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
Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that fo...Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.展开更多
In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the met...In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.展开更多
In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation ...In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.展开更多
In this article,we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation.This problem is ill-posed and the quasi-boundary value method is proposed to deal wi...In this article,we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation.This problem is ill-posed and the quasi-boundary value method is proposed to deal with this inverse problem and obtain the series expression of the regularized solution for the inverse initial value problem.We prove the error estimates between the regularization solution and the exact solution by using an a priori regularization parameter and an a posteriori regularization parameter choice rule.Some numerical results in one-dimensional case and two-dimensional case show that our method is efficient and stable.展开更多
In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of partic...In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.展开更多
A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an ...A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an adjustable high order for the functions over a bounded interval, which allows the expansion coefficients to be explicitly expressed by the function values at a series of single points. When the solution method is used, the nonlinear initial boundary value problems are first spatially discretized into a series of nonlinear initial value problems by combining the proposed wavelet approximation and the conventional Galerkin method, and a novel high-order step-by-step time integrating approach is then developed for the resulting nonlinear initial value problems with the same function approximation scheme based on the wavelet theory. The solution method is shown to have the N th-order accuracy, as long as the Coiflet with [0, 3 N-1]compact support is adopted, where N can be any positive even number. Typical examples in mechanics are considered to justify the accuracy and efficiency of the method.展开更多
A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions.In order to realize the establishment of this method,an approximate e...A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions.In order to realize the establishment of this method,an approximate expression of multiple integrals of a continuous function defined in a three-dimensional bounded domain is proposed by combining wavelet expansion and Lagrange boundary extension.Through applying such an integral technique,during the solution of nonlinear partial differential equations,the unknown function and its lower-order partial derivatives can be approximately expressed by its highest-order partial derivative values at nodes.A set of nonlinear algebraic equations with respect to these nodal values of the highest-order partial derivative is obtained using a collocation method.The validation and convergence of the proposed method are examined through several benchmark problems,including the eighth-order two-dimensional and fourth-order three-dimensional boundary value problems and the large deflection bending of von Karman plates.Results demonstrate that the present method has higher accuracy and convergence rate than most existing numerical methods.Most importantly,the convergence rate of the proposed method seems to be independent of the order of the differential equations,because it is always sixth order for second-,fourth-,sixth-,and even eighth-order problems.展开更多
The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and ex...The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.展开更多
This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mes...The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mesh,while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field.The boundary condition is implemented by introducing a force term into the momentum equation,and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process.Over the past decades,the diffuse-interface IBM has gained popularity and spawned many variants,effectively handling a wide range of flow problems from isothermal to thermal flows,from laminar to turbulent flows,and from complex geometries to fluidstructure interaction scenarios.This paper first outlines the basic principles of the diffuse-interface IBM,then highlights recent advancements achieved by the authors’research group,and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.展开更多
The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through...The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.展开更多
Monotone sequences are constructed that converge to the ex tremal solutions of second order three point boundary value problems when the functions involved do not possess any monotone properties.
Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data imm...Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data immersion method(BDIM)for compressible flows,which were solved using a fully self-programmed Fortran code.Results show that the predicted thrust spectrum aligns closely with the experimental measurements.In addition,it captures the thrust dipole directivity of the noise around the rotating propeller due to random pressure pulsations on the blades,as well as the flow structures simultaneously.Furthermore,the differences in the statistical characteristics,flow structures,and low-frequency broadband thrust spectra due to different turbulence levels were investigated.This analysis indicates that the interaction between the upstream,which is characterized by a lower turbulence level and a higher turbulent length of scale,and the rotating propeller results in a lower amplitude in force spectra and a slight increase in the scale of tip vortices.展开更多
Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploi...Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.展开更多
The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary....The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary.Therefore,this method has the merits of purely meshless,easy to program,high solution accuracy and so on.In this paper,we investigate the effectiveness of the BKM for solving Helmholtz-type problems under various conditions through a series of novel numerical experiments.The results demonstrate that the BKM is efficient and achieves high computational accuracy for problems with smooth or continuous boundary conditions.However,when applied to discontinuous boundary problems,the method exhibits significant numerical instability,potentially leading to substantial deviations in the computed results.Finally,three potential improvement strategies are proposed to mitigate this limitation.展开更多
This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic...This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic simulations and its high computational cost in broadband problems are examined.To improve efficiency,a Taylor series expansion is applied to decouple frequency-dependent terms in BEM.Additionally,the SecondOrder Arnoldi(SOAR)model order reduction method is integrated to reduce computational costs and enhance numerical stability.Furthermore,an isogeometric sensitivity boundary integral equation is formulated using the direct differentiation method,incorporating Cauchy principal value integrals and Hadamard finite part integrals to handle singularities.The proposed method improves the computational efficiency,and the acoustic sensitivity analysis provides theoretical support for further acoustic structure optimization.展开更多
Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the chall...Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the challenge of being computationally overpowered.This study proposes an efficient fracturing simulator to analyze fracture morphology during hydraulic fracturing processes in deep shale gas reservoirs.The simulator integrates the boundary element displacement discontinuity method and the finite volume method to model the fluid-solid coupling process by employing a pseudo-3D fracture model to calculate the fracture height.In particular,the Broyden iteration method was introduced to improve the computational efficiency and model robustness;it achieved a 46.6%reduction in computation time compared to the Newton-Raphson method.The influences of horizontal stress differences,natural fracture density,and natural fracture angle on the modified zone of the reservoir were simulated,and the following results were observed.(1)High stress difference reservoirs have smaller stimulated reservoir area than low stress difference reservoirs.(2)A higher natural fracture angle resulted in larger modification zones at low stress differences,while the effect of a natural fracture angle at high stress differences was not significant.(3)High-density and long natural fracture zones played a significant role in enhancing the stimulated reservoir area.These findings are critical for comprehending the impact of geological parameters on deep shale reservoirs.展开更多
By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution ...By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.展开更多
As a key sector in advancing China’s“carbon neutrality”goal,the machinery manufacturing industry has achieved remarkable development in recent years.Against this backdrop,the scientific and objective evaluation of ...As a key sector in advancing China’s“carbon neutrality”goal,the machinery manufacturing industry has achieved remarkable development in recent years.Against this backdrop,the scientific and objective evaluation of the financial performance of machinery manufacturing enterprises has become a pressing issue in financial research.This topic is not only crucial for optimizing enterprise management and improving operational efficiency but also essential for enhancing overall industry performance and promoting sustainable development.This paper first introduces the concept of financial performance,followed by an analysis of related financial performance evaluation theories.It then focuses on the application of the entropy method in evaluating the financial performance of machinery manufacturing enterprises,detailing its analytical steps.Finally,a financial performance evaluation index system is constructed based on four dimensions:profitability,solvency,operational efficiency,and growth potential.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This work is supported by the Foundatiorl of Zhongshan University Advanced Research Centre
文摘Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.
基金supported by the National Natural Science Foundation of China (11132004 and 51078145)the Natural Science Foundation of Guangdong Province (9251064101000016)
文摘In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.
基金financial support for this work contributed by the National Key Research and Development Program of China (grant numbers 2016YFC0600101 and 2016YFC 0600201)the National Natural Science Foundation of China (grant numbers 41874065, 41604076, 41674102, 41674095, 41522401, 41574082, and 41774097)
文摘In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.
基金The project is supported by the National Natural Science Foundation of China(11561045,11961044)the Doctor Fund of Lan Zhou University of Technology.
文摘In this article,we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation.This problem is ill-posed and the quasi-boundary value method is proposed to deal with this inverse problem and obtain the series expression of the regularized solution for the inverse initial value problem.We prove the error estimates between the regularization solution and the exact solution by using an a priori regularization parameter and an a posteriori regularization parameter choice rule.Some numerical results in one-dimensional case and two-dimensional case show that our method is efficient and stable.
基金Partially Supported by the National Natural Science Foundation of China
文摘In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.
基金Project supported by the National Natural Science Foundation of China(No.11472119)the Fundamental Research Funds for the Central Universities(No.lzujbky-2017-ot11)the 111 Project(No.B14044)
文摘A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an adjustable high order for the functions over a bounded interval, which allows the expansion coefficients to be explicitly expressed by the function values at a series of single points. When the solution method is used, the nonlinear initial boundary value problems are first spatially discretized into a series of nonlinear initial value problems by combining the proposed wavelet approximation and the conventional Galerkin method, and a novel high-order step-by-step time integrating approach is then developed for the resulting nonlinear initial value problems with the same function approximation scheme based on the wavelet theory. The solution method is shown to have the N th-order accuracy, as long as the Coiflet with [0, 3 N-1]compact support is adopted, where N can be any positive even number. Typical examples in mechanics are considered to justify the accuracy and efficiency of the method.
基金supported by the National Natural Science Foundation of China(Grant Nos.11925204 and 12172154)the 111 Project(Grant No.B14044)the National Key Project of China(Grant No.GJXM92579).
文摘A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions.In order to realize the establishment of this method,an approximate expression of multiple integrals of a continuous function defined in a three-dimensional bounded domain is proposed by combining wavelet expansion and Lagrange boundary extension.Through applying such an integral technique,during the solution of nonlinear partial differential equations,the unknown function and its lower-order partial derivatives can be approximately expressed by its highest-order partial derivative values at nodes.A set of nonlinear algebraic equations with respect to these nodal values of the highest-order partial derivative is obtained using a collocation method.The validation and convergence of the proposed method are examined through several benchmark problems,including the eighth-order two-dimensional and fourth-order three-dimensional boundary value problems and the large deflection bending of von Karman plates.Results demonstrate that the present method has higher accuracy and convergence rate than most existing numerical methods.Most importantly,the convergence rate of the proposed method seems to be independent of the order of the differential equations,because it is always sixth order for second-,fourth-,sixth-,and even eighth-order problems.
基金the Major State Basic Research Program of China(No.G19990328)the National Tackling Key Problem Program(No.20050200069)+1 种基金the National Natural Science Foundation of China(Nos.10771124,10372052)the Ph.D.Programs Foundation of Ministry of Education of China(No.20030422047)
文摘The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.
文摘This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
基金partially supported by the National Natural Science Foundation of China(Nos.92271103,12202191)。
文摘The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mesh,while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field.The boundary condition is implemented by introducing a force term into the momentum equation,and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process.Over the past decades,the diffuse-interface IBM has gained popularity and spawned many variants,effectively handling a wide range of flow problems from isothermal to thermal flows,from laminar to turbulent flows,and from complex geometries to fluidstructure interaction scenarios.This paper first outlines the basic principles of the diffuse-interface IBM,then highlights recent advancements achieved by the authors’research group,and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.
基金supported by the National Natural Science Foundation of China(Grant 12472113).
文摘The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.
文摘Monotone sequences are constructed that converge to the ex tremal solutions of second order three point boundary value problems when the functions involved do not possess any monotone properties.
基金Supported by the National Key R&D Program of China(2022YFB3303500).
文摘Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data immersion method(BDIM)for compressible flows,which were solved using a fully self-programmed Fortran code.Results show that the predicted thrust spectrum aligns closely with the experimental measurements.In addition,it captures the thrust dipole directivity of the noise around the rotating propeller due to random pressure pulsations on the blades,as well as the flow structures simultaneously.Furthermore,the differences in the statistical characteristics,flow structures,and low-frequency broadband thrust spectra due to different turbulence levels were investigated.This analysis indicates that the interaction between the upstream,which is characterized by a lower turbulence level and a higher turbulent length of scale,and the rotating propeller results in a lower amplitude in force spectra and a slight increase in the scale of tip vortices.
基金supported by the Major State BasicResearch Program of China(19990328)the National Tackling Key Problem Programs(20050200069)+4 种基金the National Natural Science Foundation of China(1077112410372052)the Doctorate Foundation of the Ministryof Education of China(20030422047)Shandong Provance Natural Science Foundation(2R2009AQ12)the Independent Innovation Foundation of Shandong University(2010TS031)
文摘Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.
基金Supported by the Key Scientific Research Plan of Colleges and Universities in Henan Province(23B140006)。
文摘The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary.Therefore,this method has the merits of purely meshless,easy to program,high solution accuracy and so on.In this paper,we investigate the effectiveness of the BKM for solving Helmholtz-type problems under various conditions through a series of novel numerical experiments.The results demonstrate that the BKM is efficient and achieves high computational accuracy for problems with smooth or continuous boundary conditions.However,when applied to discontinuous boundary problems,the method exhibits significant numerical instability,potentially leading to substantial deviations in the computed results.Finally,three potential improvement strategies are proposed to mitigate this limitation.
基金supported by the Shanxi Scholarship Council of China(Grant No.2023-036)the Natural Science Foundation of Shanxi Province(Grant No.202303021222020).
文摘This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic simulations and its high computational cost in broadband problems are examined.To improve efficiency,a Taylor series expansion is applied to decouple frequency-dependent terms in BEM.Additionally,the SecondOrder Arnoldi(SOAR)model order reduction method is integrated to reduce computational costs and enhance numerical stability.Furthermore,an isogeometric sensitivity boundary integral equation is formulated using the direct differentiation method,incorporating Cauchy principal value integrals and Hadamard finite part integrals to handle singularities.The proposed method improves the computational efficiency,and the acoustic sensitivity analysis provides theoretical support for further acoustic structure optimization.
文摘Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the challenge of being computationally overpowered.This study proposes an efficient fracturing simulator to analyze fracture morphology during hydraulic fracturing processes in deep shale gas reservoirs.The simulator integrates the boundary element displacement discontinuity method and the finite volume method to model the fluid-solid coupling process by employing a pseudo-3D fracture model to calculate the fracture height.In particular,the Broyden iteration method was introduced to improve the computational efficiency and model robustness;it achieved a 46.6%reduction in computation time compared to the Newton-Raphson method.The influences of horizontal stress differences,natural fracture density,and natural fracture angle on the modified zone of the reservoir were simulated,and the following results were observed.(1)High stress difference reservoirs have smaller stimulated reservoir area than low stress difference reservoirs.(2)A higher natural fracture angle resulted in larger modification zones at low stress differences,while the effect of a natural fracture angle at high stress differences was not significant.(3)High-density and long natural fracture zones played a significant role in enhancing the stimulated reservoir area.These findings are critical for comprehending the impact of geological parameters on deep shale reservoirs.
基金Supported by the National Natural Science Foundation of Chinathe Doctoral Training of the State Education Commission of China
文摘By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.
文摘As a key sector in advancing China’s“carbon neutrality”goal,the machinery manufacturing industry has achieved remarkable development in recent years.Against this backdrop,the scientific and objective evaluation of the financial performance of machinery manufacturing enterprises has become a pressing issue in financial research.This topic is not only crucial for optimizing enterprise management and improving operational efficiency but also essential for enhancing overall industry performance and promoting sustainable development.This paper first introduces the concept of financial performance,followed by an analysis of related financial performance evaluation theories.It then focuses on the application of the entropy method in evaluating the financial performance of machinery manufacturing enterprises,detailing its analytical steps.Finally,a financial performance evaluation index system is constructed based on four dimensions:profitability,solvency,operational efficiency,and growth potential.
