply and able to reduce reflections significantly. For numerical solution, finite difference method is applied to develop numerical scheme using 2D wave equation. Using the developed numerical scheme, we obtain the numerical solution of the governing equation as an initial boundary value problem and realize the qualitative behavior of the solution in infinite space. The finite difference numerical scheme has been investigated by developing MATLAB programming language code. Numerical results have been discussed and analyzed with presenting different qualitative behavior of the numerical scheme. The accuracy and efficiency of the numerical scheme has been illustrated. The stability analysis was discussed and verified stability condition. Using the numerical scheme and absorbing boundary conditions, the boundary effects and absorption of spurious reflection of boundary have been demonstrated.
基金supported by the National Natural ScienceFoundation of China(Grant Nos.10534040,40574049 and 40874097)the Research Fund for the Doctoral Programof Higher Education(Grant No.20070425028)the Foundation of State Key Laboratory of Petroleum Resourceand Prospecting,China University of Petroleum(Grant No.PRPDX2008-08).
文摘The acoustic tools widely used in borehole well logging and being developed in borehole acoustic reflection imaging do not have the function of azimuthal measurement due to a symmetric source, so they can not be used to evaluate the azimuthal character of borehole formation. In this paper, a 3D finite difference method was used to simulate the acoustic fields in a fluid-filled borehole generated by a traditional monopole source and a phased arc array. Acoustic waveforms were presented for both cases. The analysis of the simulated waveforms showed that different from the monopole source, the acoustic energy generated by the phased arc array transmitter mainly radiated to the borehole in a narrow azimuthal range, which was the key technique to implement azimuthal acoustic well logging. Similar to the monopole source, the waveforms generated by the phased arc array in the fluid-filled borehole also contain compressional （P） waves and shear （S） waves refracted along the borehole, which is the theoretical foundation of phased arc array acoustic well logging.
文摘The Ginzbury-Landau theory for bainitic transformation was devised, which contains two first-order phase transformations, one being reconstructive represented by the diffusional proeutectoidal precipitation of ferrite, and the other the displacive transformation. It provides a coupled mechanism for the formation of bainite. With the numerical simulation results, a diffusion-induced nucleation and a diffusion-accompanied growth of displacive transformation were suggested. This theory can be helpful to over- throw the thermodynamic difficulty of displacive transformation above the Ms temperature, and also helpful to understand the Bs temperature, the partial supersaturation, the single variation of bainitic carbides, and the incomplete-reaction phenomenon of bainitic transformation, etc..
文摘A number of phenomena and processes in geosciences can be summarized by second order partial differential equations. The major numerical methods for their solution include the classical finite difference method and the finite element method newly developed in the last two or three decades. Since 1977 the author has proved that for the Laplace and Poisson equations, these two methods are identical and are different only in the process of formulation. For transient problems, such as heat conduction in the earth and the groundwater and oil-gas unsteady flow in porous media, there are some differences in resulting linear algebraic euqations. In general, two methods give similar results, but when the time step is decreased to some extent, the resulting algebraic equation will be consistent with the anti-heat conduction equation rather than the original heat conduction equation. This is the reason why unrealistic potentials are produced by the finite element method. Such a problem can be overcome by using the lumped mass procedure, but it makes the two methods identical again.To improve the traditional finite difference method, it is quite desirable to introduce the common practice of the finite element method to define the parameters in elements rather than on nodes.
基金Project supported by the National Natural Science Foundation of China(No.11272053)
文摘This study carries out a complete analysis of time-space solution of hy- drodynamics of pentagonal/decagonal quasicrystals. The behaviors of wave propagation for phonons and diffusion for phasons and coupling between phonon-phason fields are explored explicitly. Comprehensive discussion on physical time-space variations of all hydrodynamic field variables of the alloy quasicrystals is given. The computational spec- imen is simple, convenient in testing computational results, and provides a possibility that is easy to test experimentally. The quantitative results of mass density, viscosity ve- locities, phonon displacements, phason displacements, phonon stresses, phason stresses, viscosity stresses, and their time-space variations help us understand the motion of solid quasicrystals in a hydrodynamic condition （long-wavelength and low-frequency）. The analysis presented in this paper can be used for octagonal and dodecagonal quasicrys- tals and is easily extended to other two-dimensional quasicrystals and three-dimensional icosahedral quasicrystals. Some problems explored by the computational results are also discussed.
文摘This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified HoekeBrown failure criterion.Although this criterion is considered a reference value for empirical and numerical calculations,some limitations of its basic simplifications have not been clarified yet.This research compares the analytical results obtained from the novel discontinuity layout optimization(DLO)method and the numerical solutions from the finite difference method(FDM).The limitations of the analytical solution are considered by comparing different DLO failure modes,thus allowing for the first time a critical evaluation of its scope and conditioning for implementation.Errors of up to 40%in the bearing capacity and unrealistic failure modes are the main issues in the analytical solution.The main aspects of the DLO method are also analyzed with an emphasis on the linearization of the rock failure criterion and the accuracy resulting from the discretization size.The analysis demonstrates DLO as a very efficient and accurate tool to address the pile tip bearing capacity,presenting considerable advantages over other methods.
文摘A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.
文摘In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform and finite differences, are used in different subdomains. Our aim of this approach is to combine the flexibility of differential transform and the efficiency of finite differences. An explicit hybrid method for the transient response of inhomogeneous nonlinear partial differential equations is presented;applying finite difference scheme on the fixed grid size is used to approximate the space discretisation, whereas the differential transform method is used for time operator. Comparison of the efficiency of the different approaches is a very important aspect of this study. In our test cases, the hybrid approach is faster than the corresponding highly optimized finite difference method in two dimensional computations. We compared our hybrid approach’s results with the exact and/or numerical solutions of PDE which obtained from Adomian Decomposition Method. Results show that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations and get remarkable results in predicting the solutions of nonlinear initial value problems.
文摘This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kutta method and it's datum results are discussed. This paper solves ODES of general form using variable mesh-length, linearizing the nonlinear terms by finite analysis method, fuilding an iteration sequence, and amending the nonlinear terms by iteration . The conditions of convergent operation of iteration solution is checked. The movement orbit and velocity of the pellets are calculated. Analysis of research results and it's application examples are illustrated.
基金Yanhai Lin was supported by the National Natural Science Foundation of China(Grant No.11702101)the Fundamental Research Funds for the Central Universities and the Promo-tion Program for Young and Middle aged Teacher in Science and Technology Research of Huaqiao University(Grant No.ZQN-PY502)+1 种基金the Natural Science Foundation of Fujian Province(Grant No.2019105093)Quanzhou High-Level Talents Support Plan.
文摘In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using the finite element scheme.The mass conservation and current density continuous equation with the penalty scheme was applied 10 improve the stability.According to the phase-field model coupled with the energy law preserving method,the GMAW model was discretized and a metal transfer process with a pulse current was simulated.It was found that the numerical solution agrees well with the data of the metal transfer process obtained by high-speed photography.Compared with the numerical solution of the volume of fuid model,which was widely studied in the GMAW system based on the finite element method Euler scheme,the energy law preserving method can provide better accuracy in predicting the shape evolution of the droplet and with a greater computing efficiency.
基金Supported by the Major State Basic Research Program of China (Grant No.1999032803)the National Natural Science Foundation of China (Grant No.10372052,10271066)the Decorate Foundation of the Ministry Education of China (Grant No.20030422047)
文摘For compressible two-phase displacement problem,the modified upwind finite difference fractionalsteps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplicationof difference operators,decomposition of high order difference operators,the theory of prior estimates and tech-niques are used.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.Thismethod has already been applied to the numerical simulation of seawater intrusion and migration-accumulationof oil resources.
基金financially supported by the National Natural Science Foundation of China(General Program,Grant No.52374011)the Research and Innovation Fund for Graduate Students of Southwest Petroleum University(Grant No.2021CXYB04)the Sichuan Province Science and Technology Support Program(Grant No.2023NSFSC1980)。
文摘The numerical simulation and analysis of natural gas hydrates with heat and mass transfer are essential for identifying and predicting reservoir states during dissociation and seepage processes.In specific cases,the transported substance may undergo phase transitions between solid,liquid,or gas states during dissociation and hydration processes.To effectively predict hydrate dissociation performance influenced by multi-field coupling processes,this study proposes a novel bond-based peridynamic coupled finite difference model that accounts for gas-liquid two-phase seepage behavior.The developed peridynamic(PD)model simulates hydrate dissociation reactions accompanied by gas-liquid seepage,mass transfer,and heat transfer phenomena.The formulation demonstrates strong agreement with established analytical solutions for one-dimensional problems and finite element transient solutions for two-dimensional problems in the literature,validating the accuracy and reliability of the newly constructed model.This research presents an innovative approach to simulate heat transport and multiphase flow phenomena associated with hydrate dissociation.
文摘波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。
