Developing efficient and stable electrocatalysts has always been the focus of electrochemical research.Here,sea urchin-like nickel-molybdenum bimetallic phosphide nickel-molybdenum alloy(Ni_(4)Mo)and(Ni-Mo-P)were succ...Developing efficient and stable electrocatalysts has always been the focus of electrochemical research.Here,sea urchin-like nickel-molybdenum bimetallic phosphide nickel-molybdenum alloy(Ni_(4)Mo)and(Ni-Mo-P)were successfully synthesized by hydrothermal,annealing and phosphating methods on nickel foam(NF).The unusual shape of the sea urchin facilitates gas release and mass transfer and increases the interaction between catalysts and electrolytes.The Ni_(4)Mo/NF and Ni-Mo-P/NF electrodes only need overpotentials of 72 and 197 mV to reach 50 mA·cm^(−2) under alkaline conditions for hydrogen evolution reaction and oxygen evolution reaction,respectively.The Ni_(4)Mo/NF and Ni-Mo-P/NF asymmetric electrodes were used as anode and cathode for the overall water splitting,respectively.In 1.0 M KOH,at a voltage of 1.485 V,the electrolytic device generated 50 mA·cm^(−2) current density,maintaining for 24 h without reduction.The labor presents a simple method to synthesize a highly active,low-cost,and strongly durable self-supporting electrode for over-water splitting.展开更多
Hydrogen(H2)production is a latent feasibility of renewable clean energy.The industrial H2 production is obtained from reforming of natural gas,which consumes a large amount of nonrenewable energy and simultaneously p...Hydrogen(H2)production is a latent feasibility of renewable clean energy.The industrial H2 production is obtained from reforming of natural gas,which consumes a large amount of nonrenewable energy and simultaneously produces greenhouse gas carbon dioxide.Electrochemical water splitting is a promising approach for the H2 production,which is sustainable and pollution-free.Therefore,developing efficient and economic technologies for electrochemical water splitting has been an important goal for researchers around the world.The utilization of green energy systems to reduce overall energy consumption is more important for H2 production.Harvesting and converting energy from the environment by different green energy systems for water splitting can efficiently decrease the external power consumption.A variety of green energy systems for efficient producing H2,such as two-electrode electrolysis of water,water splitting driven by photoelectrode devices,solar cells,thermoelectric devices,triboelectric nanogenerator,pyroelectric device or electrochemical water-gas shift device,have been developed recently.In this review,some notable progress made in the different green energy cells for water splitting is discussed in detail.We hoped this review can guide people to pay more attention to the development of green energy system to generate pollution-free H2 energy,which will realize the whole process of H2 production with low cost,pollution-free and energy sustainability conversion.展开更多
This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-d...This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.展开更多
In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on...In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface,a nonlinear initial-boundary value problem satisfies by stream function is obtained,existence and uniqueness of its solution are proven.Based this theory we proposal a new method called"dimension split method"to solve 3D NSE.展开更多
In an attempt to develop low-cost,non-noble-metal bifunctional electrocatalysts for water electrolysis in alkaline media,cobalt-doped molybdenum carbide@N-doped carbon nanosheets/nanotubes were fabricated by using C3N...In an attempt to develop low-cost,non-noble-metal bifunctional electrocatalysts for water electrolysis in alkaline media,cobalt-doped molybdenum carbide@N-doped carbon nanosheets/nanotubes were fabricated by using C3N4 as the carbon source on a 3D porous nickel foam substrate.Benefiting from the optimized electronic structure and enhanced mass and charge transport,as well as the 3D conducting pathway,MoxCoy@N-CNSs/CNTs shows superior performance towards both the hydrogen evolution reaction(HER)and oxygen evolution reaction(OER)in an alkaline medium.The optimal electrocatalyst is Mo2Co1@N-CNSs/CNTs,which reveals a current density of 10 mA cm^-2 at the low overpotentials of 99 mV and 300 mV for the HER and OER,respectively,and a relatively low cell voltage(1.63 V)for the overall water electrolysis.The method of optimizing the composition and nanostructure of a material provides a new avenue for the development and utilization of high-performance electrocatalysts.展开更多
The synthesis of low-cost and highly active electrodes for both oxygen evolution reaction(OER)and hydrogen evolution reaction(HER)is very important for water splitting.In this work,the novel amorphous iron-nickel phos...The synthesis of low-cost and highly active electrodes for both oxygen evolution reaction(OER)and hydrogen evolution reaction(HER)is very important for water splitting.In this work,the novel amorphous iron-nickel phosphide(FeP-Ni)nanocone arrays as efficient bifunctional electrodes for overall water splitting have been in-situ assembled on conductive three-dimensional(3D)Ni foam via a facile and mild liquid deposition process.It is found that the FeP-Ni electrode demonstrates highly efficient electrocatalytic performance toward overall water splitting.In 1 M KOH electrolyte,the optimal FeP-Ni electrode drives a current density of 10 mA cm^(-2) at overpotential of 218 mV for the OER and120 mV for the HER,and can attain such current density for 25 h without performance regression.Moreover,a two-electrode electrolyzer comprising the FeP-Ni electrodes can afford 10 mA cm^(-2) electrolysis current at a low cell voltage of 1.62 V and maintain long-term stability,as well as superior to that of the coupled RuO_(2)/NFk Pt/C/NF cell.Detailed characterizations confirm that the excellent electrocatalytic performances for water splitting are attributed to the unique 3D morphology of nanocone arrays,which could expose more surface active sites,facilitate electrolyte diffusion,and benefit charge transfer and also favorable bubble detachment behavior.Our work presents a facile and cost-effective pathway to design and develop active self-supported electrodes with novel 3D morphology for water electrolysis.展开更多
Efficient,stable,and noble‐metal‐free electrocatalysts for both the oxygen evolution reaction and the hydrogen evolution reaction are highly imperative for the realization of low‐cost commercial water‐splitting el...Efficient,stable,and noble‐metal‐free electrocatalysts for both the oxygen evolution reaction and the hydrogen evolution reaction are highly imperative for the realization of low‐cost commercial water‐splitting electrolyzers.Herein,a cost‐effective and ecofriendly strategy is reported to fabricate coral‐like FeNi(OH)x/Ni as a bifunctional electrocatalyst for overall water splitting in alkaline media.With the assistance of mild corrosion of Ni by Fe(NO3)3,in situ generated FeNi(OH)x nanosheets are intimately attached on metallic coral‐like Ni.Integration of these nanosheets with the electrodeposited coral‐like Ni skeleton and the supermacroporous Ni foam substrate forms a binder‐free hierarchical electrode,which is beneficial for exposing catalytic active sites,accelerating mass transport,and facilitating the release of gaseous species.In 1.0 mol L^-1 KOH solution,a symmetric electrolyzer constructed with FeNi(OH)x/Ni as both the anode and the cathode exhibits an excellent activity with an applied potential difference of 1.52 V at 10 mA cm^-2,which is superior to that of an asymmetric electrolyzer constructed with the state‐of‐the‐art RuO2‐PtC couple(applied potential difference of 1.55 V at 10 mA cm^-2).This work contributes a facile and reliable strategy for manufacturing affordable,practical,and promising water‐splitting devices.展开更多
The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation wit...The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.展开更多
In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the...In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.展开更多
In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and ...In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.展开更多
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this pap...Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.展开更多
Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is...Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.展开更多
The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation dur...The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation during the tests.In this study,splitting tests were performed on sea ice,with 32 samples subjected to the regular procedure and 8 samples subjected to the digital image correlation method.The salinity,density,and temperature were measured to determine the total porosity.With the advantage of the digital image correlation method,the full-field deformation of the ice samples could be determined.In the loading direction,the samples mainly deformed at the ice-platen contact area.In the direction vertical to the loading,deformation appears along the central line where the splitting crack occurs.Based on the distribution of the sample deformation,a modified solution was derived to calculate the tensile strength with the maximum load.Based on the modified solution,the tensile strength was further calculated together with the splitting test results.The results show that the tensile strength has a negative correlation with the total porosity,which agrees with previous studies based on uniaxial tension tests.展开更多
In order to make a more effective use of the data from regional digital seismograph networks and to promote the study on shear wave splitting and its application to earthquake stress-forecasting, SAM software system, ...In order to make a more effective use of the data from regional digital seismograph networks and to promote the study on shear wave splitting and its application to earthquake stress-forecasting, SAM software system, i.e., the software on systematic analysis method of shear wave splitting has been developed. This paper introduces the design aims, system structure, function and characteristics about the SAM software system and shows some graphical interfaces of data input and result output. Lastly, it discusses preliminarily the study of shear wave splitting and its application to earthquake forecasting.展开更多
By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is propose...By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.展开更多
This paper briefly discusses the new methods that the authors have put forward to distinguish splitting shear-waves.By combining these new methods with other methods,the authors have processed the recorded data of an ...This paper briefly discusses the new methods that the authors have put forward to distinguish splitting shear-waves.By combining these new methods with other methods,the authors have processed the recorded data of an earthquake.The study results are consistent with each other.展开更多
In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the sol...In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.展开更多
Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The ...Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.展开更多
During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the fi...During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the finite element method in splitting rolling. The reproducing kernel particle method can solve this problem because the continuum body is discretized by a set of nodes, and a finite element mesh is unnecessary, and there is no explicit limitation of mesh when the metal is split. To ensure stability in the large deformation elastoplastic analysis, the Lagrange material shape function was introduced. The transformation method was utilized to impose the essential boundary conditions. The splitting rolling method was simulated and the simulation results were in accordance with the experimental ones in the literature.展开更多
基金supported by the Natural Science Research Project of Jiangsu Higher Education Institutions(No.23KJD150005)the Scientific Research Project of Nanjing Xiaozhuang University(No.2022NXY29).
文摘Developing efficient and stable electrocatalysts has always been the focus of electrochemical research.Here,sea urchin-like nickel-molybdenum bimetallic phosphide nickel-molybdenum alloy(Ni_(4)Mo)and(Ni-Mo-P)were successfully synthesized by hydrothermal,annealing and phosphating methods on nickel foam(NF).The unusual shape of the sea urchin facilitates gas release and mass transfer and increases the interaction between catalysts and electrolytes.The Ni_(4)Mo/NF and Ni-Mo-P/NF electrodes only need overpotentials of 72 and 197 mV to reach 50 mA·cm^(−2) under alkaline conditions for hydrogen evolution reaction and oxygen evolution reaction,respectively.The Ni_(4)Mo/NF and Ni-Mo-P/NF asymmetric electrodes were used as anode and cathode for the overall water splitting,respectively.In 1.0 M KOH,at a voltage of 1.485 V,the electrolytic device generated 50 mA·cm^(−2) current density,maintaining for 24 h without reduction.The labor presents a simple method to synthesize a highly active,low-cost,and strongly durable self-supporting electrode for over-water splitting.
基金supported by Taishan Scholars Project Special Funds(tsqn201812083)Natural Science Foundation of Shandong Province(ZR2019YQ20,2019JMRH0410)the National Natural Science Foundation of China(51972147)。
文摘Hydrogen(H2)production is a latent feasibility of renewable clean energy.The industrial H2 production is obtained from reforming of natural gas,which consumes a large amount of nonrenewable energy and simultaneously produces greenhouse gas carbon dioxide.Electrochemical water splitting is a promising approach for the H2 production,which is sustainable and pollution-free.Therefore,developing efficient and economic technologies for electrochemical water splitting has been an important goal for researchers around the world.The utilization of green energy systems to reduce overall energy consumption is more important for H2 production.Harvesting and converting energy from the environment by different green energy systems for water splitting can efficiently decrease the external power consumption.A variety of green energy systems for efficient producing H2,such as two-electrode electrolysis of water,water splitting driven by photoelectrode devices,solar cells,thermoelectric devices,triboelectric nanogenerator,pyroelectric device or electrochemical water-gas shift device,have been developed recently.In this review,some notable progress made in the different green energy cells for water splitting is discussed in detail.We hoped this review can guide people to pay more attention to the development of green energy system to generate pollution-free H2 energy,which will realize the whole process of H2 production with low cost,pollution-free and energy sustainability conversion.
基金supported by the National Natural Science Foundation of China (Grants 11571223, 51404160)Shanxi Province Science Foundation for Youths (Grant 2014021025-1)
文摘This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.
文摘In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface,a nonlinear initial-boundary value problem satisfies by stream function is obtained,existence and uniqueness of its solution are proven.Based this theory we proposal a new method called"dimension split method"to solve 3D NSE.
基金supported by the National Natural Science Foundation of China(51622102,51571124,21421001)the 111 Project(B12015)+1 种基金the Natural Science Foundation of Tianjin(18ZXJMTG00040,16PTSYJC00030)the Fundamental Research Funds for the Central Universities~~
文摘In an attempt to develop low-cost,non-noble-metal bifunctional electrocatalysts for water electrolysis in alkaline media,cobalt-doped molybdenum carbide@N-doped carbon nanosheets/nanotubes were fabricated by using C3N4 as the carbon source on a 3D porous nickel foam substrate.Benefiting from the optimized electronic structure and enhanced mass and charge transport,as well as the 3D conducting pathway,MoxCoy@N-CNSs/CNTs shows superior performance towards both the hydrogen evolution reaction(HER)and oxygen evolution reaction(OER)in an alkaline medium.The optimal electrocatalyst is Mo2Co1@N-CNSs/CNTs,which reveals a current density of 10 mA cm^-2 at the low overpotentials of 99 mV and 300 mV for the HER and OER,respectively,and a relatively low cell voltage(1.63 V)for the overall water electrolysis.The method of optimizing the composition and nanostructure of a material provides a new avenue for the development and utilization of high-performance electrocatalysts.
基金supported by the National Natural Science Foundation of China(No.21878204)Key R&D program of Shanxi Province(International Cooperation,201903D421073)。
文摘The synthesis of low-cost and highly active electrodes for both oxygen evolution reaction(OER)and hydrogen evolution reaction(HER)is very important for water splitting.In this work,the novel amorphous iron-nickel phosphide(FeP-Ni)nanocone arrays as efficient bifunctional electrodes for overall water splitting have been in-situ assembled on conductive three-dimensional(3D)Ni foam via a facile and mild liquid deposition process.It is found that the FeP-Ni electrode demonstrates highly efficient electrocatalytic performance toward overall water splitting.In 1 M KOH electrolyte,the optimal FeP-Ni electrode drives a current density of 10 mA cm^(-2) at overpotential of 218 mV for the OER and120 mV for the HER,and can attain such current density for 25 h without performance regression.Moreover,a two-electrode electrolyzer comprising the FeP-Ni electrodes can afford 10 mA cm^(-2) electrolysis current at a low cell voltage of 1.62 V and maintain long-term stability,as well as superior to that of the coupled RuO_(2)/NFk Pt/C/NF cell.Detailed characterizations confirm that the excellent electrocatalytic performances for water splitting are attributed to the unique 3D morphology of nanocone arrays,which could expose more surface active sites,facilitate electrolyte diffusion,and benefit charge transfer and also favorable bubble detachment behavior.Our work presents a facile and cost-effective pathway to design and develop active self-supported electrodes with novel 3D morphology for water electrolysis.
文摘Efficient,stable,and noble‐metal‐free electrocatalysts for both the oxygen evolution reaction and the hydrogen evolution reaction are highly imperative for the realization of low‐cost commercial water‐splitting electrolyzers.Herein,a cost‐effective and ecofriendly strategy is reported to fabricate coral‐like FeNi(OH)x/Ni as a bifunctional electrocatalyst for overall water splitting in alkaline media.With the assistance of mild corrosion of Ni by Fe(NO3)3,in situ generated FeNi(OH)x nanosheets are intimately attached on metallic coral‐like Ni.Integration of these nanosheets with the electrodeposited coral‐like Ni skeleton and the supermacroporous Ni foam substrate forms a binder‐free hierarchical electrode,which is beneficial for exposing catalytic active sites,accelerating mass transport,and facilitating the release of gaseous species.In 1.0 mol L^-1 KOH solution,a symmetric electrolyzer constructed with FeNi(OH)x/Ni as both the anode and the cathode exhibits an excellent activity with an applied potential difference of 1.52 V at 10 mA cm^-2,which is superior to that of an asymmetric electrolyzer constructed with the state‐of‐the‐art RuO2‐PtC couple(applied potential difference of 1.55 V at 10 mA cm^-2).This work contributes a facile and reliable strategy for manufacturing affordable,practical,and promising water‐splitting devices.
基金This work was supported by China State Major Key Project for Basic Researches.
文摘The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.
基金Partly supported by the State Major Key Project for Basic Researches
文摘In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.
基金Partly supported by the State Major Key Project for Researches and Project 85-906-04.
文摘In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.
基金Supported by the Natural Science Foundation of China under Grant No.0971226the 973 Project of China under Grant No.2009CB723802+1 种基金the Research Innovation Fund of Hunan Province under Grant No.CX2011B011the Innovation Fund of NUDT under Grant No.B110205
文摘Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
文摘Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.
基金This study was supported financially by the National Key Research and Development Program of China(Grant no.2018YFA0605902)the National Natural Science Foundation of China(Grant no.52101300)+1 种基金the Fundamental Research Funds for the Central Universities(Grant no.DUT21LK03)Joint Scientific Research Fund Project of DBJI(Grant no.ICR2102).
文摘The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation during the tests.In this study,splitting tests were performed on sea ice,with 32 samples subjected to the regular procedure and 8 samples subjected to the digital image correlation method.The salinity,density,and temperature were measured to determine the total porosity.With the advantage of the digital image correlation method,the full-field deformation of the ice samples could be determined.In the loading direction,the samples mainly deformed at the ice-platen contact area.In the direction vertical to the loading,deformation appears along the central line where the splitting crack occurs.Based on the distribution of the sample deformation,a modified solution was derived to calculate the tensile strength with the maximum load.Based on the modified solution,the tensile strength was further calculated together with the splitting test results.The results show that the tensile strength has a negative correlation with the total porosity,which agrees with previous studies based on uniaxial tension tests.
文摘In order to make a more effective use of the data from regional digital seismograph networks and to promote the study on shear wave splitting and its application to earthquake stress-forecasting, SAM software system, i.e., the software on systematic analysis method of shear wave splitting has been developed. This paper introduces the design aims, system structure, function and characteristics about the SAM software system and shows some graphical interfaces of data input and result output. Lastly, it discusses preliminarily the study of shear wave splitting and its application to earthquake forecasting.
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY20A010021,LY19A010002,LY20G030025)the Natural Science Founda-tion of Ningbo City,China(Grant Nos.2021J147,2021J235).
文摘By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.
文摘This paper briefly discusses the new methods that the authors have put forward to distinguish splitting shear-waves.By combining these new methods with other methods,the authors have processed the recorded data of an earthquake.The study results are consistent with each other.
文摘In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.
文摘Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.
基金Item Sponsored by National Natural Science Foundation of China(50474016)
文摘During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the finite element method in splitting rolling. The reproducing kernel particle method can solve this problem because the continuum body is discretized by a set of nodes, and a finite element mesh is unnecessary, and there is no explicit limitation of mesh when the metal is split. To ensure stability in the large deformation elastoplastic analysis, the Lagrange material shape function was introduced. The transformation method was utilized to impose the essential boundary conditions. The splitting rolling method was simulated and the simulation results were in accordance with the experimental ones in the literature.
