A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditiona...A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditional numerical method of the same equations corroborates well the reliability and rate of FEFDM.Moreover,a flow rate estimate method was developed for the project whose injection rate has not been clearly determined.A wellhead pressure regime determined by this method was successfully applied to the trial injection operations in Shihezi formation of Shenhua CCS Project,which is a good practice verification of FEFDM.At last,this method was used to evaluate the effect of friction and acceleration terms on the flow equation on the wellhead pressure.The result shows that for deep wellbore,the friction term can be omitted when flow rate is low and in a wide range of velocity the acceleration term can always be deleted.It is also shown that with flow rate increasing,the friction term can no longer be neglected.展开更多
Two elastoplastic constitutive models based on the unified strength the- ory （UST） are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua （FLAC/FLAC3D）, which i...Two elastoplastic constitutive models based on the unified strength the- ory （UST） are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua （FLAC/FLAC3D）, which includes an associated/non- associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different （SD） materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening be- havior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD mate- rial structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.展开更多
Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been n...Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been non-dimensionalized by useful dimensionless variables. The explicit finite difference method has been used to solve dimensionless equations. The numerical results have been calculated by studio developer FORTRAN 6.6a and MATLAB 2018a. For perfect conducting case, Magnetic Diffusivity Parameter <span style="white-space:nowrap;">5 <span style="white-space:nowrap;">≤</span><em> P</em><em><sub>m</sub> </em><span style="white-space:nowrap;">≤ </span>15</span> has been taken in induction equation. For good accuracy, stability and convergence analysis have been analyzed. Mesh Sensitivity test, steady-state solution test, and code validation test have been performed. For time step<em> </em><em></em><span style="white-space:nowrap;"><em><span style="white-space:nowrap;">τ</span></em></span> <span style="white-space:nowrap;">= 1</span>, the numerical results have been found for the primary velocity, secondary velocity, angular velocity, primary induced magnetic field, secondary induced magnetic field, temperature as well as shear stresses along <em>x</em> and<em> z</em> direction, couple stress along<em> z</em> direction, current densities along <em>x</em> and <em>z</em> direction and the Nusselt number. Finally, the effects of various parameters have been separately discussed and illustrated graphically.展开更多
Arterial stenosis is a critical condition with increasing prevalence among pediatric patients and young adults,making its investigation highly significant.Despite extensive studies on blood flow dynamics,limited resea...Arterial stenosis is a critical condition with increasing prevalence among pediatric patients and young adults,making its investigation highly significant.Despite extensive studies on blood flow dynamics,limited research addresses the combined effects of nanoparticles and arterial curvature on unsteady pulsatile flow through multiple stenoses.This study aims to analyze the influence of nanoparticles on blood flow characteristics in realistic curved arteries with mild to severe overlapped constrictions.Using curvilinear coordinates,the thermal energy and momentum equations for nanoparticle-laden blood were derived,and numerical results were obtained through an explicit finite difference method.Key findings reveal that nanoparticle injections reduce blood temperature intensity,while arterial curvature strongly affects flow symmetry.Moreover,temperature,axial velocity,wall shear stress,and volumetric flow rate decrease significantly in severe stenosis compared to mild and moderate cases.These results provide new insights into nanoparticle-assisted blood flow under complex stenotic conditions and may contribute to improved diagnostic and therapeutic strategies for cardiovascular diseases.展开更多
The chief objective of the article is to learn the spatial characteristics of stress distribution around a shallow buried cylinder Karst cave in limestone strata.Firstly,taking into account the geometry of limestone f...The chief objective of the article is to learn the spatial characteristics of stress distribution around a shallow buried cylinder Karst cave in limestone strata.Firstly,taking into account the geometry of limestone formations,and the characteristics of Karst geomorphology in China,a spatial axialsymmetrical hollow model was established.Concurrently,combining available work and the concept of elasticity,the boundary conditions are determined.Subsequently,Love displacement method was introduced,the expressions of stress components were gained.The diagram characteristics of each stress component are summarized,which are affected by various influencing factors.Finally,in order to prove the rationality of the general solution,numerical simulation was carried out on the basis of practical engineering,and the maximum error is less than 5%.Thus,the analytical solution could represent the spatial characteristics of stress distribution around a shallow buried cylinder Karst cave in limestone strata.展开更多
An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete fo...An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.展开更多
In this paper, unsteady free convection heat transfer flow over a vertical plate in the presence of a magnetic field is discussed in detail. The dimensionless partial differential equations of continuity, momentum alo...In this paper, unsteady free convection heat transfer flow over a vertical plate in the presence of a magnetic field is discussed in detail. The dimensionless partial differential equations of continuity, momentum along energy are analyzed with suitable transformations. For numerical calculation, an implicit finite difference method is applied to solve a set of nonlinear dimensionless partial differential equations. Dimensionless velocity and temperature profile are also investigated due to the effects of assumed parameters in the concerned problem. An explicit finite difference technique is used to compute velocity and temperature profiles. The stability conditions are also examined.展开更多
Unsteady electromagnetic free convection flows of two-dimensional micropolar fluid through in a porous medium parallel to a vertical porous plate have been investigated numerically. Similarity analysis has been used t...Unsteady electromagnetic free convection flows of two-dimensional micropolar fluid through in a porous medium parallel to a vertical porous plate have been investigated numerically. Similarity analysis has been used to transform the governing equations into its non-dimensional form by using the explicit finite difference method to obtain numerical solutions. Estimated results have been gained for various values of Prandtl number, Grashof number, material parameters, micropolar parameter, electric conductivity, electric permeability, thermal relaxation time and the permeability of the porous medium. The effect<span style="font-family:Verdana;">s</span><span style="font-family:Verdana;"> of pertinent parameters on the velocity, electric induction, magnetic induction, microrotation and temperature distributions have been investigated briefly and illustrate</span><span style="font-family:Verdana;">d</span><span style="font-family:Verdana;"> graphically.</span>展开更多
This article is based on the impulsively started horizontal Riga plate in two dimensional unsteady Casson fluid flows with rotation. The plate starts abruptly from the rest relative to the rotating fluids moving with ...This article is based on the impulsively started horizontal Riga plate in two dimensional unsteady Casson fluid flows with rotation. The plate starts abruptly from the rest relative to the rotating fluids moving with uniform acceleration in its plane. Numerical solutions are acquired by using explicit finite difference method and estimated results have been gained for various values of the Rotational parameter, modified Hartmann number, Prandtl number, Radiative parameter, Eckert number, Heat source parameter, Schmidt number, and the Soret number. Both the Compaq visual FORTRAN 6.6a and MATLAB R2015a tools have been used to find the numerical solutions and the graphical presentation. The Skin friction, Nusselt number and Sherwood number have been computed and the effects of some pertinent parameters on various distributions are discussed briefly and presented graphically.展开更多
An explicit finite difference method is performed to evaluate the significance of topography effects on the seismic response of viscoelastic sites.The real accelerograms and bell-shape impulse wavelets,slope angle of ...An explicit finite difference method is performed to evaluate the significance of topography effects on the seismic response of viscoelastic sites.The real accelerograms and bell-shape impulse wavelets,slope angle of cliff and angle of incidence on the spectrum property of the incoming waves are all discussed in detail.The conclusions show that the presence of topographic factors and the direction of the incident waves not only significantly affect the peak ground acceleration of a site,but also affect the spectrum properties of the incoming waves,and the effect on the direction of the incident waves is especially remarkable.The study also finds that it is reasonable to analyse spectrum properties with the input of impulse wavelets in the finite element simulation of wave motion.展开更多
基金Project(Z110803)supported by the State Key Laboratory of Geomechanics and Geotechnical Engineering,ChinaProject(2008AA062303)supported by the National High Technology Research and Development Program of China
文摘A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditional numerical method of the same equations corroborates well the reliability and rate of FEFDM.Moreover,a flow rate estimate method was developed for the project whose injection rate has not been clearly determined.A wellhead pressure regime determined by this method was successfully applied to the trial injection operations in Shihezi formation of Shenhua CCS Project,which is a good practice verification of FEFDM.At last,this method was used to evaluate the effect of friction and acceleration terms on the flow equation on the wellhead pressure.The result shows that for deep wellbore,the friction term can be omitted when flow rate is low and in a wide range of velocity the acceleration term can always be deleted.It is also shown that with flow rate increasing,the friction term can no longer be neglected.
基金Project supported by the National Natural Science Foundation of China (No. 41172276)the Central Financial Funds for the Development of Characteristic Key Disciplines in Local Universities(Nos. 106-00X101 and 106-5X1205)
文摘Two elastoplastic constitutive models based on the unified strength the- ory （UST） are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua （FLAC/FLAC3D）, which includes an associated/non- associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different （SD） materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening be- havior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD mate- rial structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.
文摘Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been non-dimensionalized by useful dimensionless variables. The explicit finite difference method has been used to solve dimensionless equations. The numerical results have been calculated by studio developer FORTRAN 6.6a and MATLAB 2018a. For perfect conducting case, Magnetic Diffusivity Parameter <span style="white-space:nowrap;">5 <span style="white-space:nowrap;">≤</span><em> P</em><em><sub>m</sub> </em><span style="white-space:nowrap;">≤ </span>15</span> has been taken in induction equation. For good accuracy, stability and convergence analysis have been analyzed. Mesh Sensitivity test, steady-state solution test, and code validation test have been performed. For time step<em> </em><em></em><span style="white-space:nowrap;"><em><span style="white-space:nowrap;">τ</span></em></span> <span style="white-space:nowrap;">= 1</span>, the numerical results have been found for the primary velocity, secondary velocity, angular velocity, primary induced magnetic field, secondary induced magnetic field, temperature as well as shear stresses along <em>x</em> and<em> z</em> direction, couple stress along<em> z</em> direction, current densities along <em>x</em> and <em>z</em> direction and the Nusselt number. Finally, the effects of various parameters have been separately discussed and illustrated graphically.
文摘Arterial stenosis is a critical condition with increasing prevalence among pediatric patients and young adults,making its investigation highly significant.Despite extensive studies on blood flow dynamics,limited research addresses the combined effects of nanoparticles and arterial curvature on unsteady pulsatile flow through multiple stenoses.This study aims to analyze the influence of nanoparticles on blood flow characteristics in realistic curved arteries with mild to severe overlapped constrictions.Using curvilinear coordinates,the thermal energy and momentum equations for nanoparticle-laden blood were derived,and numerical results were obtained through an explicit finite difference method.Key findings reveal that nanoparticle injections reduce blood temperature intensity,while arterial curvature strongly affects flow symmetry.Moreover,temperature,axial velocity,wall shear stress,and volumetric flow rate decrease significantly in severe stenosis compared to mild and moderate cases.These results provide new insights into nanoparticle-assisted blood flow under complex stenotic conditions and may contribute to improved diagnostic and therapeutic strategies for cardiovascular diseases.
基金supported by National Natural Science Foundation of China(42002293,52068019)Hainan Provincial Natural Science Foundation of China(520QN229,422RC599)+2 种基金Independent Innovation Fund Project of Tianjin University and Hainan University(KF2022⁃03)Scientific Research Startup Foundation of Hainan university(KYQD(2R)1969)Systematic Project of Key Laboratory of Geological Hazards on Three Gorges Reservoir Area(Three Gorges University),Ministry of Education(2020KDZ04).
文摘The chief objective of the article is to learn the spatial characteristics of stress distribution around a shallow buried cylinder Karst cave in limestone strata.Firstly,taking into account the geometry of limestone formations,and the characteristics of Karst geomorphology in China,a spatial axialsymmetrical hollow model was established.Concurrently,combining available work and the concept of elasticity,the boundary conditions are determined.Subsequently,Love displacement method was introduced,the expressions of stress components were gained.The diagram characteristics of each stress component are summarized,which are affected by various influencing factors.Finally,in order to prove the rationality of the general solution,numerical simulation was carried out on the basis of practical engineering,and the maximum error is less than 5%.Thus,the analytical solution could represent the spatial characteristics of stress distribution around a shallow buried cylinder Karst cave in limestone strata.
基金the National Key Development and Planning Project for the Basic Research (973) (Grant No.2005CB321703)the Science Funds for Creative Research Groups (Grant No.40221503)
文摘An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.
文摘In this paper, unsteady free convection heat transfer flow over a vertical plate in the presence of a magnetic field is discussed in detail. The dimensionless partial differential equations of continuity, momentum along energy are analyzed with suitable transformations. For numerical calculation, an implicit finite difference method is applied to solve a set of nonlinear dimensionless partial differential equations. Dimensionless velocity and temperature profile are also investigated due to the effects of assumed parameters in the concerned problem. An explicit finite difference technique is used to compute velocity and temperature profiles. The stability conditions are also examined.
文摘Unsteady electromagnetic free convection flows of two-dimensional micropolar fluid through in a porous medium parallel to a vertical porous plate have been investigated numerically. Similarity analysis has been used to transform the governing equations into its non-dimensional form by using the explicit finite difference method to obtain numerical solutions. Estimated results have been gained for various values of Prandtl number, Grashof number, material parameters, micropolar parameter, electric conductivity, electric permeability, thermal relaxation time and the permeability of the porous medium. The effect<span style="font-family:Verdana;">s</span><span style="font-family:Verdana;"> of pertinent parameters on the velocity, electric induction, magnetic induction, microrotation and temperature distributions have been investigated briefly and illustrate</span><span style="font-family:Verdana;">d</span><span style="font-family:Verdana;"> graphically.</span>
文摘This article is based on the impulsively started horizontal Riga plate in two dimensional unsteady Casson fluid flows with rotation. The plate starts abruptly from the rest relative to the rotating fluids moving with uniform acceleration in its plane. Numerical solutions are acquired by using explicit finite difference method and estimated results have been gained for various values of the Rotational parameter, modified Hartmann number, Prandtl number, Radiative parameter, Eckert number, Heat source parameter, Schmidt number, and the Soret number. Both the Compaq visual FORTRAN 6.6a and MATLAB R2015a tools have been used to find the numerical solutions and the graphical presentation. The Skin friction, Nusselt number and Sherwood number have been computed and the effects of some pertinent parameters on various distributions are discussed briefly and presented graphically.
基金This project was supported by the Research Fund for the Basic Operation of National Social Welfare Institutions (J2207831)the National Science Supporting Program(2006BAC13B01)
文摘An explicit finite difference method is performed to evaluate the significance of topography effects on the seismic response of viscoelastic sites.The real accelerograms and bell-shape impulse wavelets,slope angle of cliff and angle of incidence on the spectrum property of the incoming waves are all discussed in detail.The conclusions show that the presence of topographic factors and the direction of the incident waves not only significantly affect the peak ground acceleration of a site,but also affect the spectrum properties of the incoming waves,and the effect on the direction of the incident waves is especially remarkable.The study also finds that it is reasonable to analyse spectrum properties with the input of impulse wavelets in the finite element simulation of wave motion.
