A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 a...A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.展开更多
It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit method.The constant acceleration method's concom...It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit method.The constant acceleration method's concomitant explicit method was used as an example and is described in detail in this paper.The relationship between the implicit method and explicit method is defined,which provides some guidance about how to create a new explicit method that has high precision and computational efficiency.展开更多
Natural gas hydrate, as a potential energy resource, deposits in permafrost and marine sediment with large quantities. The current exploitation methods include depressurization, thermal stimulation, and inhibitor inje...Natural gas hydrate, as a potential energy resource, deposits in permafrost and marine sediment with large quantities. The current exploitation methods include depressurization, thermal stimulation, and inhibitor injection. However, many issues have to be resolved before the commercial production. In the present study, a 2-D axisymmetric simulator for gas production from hydrate reservoirs is developed. The simulator includes equations of conductive and convective heat transfer, kinetic of hydrate decomposition, and multiphase flow. These equations are discretized based on the finite difference method and are solved with the fully implicit simultaneous solution method. The process of laboratory-scale hydrate decomposition by depressurization is simulated. For different surrounding temperatures and outlet pressures, time evolutions of gas and water generations during hydrate dissociation are evaluated, and variations of temperature, pressure, and multiphase fluid flow conditions are analyzed. The results suggest that the rate of heat transfer plays an important role in the process. Furthermore, high surrounding temperature and low outlet valve pressure may increase the rate of hydrate dissociation with insignificant impact on final cumulative gas volume.展开更多
Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian g...Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.展开更多
A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.展开更多
This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditiona...This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.展开更多
In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examp...In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale.This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.展开更多
This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. ...This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. A new total pressure equation of viscous incompressible flow is introduced in this paper and the equation is numerically computed by the implicit method. It is shown from the computational results of examples that the implicit method of streamline iteration can speed up the convergence and decrease the computational time.展开更多
This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods...This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.展开更多
The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF me...The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.展开更多
In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear ...In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.展开更多
In this paper two implicit 2-step hybrid methods are proposed! one has order five, the other six. The stability properties of the methods are analysed. The 5th order method is proved to be A-stable and the 6th order o...In this paper two implicit 2-step hybrid methods are proposed! one has order five, the other six. The stability properties of the methods are analysed. The 5th order method is proved to be A-stable and the 6th order one is not, but still has a relatively large region of absolute stability. The implementation of the 5th order method is also discussed.展开更多
In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactor...In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived.展开更多
In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coeffic...In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.展开更多
In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate init...In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.展开更多
Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numer...Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numerical wave, we combine the MPS method with large eddy simulation(LES) which can simulate the turbulence in the flow. The intense pressure fluctuation is a significant shortcoming in MPS method. So, we improve the original MPS method by using a new pressure Poisson equation to ease the pressure fluctuation. Divergencefree condition representing fluid incompressible is used to calculate pressure smoothly. Then, area-time average technique is used to deal with the calculation. With these improvements, the modified MPS-LES method is applied to the simulation of numerical wave. As a contrast, we also use the original MPS-LES method to simulate the wave in a numerical wave tank. The result shows that the new method is better than the original MPS-LES method.展开更多
In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and di...In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large.展开更多
Most algorithms of the immersed boundary method originated by Peskin are explicit when it comes to the computation of the elastic forces exerted by the immersed boundary to the fluid. A drawback of such an explicit ap...Most algorithms of the immersed boundary method originated by Peskin are explicit when it comes to the computation of the elastic forces exerted by the immersed boundary to the fluid. A drawback of such an explicit approach is a severe restriction on the time step size for maintaining numerical stability. An implicit immersed boundary method in two dimensions using the lattice Boltzmann approach has been proposed. This paper reports an extension of the method to three dimensions and its application to simulation of a massive flexible sheet interacting with an incompressible viscous flow.展开更多
In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta method(SRK). Two ...In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta method(SRK). Two fully implicit schemes are presented and their stability qualities are discussed. And the numerical report illustrates the better numerical behavior.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the National Natural Science Foundation of China (Grant No.50579035)
文摘A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.
基金Fundamental Research Funds for the Central Universities
文摘It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit method.The constant acceleration method's concomitant explicit method was used as an example and is described in detail in this paper.The relationship between the implicit method and explicit method is defined,which provides some guidance about how to create a new explicit method that has high precision and computational efficiency.
基金supported by the National High Technology Research and Development Program of China(863 Program, Grant No.2006AA09A209-5)the National Natural Science Foundation of China (Key Program,Grant No.50736001)the Major Research Project of Ministry of Education of China (Grant No.306005)
文摘Natural gas hydrate, as a potential energy resource, deposits in permafrost and marine sediment with large quantities. The current exploitation methods include depressurization, thermal stimulation, and inhibitor injection. However, many issues have to be resolved before the commercial production. In the present study, a 2-D axisymmetric simulator for gas production from hydrate reservoirs is developed. The simulator includes equations of conductive and convective heat transfer, kinetic of hydrate decomposition, and multiphase flow. These equations are discretized based on the finite difference method and are solved with the fully implicit simultaneous solution method. The process of laboratory-scale hydrate decomposition by depressurization is simulated. For different surrounding temperatures and outlet pressures, time evolutions of gas and water generations during hydrate dissociation are evaluated, and variations of temperature, pressure, and multiphase fluid flow conditions are analyzed. The results suggest that the rate of heat transfer plays an important role in the process. Furthermore, high surrounding temperature and low outlet valve pressure may increase the rate of hydrate dissociation with insignificant impact on final cumulative gas volume.
文摘Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
基金The project supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China （G2000048702, 2003CB716707）the National Science Fund for Distinguished Young Scholars （10025208）+1 种基金 the National Natural Science Foundation of China （Key Program） （10532040） the Research Fund for 0versea Chinese （10228028）.
文摘This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.
基金ONR grant N00014-01-0674.TLi is partially supported by National Science Foundation of China grants 10401004the National Basic Research Program under grant 2005CB321704.
文摘In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale.This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.
文摘This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. A new total pressure equation of viscous incompressible flow is introduced in this paper and the equation is numerically computed by the implicit method. It is shown from the computational results of examples that the implicit method of streamline iteration can speed up the convergence and decrease the computational time.
基金This work was supported by the National Natural Science Foundation of China
文摘This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.
文摘The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.
基金supported by the Key Disciplines of Shanghai Municipality (Operations Research & Cybernetics, No. S30104)the Shanghai Leading Academic Discipline Project (No. J50101)
文摘In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.
文摘In this paper two implicit 2-step hybrid methods are proposed! one has order five, the other six. The stability properties of the methods are analysed. The 5th order method is proved to be A-stable and the 6th order one is not, but still has a relatively large region of absolute stability. The implementation of the 5th order method is also discussed.
文摘In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived.
基金Supported by the national natural science foundation.
文摘In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.
文摘In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.
基金the National Natural Science Foundation of China(Nos.50979059 and 11272213)
文摘Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numerical wave, we combine the MPS method with large eddy simulation(LES) which can simulate the turbulence in the flow. The intense pressure fluctuation is a significant shortcoming in MPS method. So, we improve the original MPS method by using a new pressure Poisson equation to ease the pressure fluctuation. Divergencefree condition representing fluid incompressible is used to calculate pressure smoothly. Then, area-time average technique is used to deal with the calculation. With these improvements, the modified MPS-LES method is applied to the simulation of numerical wave. As a contrast, we also use the original MPS-LES method to simulate the wave in a numerical wave tank. The result shows that the new method is better than the original MPS-LES method.
基金national natural science foundation natural science foundation of Gansu province.
文摘In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large.
基金supported by the US National Science Foundation (DMS-0713718)
文摘Most algorithms of the immersed boundary method originated by Peskin are explicit when it comes to the computation of the elastic forces exerted by the immersed boundary to the fluid. A drawback of such an explicit approach is a severe restriction on the time step size for maintaining numerical stability. An implicit immersed boundary method in two dimensions using the lattice Boltzmann approach has been proposed. This paper reports an extension of the method to three dimensions and its application to simulation of a massive flexible sheet interacting with an incompressible viscous flow.
文摘In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta method(SRK). Two fully implicit schemes are presented and their stability qualities are discussed. And the numerical report illustrates the better numerical behavior.
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.
