The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of dril...The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.展开更多
The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of t...The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.展开更多
In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical a...In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.展开更多
The rapid advancement of technology and the increasing speed of vehicles have led to a substantial rise in energy consumption and growing concern over environmental pollution.Beyond the promotion of new energy vehicle...The rapid advancement of technology and the increasing speed of vehicles have led to a substantial rise in energy consumption and growing concern over environmental pollution.Beyond the promotion of new energy vehicles,reducing aerodynamic drag remains a critical strategy for improving energy efficiency and lowering emissions.This study investigates the influence of key geometric parameters on the aerodynamic drag of vehicles.A parametric vehicle model was developed,and computational fluid dynamics(CFD)simulations were conducted to analyse variations in the drag coefficient(C_(d))and pressure distribution across different design configurations.The results reveal that the optimal aerodynamic performance—characterized by a minimized drag coefficient—is achieved with the following parameter settings:engine hood angle(α)of 15°,windshield angle(β)of 25°,rear window angle(γ)of 40°,rear upwards tail lift angle(θ)of 10°,ground clearance(d)of 100 mm,and side edge angle(s)of 5°.These findings offer valuable guidance for the aerodynamic optimization of vehicle body design and contribute to strategies aimed at energy conservation and emission reduction in the automotive sector.展开更多
The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to ...The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.展开更多
In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a gene...In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.展开更多
为提升低空风切变预报精度,本文综合运用欧洲中期天气预报中心第五代再分析资料[European Centre for Medium-Range Weather Forecasts(ECMWF)fifth-generation reanalysis data,ERA5]和美国国家环境预报中心(National Centers for Envi...为提升低空风切变预报精度,本文综合运用欧洲中期天气预报中心第五代再分析资料[European Centre for Medium-Range Weather Forecasts(ECMWF)fifth-generation reanalysis data,ERA5]和美国国家环境预报中心(National Centers for Environmental Prediction,NCEP)的FNL全球再分析资料(Final Operational Global Analysis)、先进星载热发射和反射辐射仪全球数字高程模型以及兰州中川机场的实况观测资料,采用中尺度数值天气预报模式(Weather Research and Forecasting Model,WRF)、WRF结合计算流体动力学(Computational Fluid Dynamics,CFD)方法、长短期神经网络(Long Short-Term Memory,LSTM)方法,对2021年4月15-16日兰州中川机场的两次风切变过程进行模拟分析。结果表明:(1)在小于1 km的网格中使用大涡模拟,WRF模式在单个站点风速模拟任务中表现更好,但在近地面水平风场风速模拟效果上,不如WRF模式结合计算流体力学模型方案;(2)对于飞机降落过程中遭遇的两次低空风切变的模拟,WRF-LES和WRF-CFD两种模式都可以模拟出第一次低空风切变,而第二次受传入模式的WRF风速数据值较小的影响,两种模式风速差都没有达到阈值,需要在后续工作中进一步验证;(3)低风速条件(6 m·s^(-1))下,基于LSTM的单变量风速预测模型平均绝对误差基本维持在0.59 m·s^(-1),能较好地把握不同地形与环流背景条件下风速变化的非线性关系,虽然受到WRF误差和观测要素不全的限制,多变量风速预测能在保证平均绝对百分比误差小于6.60%的情况下,以更高的计算效率和泛化能力实现风速预测。本文不仅验证了WRF-CFD和WRF-LES耦合方案在风场和低空风切变预报中的差异,还探讨了基于LSTM的风速预测的可行性和准确性,期望为提高风场模拟精度,缩短精细风场模拟时间提供新的视角和方法。展开更多
Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynam...Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynamics(MD)methods,provide powerful tools for the design of solid-state electrolytes.The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures.However,it relies on simulations at temperatures much higher than working temperature.This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark.We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV.The calculated diffusion barrier is 0.31 eV from both methods.The diffusion coefficients at room temperature are 4.3×10^(-9) cm^(2)⋅s^(−1) and 2.2×10^(-9) cm^(2)⋅s^(−1),respectively,from the NEB and MD methods.Our results justify the reliability of the MD method,even though high temperature simulations have to be employed to overcome the limitation on simulation time.展开更多
Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the ...Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids.However,traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time,and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids.In this paper,a universal multiscale method coupling an improved smoothed particle hydrodynamics(SPH)and multiscale universal interface(MUI)library is presented for viscoelastic flows.The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain.We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows.In the first example,the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions.The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain.In the second example,the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics(DPD)method.The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain.Moreover,transferring different physical quantities has an important effect on the numerical results.展开更多
基金supported by the National Natural Science Foundation of China(52174003,52374008).
文摘The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.
文摘The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.
基金supported by the National Natural Science Foundation of China(Nos.52401342 and 12572025)the Fundamental Research Funds for the Central Universities of China(Nos.D5000240076 and G2025KY05171)+1 种基金the Natural Science Basic Research Program of Shaanxi Province(No.2025JCYBMS-026)the Basic Research Programs of Taicang(No.TC2024JC36)。
文摘In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.
基金funded by the“Hundred Outstanding Talents”Support Program of Jining University,a provincial-level key project in the field of natural sciences,grant number 2023ZYRC23Jining Key R&D Program(Soft Science)Project,No.2024JNZC010Shandong Province Key Research and Development Program(Technology-Based Small and Medium-sized Enterprises Innovation Capability Improvement)Project No.2025TSGCCZZB0679.
文摘The rapid advancement of technology and the increasing speed of vehicles have led to a substantial rise in energy consumption and growing concern over environmental pollution.Beyond the promotion of new energy vehicles,reducing aerodynamic drag remains a critical strategy for improving energy efficiency and lowering emissions.This study investigates the influence of key geometric parameters on the aerodynamic drag of vehicles.A parametric vehicle model was developed,and computational fluid dynamics(CFD)simulations were conducted to analyse variations in the drag coefficient(C_(d))and pressure distribution across different design configurations.The results reveal that the optimal aerodynamic performance—characterized by a minimized drag coefficient—is achieved with the following parameter settings:engine hood angle(α)of 15°,windshield angle(β)of 25°,rear window angle(γ)of 40°,rear upwards tail lift angle(θ)of 10°,ground clearance(d)of 100 mm,and side edge angle(s)of 5°.These findings offer valuable guidance for the aerodynamic optimization of vehicle body design and contribute to strategies aimed at energy conservation and emission reduction in the automotive sector.
基金supported by the major advanced research project of Civil Aerospace from State Administration of Science,Technology and Industry of China.
文摘The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.
基金supported by the Swiss National Science Foundation(Grant No.189882)the National Natural Science Foundation of China(Grant No.41961134032)support provided by the New Investigator Award grant from the UK Engineering and Physical Sciences Research Council(Grant No.EP/V012169/1).
文摘In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.
文摘为提升低空风切变预报精度,本文综合运用欧洲中期天气预报中心第五代再分析资料[European Centre for Medium-Range Weather Forecasts(ECMWF)fifth-generation reanalysis data,ERA5]和美国国家环境预报中心(National Centers for Environmental Prediction,NCEP)的FNL全球再分析资料(Final Operational Global Analysis)、先进星载热发射和反射辐射仪全球数字高程模型以及兰州中川机场的实况观测资料,采用中尺度数值天气预报模式(Weather Research and Forecasting Model,WRF)、WRF结合计算流体动力学(Computational Fluid Dynamics,CFD)方法、长短期神经网络(Long Short-Term Memory,LSTM)方法,对2021年4月15-16日兰州中川机场的两次风切变过程进行模拟分析。结果表明:(1)在小于1 km的网格中使用大涡模拟,WRF模式在单个站点风速模拟任务中表现更好,但在近地面水平风场风速模拟效果上,不如WRF模式结合计算流体力学模型方案;(2)对于飞机降落过程中遭遇的两次低空风切变的模拟,WRF-LES和WRF-CFD两种模式都可以模拟出第一次低空风切变,而第二次受传入模式的WRF风速数据值较小的影响,两种模式风速差都没有达到阈值,需要在后续工作中进一步验证;(3)低风速条件(6 m·s^(-1))下,基于LSTM的单变量风速预测模型平均绝对误差基本维持在0.59 m·s^(-1),能较好地把握不同地形与环流背景条件下风速变化的非线性关系,虽然受到WRF误差和观测要素不全的限制,多变量风速预测能在保证平均绝对百分比误差小于6.60%的情况下,以更高的计算效率和泛化能力实现风速预测。本文不仅验证了WRF-CFD和WRF-LES耦合方案在风场和低空风切变预报中的差异,还探讨了基于LSTM的风速预测的可行性和准确性,期望为提高风场模拟精度,缩短精细风场模拟时间提供新的视角和方法。
基金supported by the National Natural Science Foundation of China (Grant Nos.12164019,11991060,12088101,and U1930402)the Natural Science Foundation of Jiangxi Province of China (Grant No.20212BAB201017).
文摘Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynamics(MD)methods,provide powerful tools for the design of solid-state electrolytes.The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures.However,it relies on simulations at temperatures much higher than working temperature.This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark.We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV.The calculated diffusion barrier is 0.31 eV from both methods.The diffusion coefficients at room temperature are 4.3×10^(-9) cm^(2)⋅s^(−1) and 2.2×10^(-9) cm^(2)⋅s^(−1),respectively,from the NEB and MD methods.Our results justify the reliability of the MD method,even though high temperature simulations have to be employed to overcome the limitation on simulation time.
基金Project supported by the National Natural Science Foundation of China(No.52109068)the Water Conservancy Technology Project of Jiangsu Province of China(No.2022060)。
文摘Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids.However,traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time,and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids.In this paper,a universal multiscale method coupling an improved smoothed particle hydrodynamics(SPH)and multiscale universal interface(MUI)library is presented for viscoelastic flows.The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain.We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows.In the first example,the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions.The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain.In the second example,the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics(DPD)method.The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain.Moreover,transferring different physical quantities has an important effect on the numerical results.
