<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the...<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>展开更多
In this paper, a second-order implicit-explicit upwind algorithmhas been developed for three-dimensional Parabolized Navier-Stokes(PNS) equations.The agreement between the results of the new upwind algorithm and those...In this paper, a second-order implicit-explicit upwind algorithmhas been developed for three-dimensional Parabolized Navier-Stokes(PNS) equations.The agreement between the results of the new upwind algorithm and those of the im-plicit upwind algorithm and its ability in marching a long distance along the stream-wise direction have been shown for the supersonic viscous flow past a sphere-conebody. The CPU time is greatly reduced.展开更多
For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation r...For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decompo-sition of high order difference operators and prior estimates are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution.展开更多
WT5,5”BX] A new class of numerical schemes is proposed to solve convection diffusion equations by combining the upwind technique and the method of operator splitting. For every time step, the multi dimensional approx...WT5,5”BX] A new class of numerical schemes is proposed to solve convection diffusion equations by combining the upwind technique and the method of operator splitting. For every time step, the multi dimensional approximation is performed in several independent directions alternatively, while the upwind technique is applied to treat the convection term in every individual direction. This scheme possesses maximum principle. Stability and convergence are analysed by energy method.[WT5,5”HZ]展开更多
This paper shows the usefulness of the exponential upwinding technique in convection diffusion computations. In particular, it is demonstrated that, even when convection is dominant, if exponential upwinding is employ...This paper shows the usefulness of the exponential upwinding technique in convection diffusion computations. In particular, it is demonstrated that, even when convection is dominant, if exponential upwinding is employed in conjunction with either the Jacobi or the Gauss-Seidel iteration process, one can obtain computed solutions that are accurate and free of unphysical展开更多
In this paper, a stochastic finite-volume solver based on polynomial chaos expansion is developed. The upwind scheme is used to avoid the numerical instabilities. The Burgers’ equation subjected to deterministic boun...In this paper, a stochastic finite-volume solver based on polynomial chaos expansion is developed. The upwind scheme is used to avoid the numerical instabilities. The Burgers’ equation subjected to deterministic boundary conditions and random viscosity is solved. The solution uncertainty is quantified for different values of viscosity. Monte-Carlo simulations are used to validate and compare the developed solver. The mean, standard deviation and the probability distribution function (p.d.f) of the stochastic Burgers’ solution is quantified and the effect of some parameters is investigated. The large sparse linear system resulting from the stochastic solver is solved in parallel to enhance the performance. Also, Monte-Carlo simulations are done in parallel and the execution times are compared in both cases.展开更多
Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-var...Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-variable cell population balance models (PBMs) offer the most general way to describe the complicated phenomena associated with cell growth, substrate consumption and product formation. For that reason, solving and understanding of such models are essential to predict and control cell growth in the processes of biotechnological interest. Such models typically consist of a partial integro-differential equation for describing cell growth and an ordinary integro-differential equation for representing substrate consumption. However, the involved mathematical complexities make their numerical solutions challenging for the given numerical scheme. In this article, the central upwind scheme is applied to solve the single-variate and bivariate cell population balance models considering equal and unequal partitioning of cellular materials. The validity of the developed algorithms is verified through several case studies. It was found that the suggested scheme is more reliable and effective.展开更多
We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the fini...We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the finite difference upwind scheme,the first-order line integral is used as its update rule.With sufficient accuracy,the new simplified method can greatly speed up the computational time.Once the quasi-potential has been computed,the minimum action path(MAP)can also be obtained.Since the MAP is of concern in most stochastic situations,the effectiveness of this new method is checked by analyzing the accuracy of the MAP.Two cases of isotropic diffusion and anisotropic diffusion are considered.It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time.Meanwhile anisotropy will affect the accuracy of the computed MAP.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
Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations ...Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, two kinds of finite difference fractional steps pro- cedures are put forward. Optimal order estimates in norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.展开更多
The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differenti...The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.展开更多
In this paper, we discuss the uniform convergence of the simple upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh for solving a singularly perturbed Robin boundary value problem, and investigate the m...In this paper, we discuss the uniform convergence of the simple upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh for solving a singularly perturbed Robin boundary value problem, and investigate the midpoint upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh to achieve better uniform convergence. The elaborate ε-uniform pointwise estimates are proved by using the comparison principle and barrier functions. The numerical experiments support the theoretical results for the schemes on the meshes.展开更多
The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase...The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.展开更多
In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial deriv...In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.展开更多
Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value condition...Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.展开更多
The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here ...The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method.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 effciency 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
The research of the miscible oil and water displacement problem with mov- ing boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational ev...The research of the miscible oil and water displacement problem with mov- ing boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oilgas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the two-dimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal order l2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.展开更多
文摘<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>
基金The project supported by the National Natural Science Foundation of China
文摘In this paper, a second-order implicit-explicit upwind algorithmhas been developed for three-dimensional Parabolized Navier-Stokes(PNS) equations.The agreement between the results of the new upwind algorithm and those of the im-plicit upwind algorithm and its ability in marching a long distance along the stream-wise direction have been shown for the supersonic viscous flow past a sphere-conebody. The CPU time is greatly reduced.
基金the Major State Basic Research Program of China(19990328)NNSF of China(19871051,19972039) the Doctorate Foundation of the State Education Commission
文摘For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decompo-sition of high order difference operators and prior estimates are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution.
文摘WT5,5”BX] A new class of numerical schemes is proposed to solve convection diffusion equations by combining the upwind technique and the method of operator splitting. For every time step, the multi dimensional approximation is performed in several independent directions alternatively, while the upwind technique is applied to treat the convection term in every individual direction. This scheme possesses maximum principle. Stability and convergence are analysed by energy method.[WT5,5”HZ]
文摘This paper shows the usefulness of the exponential upwinding technique in convection diffusion computations. In particular, it is demonstrated that, even when convection is dominant, if exponential upwinding is employed in conjunction with either the Jacobi or the Gauss-Seidel iteration process, one can obtain computed solutions that are accurate and free of unphysical
文摘In this paper, a stochastic finite-volume solver based on polynomial chaos expansion is developed. The upwind scheme is used to avoid the numerical instabilities. The Burgers’ equation subjected to deterministic boundary conditions and random viscosity is solved. The solution uncertainty is quantified for different values of viscosity. Monte-Carlo simulations are used to validate and compare the developed solver. The mean, standard deviation and the probability distribution function (p.d.f) of the stochastic Burgers’ solution is quantified and the effect of some parameters is investigated. The large sparse linear system resulting from the stochastic solver is solved in parallel to enhance the performance. Also, Monte-Carlo simulations are done in parallel and the execution times are compared in both cases.
文摘Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-variable cell population balance models (PBMs) offer the most general way to describe the complicated phenomena associated with cell growth, substrate consumption and product formation. For that reason, solving and understanding of such models are essential to predict and control cell growth in the processes of biotechnological interest. Such models typically consist of a partial integro-differential equation for describing cell growth and an ordinary integro-differential equation for representing substrate consumption. However, the involved mathematical complexities make their numerical solutions challenging for the given numerical scheme. In this article, the central upwind scheme is applied to solve the single-variate and bivariate cell population balance models considering equal and unequal partitioning of cellular materials. The validity of the developed algorithms is verified through several case studies. It was found that the suggested scheme is more reliable and effective.
基金the National Natural Science Foundation of China(Grant Nos.11772149 and 12172167)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(Grant No.MCMS-I19G01).
文摘We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the finite difference upwind scheme,the first-order line integral is used as its update rule.With sufficient accuracy,the new simplified method can greatly speed up the computational time.Once the quasi-potential has been computed,the minimum action path(MAP)can also be obtained.Since the MAP is of concern in most stochastic situations,the effectiveness of this new method is checked by analyzing the accuracy of the MAP.Two cases of isotropic diffusion and anisotropic diffusion are considered.It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time.Meanwhile anisotropy will affect the accuracy of the computed MAP.
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.
文摘Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, two kinds of finite difference fractional steps pro- cedures are put forward. Optimal order estimates in norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.
基金supported the Natural Science Foundation of Shandong Province(ZR2016AM08)Natural Science Foundation of Hunan Province(2018JJ2028)National Natural Science Foundation of China(11871312).
文摘The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.
文摘In this paper, we discuss the uniform convergence of the simple upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh for solving a singularly perturbed Robin boundary value problem, and investigate the midpoint upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh to achieve better uniform convergence. The elaborate ε-uniform pointwise estimates are proved by using the comparison principle and barrier functions. The numerical experiments support the theoretical results for the schemes on the meshes.
文摘The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.
文摘In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.
基金supported by National Natural Science Foundation of China(11101244,11271231)National Tackling Key Problems Program(20050200069)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.
文摘The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method.
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 effciency 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.
基金supported by the Major State Basic Research Development Program of China(No.G19990328)the National Key Technologies R&D Program of China (No.20050200069)+1 种基金the National Natural Science Foundation of China (Nos.10771124 and 10372052)the Ph. D. Pro-grams Foundation of Ministry of Education of China (No.20030422047)
文摘The research of the miscible oil and water displacement problem with mov- ing boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oilgas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the two-dimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal order l2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.
