CO_(2)enhanced oil recovery plays an important role in carbon storage and utilization.However,the incomplete understanding of the underlying microscopic convection–diffusion mechanisms in complex pore structures has ...CO_(2)enhanced oil recovery plays an important role in carbon storage and utilization.However,the incomplete understanding of the underlying microscopic convection–diffusion mechanisms in complex pore structures has constrained the broader industrial application of CO_(2)geo-sequestration.This work develops a pore-scale numerical model considering molecular convection–diffusion to investigate CO_(2)-oil miscible displacement in two-and three-dimensional porous structures of conglomerate rocks.The effects of CO_(2)injection rates and pore structure properties on convection–diffusion are analyzed.By reconstructing the distribution of unexploited pores,the CO_(2)sweep efficiency is quantitatively evaluated.Furthermore,a sequestration factor is proposed to evaluate the CO_(2)storage capacity during miscible displacement.Convection significantly enhances the CO_(2)mass fraction in fractures with high flow rates.Subsequently,CO_(2)gradually diffuses into matrix pores without velocity distribution.Both convection and diffusion contribute to improving CO_(2)displacement efficiency.Diffusion facilitates the dissolution of CO_(2)into oil within small-diameter pores,and convection effectively mobilizes oil in large pore bodies.Developed and homogeneous pore structures enhance CO_(2)displacement efficiency,whereas CO_(2)flows along the main flow channels in heterogeneous pore structures,resulting in lower displacement efficiency.Diffusion plays a crucial role in CO_(2)storage within porous media.At low injection rates,dissolved CO_(2)is trapped in poorly connected and blind-end pores.The injection rate is negatively correlated with the sequestration factor.展开更多
In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d...In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.展开更多
A perturbation finite volume(PFV)method for the convective-diffusion integral equa- tion is developed in this paper.The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order in...A perturbation finite volume(PFV)method for the convective-diffusion integral equa- tion is developed in this paper.The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations,with the least nodes similar to the standard three-point schemes,that is,the number of the nodes needed is equal to unity plus the face-number of the control volume.For instance,in the two-dimensional(2-D)case,only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized,respectively.The PFV scheme is applied on a number of 1-D linear and nonlinear problems,2-D and 3-D flow model equations.Comparing with other standard three-point schemes,the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme(UDS).Its numerical accuracies are also higher than the second-order central scheme(CDS),the power-law scheme(PLS)and QUICK scheme.展开更多
A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convec...A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.展开更多
In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
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
In this paper,a streamline diffusion F.E.M. for linear Sobolev equations with convection dominated term is given.According to the range of space time F.E mesh parameter h ,two choices for artifical diffusion par...In this paper,a streamline diffusion F.E.M. for linear Sobolev equations with convection dominated term is given.According to the range of space time F.E mesh parameter h ,two choices for artifical diffusion parameter δ are presented,and for the corresponding computation schemes the stability and error estimates in suitable norms are estabilished.展开更多
A 3D model applying temperature-and carbon concentration-dependent material properties was developed to describe the scrap melting behavior and carbon diffusion under natural convection.Simulated results agreed reason...A 3D model applying temperature-and carbon concentration-dependent material properties was developed to describe the scrap melting behavior and carbon diffusion under natural convection.Simulated results agreed reasonably well with experimental ones.Scrap melting was subdivided into four stages:formation of a solidified layer,rapid melting of the solidified layer,carburization,and carburization+normal melting.The carburization stage could not be ignored at low temperature because the carburization time for the sample investigated was 214 s at 1573 K compared to 12 s at 1723 K.The thickness of the boundary layer with significant concentration difference at 1573 K increased from 130μm at 5 s to 140μm at 60 s.The maximum velocity caused by natural convection decreased from 0.029 m·s^(−1)at 5 s to 0.009 m·s^(−1)at 634 s because the differences in temperature and density between the molten metal and scrap decreased with time.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 analytical solution of the convection diffusion equation is considered by two-dimensional Fourier transform and the inverse Fourier transform. To get the numerical solution, the Crank-Nicolson finite difference me...The analytical solution of the convection diffusion equation is considered by two-dimensional Fourier transform and the inverse Fourier transform. To get the numerical solution, the Crank-Nicolson finite difference method is constructed, which is second-order accurate in time and space. Numerical simulation shows excellent agreement with the analytical solution. The dynamic visualization of the simulating results is realized on ArcGIS platform. This work provides a quick and intuitive decision-making basis for water resources protection, especially in dealing with water pollution emergencies.展开更多
Contamination between batches in multi-products pipeline transport is studied. The influences of convection and diffusion on the contamination are studied in detail. Diffusion equations, which are mainly controlled by...Contamination between batches in multi-products pipeline transport is studied. The influences of convection and diffusion on the contamination are studied in detail. Diffusion equations, which are mainly controlled by convection, are developed under turbulent pipe flow. The diffusion equation is separated into a pure convection equation and a pure diffusion equation which are solved by characteristics method and finite difference method respectively to obtain numerical solutions. The results of numerical computation explain the forming and developing of contamination very well.展开更多
The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and...The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined.Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration,three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution(the steady-state),for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.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
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
In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for c...In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.展开更多
Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method but the nonlinear term is collocated at the Legendre/C...Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method but the nonlinear term is collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval. Appropriate base functions are introduced so that the matrix of the system is sparse, and the method can be implemented efficiently and in parallel. The stability and the optimal rate of convergence of the methods are proved. Numerical results are given for both the single domain and the multidomain methods to make a comparison.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
This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using prec...This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.展开更多
基金supported by National Natural Science Foundation of China(42172159,52404048)China Postdoctoral Science Foundation(2023M743870)+1 种基金Postdoctoral Fellowship Program of CPSF(GZB20230864)Frontier Interdisciplinary Exploration Research Program of China University of Petroleum,Beijing(2462024XKQY002).
文摘CO_(2)enhanced oil recovery plays an important role in carbon storage and utilization.However,the incomplete understanding of the underlying microscopic convection–diffusion mechanisms in complex pore structures has constrained the broader industrial application of CO_(2)geo-sequestration.This work develops a pore-scale numerical model considering molecular convection–diffusion to investigate CO_(2)-oil miscible displacement in two-and three-dimensional porous structures of conglomerate rocks.The effects of CO_(2)injection rates and pore structure properties on convection–diffusion are analyzed.By reconstructing the distribution of unexploited pores,the CO_(2)sweep efficiency is quantitatively evaluated.Furthermore,a sequestration factor is proposed to evaluate the CO_(2)storage capacity during miscible displacement.Convection significantly enhances the CO_(2)mass fraction in fractures with high flow rates.Subsequently,CO_(2)gradually diffuses into matrix pores without velocity distribution.Both convection and diffusion contribute to improving CO_(2)displacement efficiency.Diffusion facilitates the dissolution of CO_(2)into oil within small-diameter pores,and convection effectively mobilizes oil in large pore bodies.Developed and homogeneous pore structures enhance CO_(2)displacement efficiency,whereas CO_(2)flows along the main flow channels in heterogeneous pore structures,resulting in lower displacement efficiency.Diffusion plays a crucial role in CO_(2)storage within porous media.At low injection rates,dissolved CO_(2)is trapped in poorly connected and blind-end pores.The injection rate is negatively correlated with the sequestration factor.
基金the National Natural Science Fund(11661058,11761053)Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2017MS0107)+1 种基金Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07)National Undergraduate Innovative Training Project of Inner Mongolia University(201710126026).
文摘In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.
基金The project supported by the National Natural Science Foundation of China(10272106,10372106)
文摘A perturbation finite volume(PFV)method for the convective-diffusion integral equa- tion is developed in this paper.The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations,with the least nodes similar to the standard three-point schemes,that is,the number of the nodes needed is equal to unity plus the face-number of the control volume.For instance,in the two-dimensional(2-D)case,only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized,respectively.The PFV scheme is applied on a number of 1-D linear and nonlinear problems,2-D and 3-D flow model equations.Comparing with other standard three-point schemes,the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme(UDS).Its numerical accuracies are also higher than the second-order central scheme(CDS),the power-law scheme(PLS)and QUICK scheme.
文摘A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.
文摘In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
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 Sciences Foundation of China(1 8971 0 51 )
文摘In this paper,a streamline diffusion F.E.M. for linear Sobolev equations with convection dominated term is given.According to the range of space time F.E mesh parameter h ,two choices for artifical diffusion parameter δ are presented,and for the corresponding computation schemes the stability and error estimates in suitable norms are estabilished.
基金the National Key R&D Program of China(No.2019YFC1905701)the National Natural Science Foundation of China(Nos.51674022,51734003)the Key projects of NSFC(No.U1960201).
文摘A 3D model applying temperature-and carbon concentration-dependent material properties was developed to describe the scrap melting behavior and carbon diffusion under natural convection.Simulated results agreed reasonably well with experimental ones.Scrap melting was subdivided into four stages:formation of a solidified layer,rapid melting of the solidified layer,carburization,and carburization+normal melting.The carburization stage could not be ignored at low temperature because the carburization time for the sample investigated was 214 s at 1573 K compared to 12 s at 1723 K.The thickness of the boundary layer with significant concentration difference at 1573 K increased from 130μm at 5 s to 140μm at 60 s.The maximum velocity caused by natural convection decreased from 0.029 m·s^(−1)at 5 s to 0.009 m·s^(−1)at 634 s because the differences in temperature and density between the molten metal and scrap decreased with time.
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.
文摘The analytical solution of the convection diffusion equation is considered by two-dimensional Fourier transform and the inverse Fourier transform. To get the numerical solution, the Crank-Nicolson finite difference method is constructed, which is second-order accurate in time and space. Numerical simulation shows excellent agreement with the analytical solution. The dynamic visualization of the simulating results is realized on ArcGIS platform. This work provides a quick and intuitive decision-making basis for water resources protection, especially in dealing with water pollution emergencies.
文摘Contamination between batches in multi-products pipeline transport is studied. The influences of convection and diffusion on the contamination are studied in detail. Diffusion equations, which are mainly controlled by convection, are developed under turbulent pipe flow. The diffusion equation is separated into a pure convection equation and a pure diffusion equation which are solved by characteristics method and finite difference method respectively to obtain numerical solutions. The results of numerical computation explain the forming and developing of contamination very well.
基金Abdus Salam School of Mathematical Sciences, GC University, Lahore, PakistanHigher Education Commission of Pakistan, for generous supporting and facilitating this research work
文摘The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined.Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration,three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution(the steady-state),for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.
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.
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.
基金Project supported by National Natural Science Foundation of China and China State Key project for Basic Researchcs.
文摘In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.
基金supported by the National Natural Science Foundation of China(No.60874039)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(No.J50101)
文摘Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method but the nonlinear term is collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval. Appropriate base functions are introduced so that the matrix of the system is sparse, and the method can be implemented efficiently and in parallel. The stability and the optimal rate of convergence of the methods are proved. Numerical results are given for both the single domain and the multidomain methods to make a comparison.
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.
文摘This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.
