Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditi...Transient behavior of three-dimensional semiconductor device with heat conduc- tion 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 ellip- tic 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 con- centrations 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 L2 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
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
A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive...A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive equation. The generalized upwind scheme is used to solve the convection equation and the finite element method is used to compute the dispersive equation.These procedures which not only overcome the phenomenon of the negative concentration and numerical dispersion appear frequently with normal FEM or FDM to solve models of convection dominating groundwater transport but also avoid the step for computing each node velocity give a more suitable method to calculate the concentrations of the well points.展开更多
The research of the miscible oil and water displacement problem with moving 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 eval...The research of the miscible oil and water displacement problem with moving 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 oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the twodimensional 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 orderl2-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
For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-d...For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L 2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy sources.展开更多
In this paper the authors discuss the numerical simulation problem of threedimensional compressible contamination treatment from nuclear waste.The mathematical model is defined by an initial-boundary nonlinear convect...In this paper the authors discuss the numerical simulation problem of threedimensional compressible contamination treatment from nuclear waste.The mathematical model is defined by an initial-boundary nonlinear convection-diffusion system of four partial differential equations:a parabolic equation for the pressure,two convection-diffusion equations for the concentrations of brine and radionuclide and a heat conduction equation for the temperature.The pressure appears within the concentration equations and heat conduction equation,and the Darcy velocity controls the concentrations and the temperature.The pressure is solved by the conservative mixed volume element method,and the order of the accuracy is improved by the Darcy velocity.The concentration of brine and temperature are computed by the upwind mixed volume element method on a changing mesh,where the diffusion is discretized by a mixed volume element and the convection is treated by an upwind scheme.The composite method can solve the convection-dominated diffusion problems well because it eliminates numerical dispersion and nonphysical oscillation and has high order computational accuracy.The mixed volume element has the local conservation of mass and energy,and it can obtain the brine and temperature and their adjoint vector functions simultaneously.The conservation nature plays an important role in numerical simulation of underground fluid.The concentrations of radionuclide factors are solved by the method of upwind fractional step difference and the computational work is decreased by decomposing a three-dimensional problem into three successive one-dimensional problems and using the method of speedup.By the theory and technique of a priori estimates of differential equations,we derive an optimal order result in L^(2) norm.Numerical examples are given to show the effectiveness and practicability and the composite method is testified as a powerful tool to solve the well-known actual problem.展开更多
For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fract...For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.展开更多
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 conduc- tion 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 ellip- tic 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 con- centrations 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 L2 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.
文摘A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive equation. The generalized upwind scheme is used to solve the convection equation and the finite element method is used to compute the dispersive equation.These procedures which not only overcome the phenomenon of the negative concentration and numerical dispersion appear frequently with normal FEM or FDM to solve models of convection dominating groundwater transport but also avoid the step for computing each node velocity give a more suitable method to calculate the concentrations of the well points.
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 moving 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 oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the twodimensional 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 orderl2-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.
基金This work was supported by the Major State Basic Research Program of China(Grant No. 1990328) the National Tackling Key Problem Program, the National Natural Science Foundation of China (Grant Nos. 19871051 and 19972039) the Doctorate Foundation
文摘For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L 2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy sources.
基金The authors express their deep appreciation to Prof.J.Douglas Jr,Prof.R.E.Ewing,and Prof.L.S.Jiang for their many helpful suggestions in the series research on numerical simulation of energy sciences.Also,the project is supported by NSAF(Grant No.U1430101)Natural Science Foundation of Shandong Province(Grant No.ZR2016AM08)National Tackling Key Problems Program(Grant Nos.2011ZX05052,2011ZX05011-004,20050200069).
文摘In this paper the authors discuss the numerical simulation problem of threedimensional compressible contamination treatment from nuclear waste.The mathematical model is defined by an initial-boundary nonlinear convection-diffusion system of four partial differential equations:a parabolic equation for the pressure,two convection-diffusion equations for the concentrations of brine and radionuclide and a heat conduction equation for the temperature.The pressure appears within the concentration equations and heat conduction equation,and the Darcy velocity controls the concentrations and the temperature.The pressure is solved by the conservative mixed volume element method,and the order of the accuracy is improved by the Darcy velocity.The concentration of brine and temperature are computed by the upwind mixed volume element method on a changing mesh,where the diffusion is discretized by a mixed volume element and the convection is treated by an upwind scheme.The composite method can solve the convection-dominated diffusion problems well because it eliminates numerical dispersion and nonphysical oscillation and has high order computational accuracy.The mixed volume element has the local conservation of mass and energy,and it can obtain the brine and temperature and their adjoint vector functions simultaneously.The conservation nature plays an important role in numerical simulation of underground fluid.The concentrations of radionuclide factors are solved by the method of upwind fractional step difference and the computational work is decreased by decomposing a three-dimensional problem into three successive one-dimensional problems and using the method of speedup.By the theory and technique of a priori estimates of differential equations,we derive an optimal order result in L^(2) norm.Numerical examples are given to show the effectiveness and practicability and the composite method is testified as a powerful tool to solve the well-known actual problem.
基金Project supported by the Major State Basic Research Program of China (No.G1999032803)the National Tackling Key Problems Program (No.20050200069)the National Natural Science Foundation of China (Nos.10372052, 10271066)the Doctoral Foundation of Ministry of Education of China (No.20030422047).
文摘For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.
