The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flo...The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.展开更多
In this work fingering double diffusive convection,i.e.the buoyancy-driven flow with fluid density being affected by two different scalar components,is investigated numerically with special efforts on the influences o...In this work fingering double diffusive convection,i.e.the buoyancy-driven flow with fluid density being affected by two different scalar components,is investigated numerically with special efforts on the influences of the physical properties of two scalar components.We show that different scalar properties can affect the global transport behaviors.The concentration flux exhibits different exponents in their power-law scalings for different combinations of scalar components.The scaling exponents of heat flux,however,depend mainly on the ratio of the diffusivities of two scalars.If one uses the local parameters of the finger layer in the bulk,the behaviors are very similar to those found in the fully periodic simulations.The horizontal width of the fingers is consistent with the wavelength of the fast growing mode.For one case we observe evidences of the thermohaline staircase,namely,the typical width of the flow structures changes significantly in different layers within the flow domain.展开更多
The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves ave found to exist, indicating that t...The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves ave found to exist, indicating that three critical thermal Darcy-Rayleigh numbers are required to specify the linear instability criteria. However, another distinguishing feature predicted from that of Newtonian fluids is the impossibility of quasi-periodic bifurcation from the rest state. Besides, the co-dimensional two bifurcation points are located in the Darcy-Prandtl number and the stress relaxation parameter plane. It is observed that the value of the stress relaxation parameter defining the crossover between stationary and oscillatory bifurcations decreases when the Darcy-Prandtl number increases. A cubic Landau equation is derived based on the weakly nonlinear stability analysis. It is found that the bifurcating oscillatory solution is either supercritical or subcritical, depending on the choice of the physical parameters. Heat and mass transfers are estimated in terms of time and area-averaged Nusselt numbers.展开更多
A high resolution upwind compact streamfunction numerical algorithm for two-dimensional(2D)double-diffusive convection(DDC)is developed.The unsteady Navier-Stokes(N-S)equations in the streamfunction-velocity form and ...A high resolution upwind compact streamfunction numerical algorithm for two-dimensional(2D)double-diffusive convection(DDC)is developed.The unsteady Navier-Stokes(N-S)equations in the streamfunction-velocity form and the scalar temperature and concentration equations are used.An optimized third-order upwind compact(UCD3 opt)scheme with a low dispersion error for the first derivatives is utilized to approximate the third derivatives of the streamfunction in the advection terms of the N-S equations and the first derivatives in the advection terms of the scalar temperature and concentration equations.The remaining first derivatives of the streamfunction(velocity),temperature,and concentration variables used in the governing equations are discretized by the fourth-order compact Pade(SCD4)schemes.With the temperature and concentration variables and their approximate values of the first derivatives obtained by the SCD4 schemes,the explicit fourth-order compact schemes are suggested to approximate the second derivatives of temperature and concentration in the diffusion terms of the energy and concentration equations.The discretization of the temporal term is executed with the second-order Crank-Nicolson(C-N)scheme.To assess the spatial behavior capability of the established numerical algorithm and verify the developed computer code,the DDC flow is numerically solved.The obtained results agree well with the benchmark solutions and some accurate results available in the literature,verifying the accuracy,effectiveness,and robustness of the provided algorithm.Finally,a preliminary application of the proposed method to the DDC is carried out.展开更多
This is the first part of direct numerical simulation(DNS)of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients.We consider the case with the thermal Ra...This is the first part of direct numerical simulation(DNS)of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients.We consider the case with the thermal Rayleigh number of 105,the Pradtle number of 1,the Lewis number of 2,the buoyancy ratio of composition to temperature being in the range of[0,1],and height-to-width aspect ration of 4.A new 7thorder upwind compact scheme was developed for approximation of convective terms,and a three-stage third-order Runge-Kutta method was employed for time advancement.Our DNS suggests that with the buoyancy ratio increasing form 0 to 1,the flow of transition is a complex series changing from the steady to periodic,chaotic,periodic,quasi-periodic,and finally back to periodic.There are two types of periodic flow,one is simple periodic flow with single fundamental frequency(FF),and another is complex periodic flow with multiple FFs.This process is illustrated by using time-velocity histories,Fourier frequency spectrum analysis and the phase-space trajectories.展开更多
This paper deals with developing a numerical boundary layer flow model to analyze convective heat transfer characteristics of a micropolar fluid past a vertical plate in a composite material with viscous-Ohmic dissipa...This paper deals with developing a numerical boundary layer flow model to analyze convective heat transfer characteristics of a micropolar fluid past a vertical plate in a composite material with viscous-Ohmic dissipations in the presence of a transverse magnetic field.The basic governing equations are solved numerically by using the Runge-Kutta-Fehlberg method.The computed results reveal a reduction in the velocity,temperature,and microrotation profiles by increasing the Prandtl number.Also,the concentration distribution is enhanced by enhancing or decreasing Soret-Dufour parameter,and there seems to be decremented in the skin-friction coefficient values with Schmidt number.展开更多
The present study deals with double-diffusive convection within a two-dimensional inclined cavity filled with an air-CO_(2) binary gas mixture.The left and the right vertical walls are differentially heated and subjec...The present study deals with double-diffusive convection within a two-dimensional inclined cavity filled with an air-CO_(2) binary gas mixture.The left and the right vertical walls are differentially heated and subjected to different locations of(CO_(2))contaminants to allow for the variation of the buoyancy strength(N).However,the horizontal walls are assumed adiabatic.The simulations are conducted using the finite volume method to solve the conservation equations of continuity,momentum,energy,and species transport.Good agreement with other numerical results in the literature is obtained.The effect of multiple parameters,namely,buoyancy ratio(N),thermal Rayleigh number(Ra),and inclination angle(α)on entropy generation rate is analyzed and discussed in the postprocessing stage,while considering both laminar and turbulent flow regimes.The computations reveal that these parameters considerably affect both the heat and mass transfer performances of the system.展开更多
A numerical investigation of laminar natural double diffusive convection in an open ended vertical cylindrical annulus with unheated entry and unheated exit is performed.Both boundary conditions of uniform wall temper...A numerical investigation of laminar natural double diffusive convection in an open ended vertical cylindrical annulus with unheated entry and unheated exit is performed.Both boundary conditions of uniform wall temperature/uniform wall concentration(UWT/UWC)and uniform heat flux/uniform mass flux(UHF/UMF)are considered.Results of dimensionless induced volume rate Q,average Nusselt number Nu and Sherwood number Sh are obtained for air flow under various buoyancy ratio N,Grashof numbers due to heat and mass transfer GrT and GrM,Schmidt number Sc and combinations of unheated entry,heated section and unheated exit length.Since the flow under consideration is a boundary layer type,the governing partial differential equations was discretized to a linear system of equations by the use of an implicit finite difference method.The nonlinear convective terms are approximated by second upwind difference method for the numerical stability.The numerical results reveal that the presence of unheated entry and unheated exit severely affects the heat and mass transfer rates.The numerical solutions are found to approach asymptotically the closed form solutions for fully developed flow.Further,the present numerical results are validated with the existing solutions for pure thermal convection and are found to be in good agreement.展开更多
In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. ...In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O（ε1/2 ＋ h1/2）hk） convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L2 norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method.展开更多
Convection and diffusion are the main factors affecting radon migration.In this paper,a coupled diffusion-convection radon migration model is presented taking into account turbulence effects.In particular,the migratio...Convection and diffusion are the main factors affecting radon migration.In this paper,a coupled diffusion-convection radon migration model is presented taking into account turbulence effects.In particular,the migration of radon is simulated in the framework of the k-εturbulence model.The model equations are solved in a complex 3D domain by the finite element method(FEM).Special attention is paid to the case study about radon migration in an abandoned air defense shelter(AADS).The results show that air convection in a confined space has a great influence on the radon migration and the radon concentration is inversely proportional to the wind speed.展开更多
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain ...The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.展开更多
A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order...A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.展开更多
This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the op...This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.展开更多
This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and t...This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,epsilon > 0 are constants.展开更多
In massive stars, convection in the interior is different from that of inter- mediate and small mass stars. In the main-sequence phase of small mass stars, there is a convective core and a radiative envelope, between ...In massive stars, convection in the interior is different from that of inter- mediate and small mass stars. In the main-sequence phase of small mass stars, there is a convective core and a radiative envelope, between which are the radiative inter- mediate layers with uneven chemical abundances. Semiconvection would occur in the intermediate layers between the convective core and the homogeneous envelope in massive stars. We treat core convective overshooting and semiconvection together as a process. We found that when decreasing overshooting, the semiconvection is more pronounced. In these two processes, we introduce one diffusive parameter D, which is different from other authors who have introduced different parameters for these two zones. The influences of the turbulent diffusion process on chemical evolution and other quantities of the stellar structure are shown in the present paper.展开更多
In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of thi...In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.展开更多
In this paper ,in the space that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) the...In this paper ,in the space that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) they ave given in the accurate form:(2)they can be calculated in the explicit way, without solving the eguations;(3) the error of the approximate solution will be monotonically decreased under the meaning of the norm of the spaces when a cardinal term is added in the procedure of numerical solution .Finally, we calculated the example in [2] the result shows that our solution is more accurate than that in [2].展开更多
Historically,streamer-to-leader transition studies mainly focused on the rod-plane gap and low altitude analysis,with limited attention paid to the sphere-plane gap at high altitude analysis.In this work,sphere-plane ...Historically,streamer-to-leader transition studies mainly focused on the rod-plane gap and low altitude analysis,with limited attention paid to the sphere-plane gap at high altitude analysis.In this work,sphere-plane gap discharge tests were carried out under the gap distance of 5 m at the Qinghai Ultra High Voltage(UHV)test base at an altitude of 2200 m.The experiments measured the physical parameters such as the discharge current,electric field intensity and instantaneous optical power.The duration of the dark period and the critical charge of streamer-toleader transition were obtained at high altitude.Based on radial thermal expansion of the streamer stem,we established a modified streamer-to-leader transition model of the sphere-plane gap discharge at high altitude,and calculated the stem temperature,stem radii and the duration of streamer-to-leader transition.Compared with the measured duration of sphere-plane electrode discharge at an altitude of 2200 m,the error rate of the modified model was 0.94%,while the classical model was 6.97%,demonstrating the effectiveness of the modified model.From the comparisons and analysis,several suggestions are proposed to improve the numerical model for further quantitative investigations of the leader inception.展开更多
基金Institutional Fund Projects under No.(IFP-A-2022-2-5-24)by Ministry of Education and University of Hafr Al Batin,Saudi Arabia.
文摘The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.
基金supported by the Major Research Plan of National Natural and Science Foundation of China for Turbulent Structures(Grants 91852107 and 91752202).
文摘In this work fingering double diffusive convection,i.e.the buoyancy-driven flow with fluid density being affected by two different scalar components,is investigated numerically with special efforts on the influences of the physical properties of two scalar components.We show that different scalar properties can affect the global transport behaviors.The concentration flux exhibits different exponents in their power-law scalings for different combinations of scalar components.The scaling exponents of heat flux,however,depend mainly on the ratio of the diffusivities of two scalars.If one uses the local parameters of the finger layer in the bulk,the behaviors are very similar to those found in the fully periodic simulations.The horizontal width of the fingers is consistent with the wavelength of the fast growing mode.For one case we observe evidences of the thermohaline staircase,namely,the typical width of the flow structures changes significantly in different layers within the flow domain.
基金the Department of Science and Technology, New Delhi for granting him a fellowship under the Innovation in Science Pursuit for the Inspired Research (INSPIRE) Program (No. DST/INSPIRE Fellowship/[IF 150253])
文摘The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves ave found to exist, indicating that three critical thermal Darcy-Rayleigh numbers are required to specify the linear instability criteria. However, another distinguishing feature predicted from that of Newtonian fluids is the impossibility of quasi-periodic bifurcation from the rest state. Besides, the co-dimensional two bifurcation points are located in the Darcy-Prandtl number and the stress relaxation parameter plane. It is observed that the value of the stress relaxation parameter defining the crossover between stationary and oscillatory bifurcations decreases when the Darcy-Prandtl number increases. A cubic Landau equation is derived based on the weakly nonlinear stability analysis. It is found that the bifurcating oscillatory solution is either supercritical or subcritical, depending on the choice of the physical parameters. Heat and mass transfers are estimated in terms of time and area-averaged Nusselt numbers.
基金supported by the National Natural Science Foundation of China(Nos.11872151,11372075,and 91330112)。
文摘A high resolution upwind compact streamfunction numerical algorithm for two-dimensional(2D)double-diffusive convection(DDC)is developed.The unsteady Navier-Stokes(N-S)equations in the streamfunction-velocity form and the scalar temperature and concentration equations are used.An optimized third-order upwind compact(UCD3 opt)scheme with a low dispersion error for the first derivatives is utilized to approximate the third derivatives of the streamfunction in the advection terms of the N-S equations and the first derivatives in the advection terms of the scalar temperature and concentration equations.The remaining first derivatives of the streamfunction(velocity),temperature,and concentration variables used in the governing equations are discretized by the fourth-order compact Pade(SCD4)schemes.With the temperature and concentration variables and their approximate values of the first derivatives obtained by the SCD4 schemes,the explicit fourth-order compact schemes are suggested to approximate the second derivatives of temperature and concentration in the diffusion terms of the energy and concentration equations.The discretization of the temporal term is executed with the second-order Crank-Nicolson(C-N)scheme.To assess the spatial behavior capability of the established numerical algorithm and verify the developed computer code,the DDC flow is numerically solved.The obtained results agree well with the benchmark solutions and some accurate results available in the literature,verifying the accuracy,effectiveness,and robustness of the provided algorithm.Finally,a preliminary application of the proposed method to the DDC is carried out.
基金The authors thank Shanghai Supercomputer Center(SSC)for providing computer timeThis work was supported by National Natural Science Foundation of China(Grant Nos.10632050,10502052).
文摘This is the first part of direct numerical simulation(DNS)of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients.We consider the case with the thermal Rayleigh number of 105,the Pradtle number of 1,the Lewis number of 2,the buoyancy ratio of composition to temperature being in the range of[0,1],and height-to-width aspect ration of 4.A new 7thorder upwind compact scheme was developed for approximation of convective terms,and a three-stage third-order Runge-Kutta method was employed for time advancement.Our DNS suggests that with the buoyancy ratio increasing form 0 to 1,the flow of transition is a complex series changing from the steady to periodic,chaotic,periodic,quasi-periodic,and finally back to periodic.There are two types of periodic flow,one is simple periodic flow with single fundamental frequency(FF),and another is complex periodic flow with multiple FFs.This process is illustrated by using time-velocity histories,Fourier frequency spectrum analysis and the phase-space trajectories.
文摘This paper deals with developing a numerical boundary layer flow model to analyze convective heat transfer characteristics of a micropolar fluid past a vertical plate in a composite material with viscous-Ohmic dissipations in the presence of a transverse magnetic field.The basic governing equations are solved numerically by using the Runge-Kutta-Fehlberg method.The computed results reveal a reduction in the velocity,temperature,and microrotation profiles by increasing the Prandtl number.Also,the concentration distribution is enhanced by enhancing or decreasing Soret-Dufour parameter,and there seems to be decremented in the skin-friction coefficient values with Schmidt number.
文摘The present study deals with double-diffusive convection within a two-dimensional inclined cavity filled with an air-CO_(2) binary gas mixture.The left and the right vertical walls are differentially heated and subjected to different locations of(CO_(2))contaminants to allow for the variation of the buoyancy strength(N).However,the horizontal walls are assumed adiabatic.The simulations are conducted using the finite volume method to solve the conservation equations of continuity,momentum,energy,and species transport.Good agreement with other numerical results in the literature is obtained.The effect of multiple parameters,namely,buoyancy ratio(N),thermal Rayleigh number(Ra),and inclination angle(α)on entropy generation rate is analyzed and discussed in the postprocessing stage,while considering both laminar and turbulent flow regimes.The computations reveal that these parameters considerably affect both the heat and mass transfer performances of the system.
文摘A numerical investigation of laminar natural double diffusive convection in an open ended vertical cylindrical annulus with unheated entry and unheated exit is performed.Both boundary conditions of uniform wall temperature/uniform wall concentration(UWT/UWC)and uniform heat flux/uniform mass flux(UHF/UMF)are considered.Results of dimensionless induced volume rate Q,average Nusselt number Nu and Sherwood number Sh are obtained for air flow under various buoyancy ratio N,Grashof numbers due to heat and mass transfer GrT and GrM,Schmidt number Sc and combinations of unheated entry,heated section and unheated exit length.Since the flow under consideration is a boundary layer type,the governing partial differential equations was discretized to a linear system of equations by the use of an implicit finite difference method.The nonlinear convective terms are approximated by second upwind difference method for the numerical stability.The numerical results reveal that the presence of unheated entry and unheated exit severely affects the heat and mass transfer rates.The numerical solutions are found to approach asymptotically the closed form solutions for fully developed flow.Further,the present numerical results are validated with the existing solutions for pure thermal convection and are found to be in good agreement.
基金Supported by National Natural Science Foundation of China (10571046, 10571053, and 10871066)Program for New Century Excellent Talents in University (NCET-06-0712)+2 种基金Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal Universitythe Project of Scientific Research Fund of Hunan Provincial Education Department (09K025)the Key Scientific Research Topic of Jiaxing University (70110X05BL)
文摘In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O（ε1/2 ＋ h1/2）hk） convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L2 norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method.
基金supported by the National Natural Science Foundation of China[grant numbers 11705083]China Postdoctoral Science Foundation[grant number 2018M632975]+1 种基金National Natural Science Foundation of Hunan Province[grant number 2019JJ50488]Hunan Province Engineering Research Center of Radioactive Control Technology in Uranium Mining and Metallurgy&Hunan Province Engineering Technology Research Center of Uranium Tailings Treatment Technology,University of South China[grant number 2019YKZX1009].
文摘Convection and diffusion are the main factors affecting radon migration.In this paper,a coupled diffusion-convection radon migration model is presented taking into account turbulence effects.In particular,the migration of radon is simulated in the framework of the k-εturbulence model.The model equations are solved in a complex 3D domain by the finite element method(FEM).Special attention is paid to the case study about radon migration in an abandoned air defense shelter(AADS).The results show that air convection in a confined space has a great influence on the radon migration and the radon concentration is inversely proportional to the wind speed.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
基金the National Natural Science Foundation of China(No.10571017)supported in part by the National Natural Science Foundation of China(No.60533020)supported in part by NSF DMS 0712744
文摘The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.
基金supported by the National Natural Science Foundation of China (No. 10601022)NSF ofInner Mongolia Autonomous Region of China (No. 200607010106)513 and Science Fund of InnerMongolia University for Distinguished Young Scholars (No. ND0702)
文摘A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.
文摘This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.
文摘This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,epsilon > 0 are constants.
基金co-sponsored by the National Natural Science Foundation of China (Grant Nos.11333006 and 10973035)the Chinese Academy of Sciences (Grant No.KJCX2-YW-T24)
文摘In massive stars, convection in the interior is different from that of inter- mediate and small mass stars. In the main-sequence phase of small mass stars, there is a convective core and a radiative envelope, between which are the radiative inter- mediate layers with uneven chemical abundances. Semiconvection would occur in the intermediate layers between the convective core and the homogeneous envelope in massive stars. We treat core convective overshooting and semiconvection together as a process. We found that when decreasing overshooting, the semiconvection is more pronounced. In these two processes, we introduce one diffusive parameter D, which is different from other authors who have introduced different parameters for these two zones. The influences of the turbulent diffusion process on chemical evolution and other quantities of the stellar structure are shown in the present paper.
基金supported by the National Natural Science Foundation of China(Nos.11701253,11971259,11801216)Natural Science Foundation of Shandong Province(No.ZR2017BA010)。
文摘In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.
文摘In this paper ,in the space that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) they ave given in the accurate form:(2)they can be calculated in the explicit way, without solving the eguations;(3) the error of the approximate solution will be monotonically decreased under the meaning of the norm of the spaces when a cardinal term is added in the procedure of numerical solution .Finally, we calculated the example in [2] the result shows that our solution is more accurate than that in [2].
基金supported by National Natural Science Foundation of China(Scientific Funds for Young Scientists)(No.52007064)。
文摘Historically,streamer-to-leader transition studies mainly focused on the rod-plane gap and low altitude analysis,with limited attention paid to the sphere-plane gap at high altitude analysis.In this work,sphere-plane gap discharge tests were carried out under the gap distance of 5 m at the Qinghai Ultra High Voltage(UHV)test base at an altitude of 2200 m.The experiments measured the physical parameters such as the discharge current,electric field intensity and instantaneous optical power.The duration of the dark period and the critical charge of streamer-toleader transition were obtained at high altitude.Based on radial thermal expansion of the streamer stem,we established a modified streamer-to-leader transition model of the sphere-plane gap discharge at high altitude,and calculated the stem temperature,stem radii and the duration of streamer-to-leader transition.Compared with the measured duration of sphere-plane electrode discharge at an altitude of 2200 m,the error rate of the modified model was 0.94%,while the classical model was 6.97%,demonstrating the effectiveness of the modified model.From the comparisons and analysis,several suggestions are proposed to improve the numerical model for further quantitative investigations of the leader inception.
