Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are t...Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.展开更多
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
A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced (chemical) oil production in porous media....A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced (chemical) oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results ate quite interesting and satisfactory.展开更多
The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and ex...The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.展开更多
From such actual conditions as the effects of characteristics of miltilayer petroleum geology and permeation fluid mechanics, a new numerical model is put forward and coupling splitting-up implicit interactive scheme ...From such actual conditions as the effects of characteristics of miltilayer petroleum geology and permeation fluid mechanics, a new numerical model is put forward and coupling splitting-up implicit interactive scheme is formed. For the actual situation of Dongying hollow (four-layer) and Tanhai region (three-layer) of Shengli Petroleum Field, the numerical simulation test results and the actual conditions are coincident.展开更多
This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type (φ(x′(t)))′+q(t)f(t,x(t),x′(t))=0,t∈(0,1),subject to the following boundary condit...This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type (φ(x′(t)))′+q(t)f(t,x(t),x′(t))=0,t∈(0,1),subject to the following boundary condition:a1φ(x(0))-a2φ(x'(0))=0,a3φ(x(1))+a4φ(x'(1))=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.展开更多
Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploi...Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.The upwind finite difference 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 change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.展开更多
Numerical simulation of careful parallel arithmetic of oil resources migration-accumulation of Tanhai Region ( three-layer) was done. Careful parallel operator splitting-up implicit iterative scheme, parallel arithmet...Numerical simulation of careful parallel arithmetic of oil resources migration-accumulation of Tanhai Region ( three-layer) was done. Careful parallel operator splitting-up implicit iterative scheme, parallel arithmetic program, parallel arithmetic information and alternating-direction mesh subdivision were put forward. Parallel arithmetic and analysis of different CPU combinations were done. This numerical simulation test and the actual conditions are basically coincident. The convergence estimation of the model problem has successfully solved the difficult problem in the fields of permeation fluid mechanics, computational mathematics and petroleum geology.展开更多
A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced (chemical) oil production with capillary force in the porou...A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced (chemical) oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.展开更多
A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium w...A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.展开更多
The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The p...The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.展开更多
In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equatio...In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.展开更多
We propose a modified upwind finite difference fractional step scheme for the computational fluid mechanics simulations of a three-dimensional photoelectric semiconductor detector. We obtain the optimal l^2-norm error...We propose a modified upwind finite difference fractional step scheme for the computational fluid mechanics simulations of a three-dimensional photoelectric semiconductor detector. We obtain the optimal l^2-norm error estimates by using the techniques including the calculus of variations, the energy methods, the induction hypothesis, and a priori estimates. The proposed scheme is successfully applied to the simulation of the photoelectric semiconductor detectors.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
From such actual conditions as the effects of fluid mechanics in porous media and three-dimensional geology characteristics, the mathematical model and a kind of modified method of second order splitting-up implicit i...From such actual conditions as the effects of fluid mechanics in porous media and three-dimensional geology characteristics, the mathematical model and a kind of modified method of second order splitting-up implicit iterative scheme were put forward. For the actual problem of Dongying hollow (single layer) and Huimin hollow (multilayer) of Shengli Petroleum Oil Field, this numerical simulation test and the actual conditions are basically coincident, thus the well-known problem has been solved.展开更多
For the system of multilayer dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus ...For the system of multilayer dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and 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.展开更多
The convolution model of reflected wave used in exploration physics has no serious physical concept and mathematical proof.Wave phenomena should be characterized by instantaneous spectrum in physics and a complex func...The convolution model of reflected wave used in exploration physics has no serious physical concept and mathematical proof.Wave phenomena should be characterized by instantaneous spectrum in physics and a complex function of three real variables(time.Place frequency)in mathematics.Reflection coefficient is also a complex function of place and frequency.Several new formulas instead of convolution model are given.Based on wavelet transform and a method of“3 basis colors”,new color sectional image is obtained from practical data.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
Applications, theoretical analysis and numerical methods are introduced for the simulation of mechanical models and principles of the porous flow in high temperature, high salt, complicated geology and large-scale res...Applications, theoretical analysis and numerical methods are introduced for the simulation of mechanical models and principles of the porous flow in high temperature, high salt, complicated geology and large-scale reservoirs in this paper. Considering petroleum geology, geochemistry, computational permeation fluid mechanics and computer technology, we state the models of permeation fluid mechanics and put forward a sequence of implicit upwind difference iteration schemes based on refined fractional steps of the upstream, which can compute the pressures, the saturation and the concentrations of different chemistry components. A type of software applicable in major industries has been completed and carried out in numerical analysis and simulations of oil extraction in Shengli Oil-field, which brings huge economic benefits and social benefits. This software gives many characters: spatial steps are taken as ten meters, the number of nodes is up to hundreds of thousands and simulation time period can be tens of years and the high-order accuracy can be promised in numerical data. Precise analysis is present for simplified models of this type and that provides a tool to solve the international famous problem.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
基金This work is supported by the Major State Basic Research Program of China (19990328), the National Tackling Key Problem Program, the National Science Foundation of China (10271066 and 0372052), and the Doctorate Foundation of the Ministry of Education of China (20030422047).
文摘Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.
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.
基金supported by the Major State Basic Research Development Program of China(G19990328)National Tackling Key Program(2011ZX05011-004+6 种基金2011ZX0505220050200069)National Natural Science Foundation of China(11101244112712311077112410372052)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced (chemical) oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results ate quite interesting and satisfactory.
基金the Major State Basic Research Program of China(No.G19990328)the National Tackling Key Problem Program(No.20050200069)+1 种基金the National Natural Science Foundation of China(Nos.10771124,10372052)the Ph.D.Programs Foundation of Ministry of Education of China(No.20030422047)
文摘The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l~2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.
文摘From such actual conditions as the effects of characteristics of miltilayer petroleum geology and permeation fluid mechanics, a new numerical model is put forward and coupling splitting-up implicit interactive scheme is formed. For the actual situation of Dongying hollow (four-layer) and Tanhai region (three-layer) of Shengli Petroleum Field, the numerical simulation test results and the actual conditions are coincident.
基金Supported by the NNSF of China(10371006) Tianyuan Youth Grant of China(10626033).
文摘This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type (φ(x′(t)))′+q(t)f(t,x(t),x′(t))=0,t∈(0,1),subject to the following boundary condition:a1φ(x(0))-a2φ(x'(0))=0,a3φ(x(1))+a4φ(x'(1))=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.
基金supported by the Major State BasicResearch Program of China(19990328)the National Tackling Key Problem Programs(20050200069)+4 种基金the National Natural Science Foundation of China(1077112410372052)the Doctorate Foundation of the Ministryof Education of China(20030422047)Shandong Provance Natural Science Foundation(2R2009AQ12)the Independent Innovation Foundation of Shandong University(2010TS031)
文摘Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.The upwind finite difference 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 change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.
基金Project supported by the National Natural Science Foundation of China (Nos. 10372052 and 10271066)the Major State Basic Research Program of China (No. 1999032803)the Special Fund of PhD Program of Education Ministry of China (No. 20030422047)
文摘Numerical simulation of careful parallel arithmetic of oil resources migration-accumulation of Tanhai Region ( three-layer) was done. Careful parallel operator splitting-up implicit iterative scheme, parallel arithmetic program, parallel arithmetic information and alternating-direction mesh subdivision were put forward. Parallel arithmetic and analysis of different CPU combinations were done. This numerical simulation test and the actual conditions are basically coincident. The convergence estimation of the model problem has successfully solved the difficult problem in the fields of permeation fluid mechanics, computational mathematics and petroleum geology.
基金Project supported by the Major State Basic Research Development Program of China(No.G19990328)the National Natural Science Foundation of China(Nos.10771124,10372052,and 11101244)+2 种基金the National Tackling Key Problems Program of China(Nos.2011ZX05011-004,2011ZX05052,and 2005020069)the Doctorate Foundation of the Ministry of Education of China(No.20030422047)the Natural Science Foundation of Shandong Province of China(No.ZR2011AM015)
文摘A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced (chemical) oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.
基金Project supported by the Major State Basic Research Program of China (No. 19990328)the National Tackling Key Problems Program (No. 20050200069)+4 种基金the National Natural Science Foundation of China (Nos. 10771124, 10372052, 11101244, and 11271231)the Doctorate Foundation of the Ministry of Education of China (No. 20030422047)the Shandong Province Natural Science Foundation (No. ZR2009AQ012)the Independent Innovation Foundation of Shandong University(No. 2010TS031)the Scientific Research Award Fund for Excellent Middle-Aged and Young Scientists of Shandong Province (No. BS2009NJ003)
文摘A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.
基金Supported by the National Natural Science Foundation of China(11101124 and 11271231)Natural Science Foundation of Shandong Province(ZR2016AM08)National Tackling Key Problems Program(2011ZX05052,2011ZX05011-004)
文摘The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.
基金This research was supported by the National Natural Science Foundation of China
文摘In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.
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. Programs Foundation of Ministry of Eduction of China (No. 20030422647)
文摘We propose a modified upwind finite difference fractional step scheme for the computational fluid mechanics simulations of a three-dimensional photoelectric semiconductor detector. We obtain the optimal l^2-norm error estimates by using the techniques including the calculus of variations, the energy methods, the induction hypothesis, and a priori estimates. The proposed scheme is successfully applied to the simulation of the photoelectric semiconductor detectors.
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.
文摘From such actual conditions as the effects of fluid mechanics in porous media and three-dimensional geology characteristics, the mathematical model and a kind of modified method of second order splitting-up implicit iterative scheme were put forward. For the actual problem of Dongying hollow (single layer) and Huimin hollow (multilayer) of Shengli Petroleum Oil Field, this numerical simulation test and the actual conditions are basically coincident, thus the well-known problem has been solved.
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 system of multilayer dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and 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.
基金Supported by the National Natural Sciense Foundation of China under Grant No.69575010.
文摘The convolution model of reflected wave used in exploration physics has no serious physical concept and mathematical proof.Wave phenomena should be characterized by instantaneous spectrum in physics and a complex function of three real variables(time.Place frequency)in mathematics.Reflection coefficient is also a complex function of place and frequency.Several new formulas instead of convolution model are given.Based on wavelet transform and a method of“3 basis colors”,new color sectional image is obtained from practical data.
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Applications, theoretical analysis and numerical methods are introduced for the simulation of mechanical models and principles of the porous flow in high temperature, high salt, complicated geology and large-scale reservoirs in this paper. Considering petroleum geology, geochemistry, computational permeation fluid mechanics and computer technology, we state the models of permeation fluid mechanics and put forward a sequence of implicit upwind difference iteration schemes based on refined fractional steps of the upstream, which can compute the pressures, the saturation and the concentrations of different chemistry components. A type of software applicable in major industries has been completed and carried out in numerical analysis and simulations of oil extraction in Shengli Oil-field, which brings huge economic benefits and social benefits. This software gives many characters: spatial steps are taken as ten meters, the number of nodes is up to hundreds of thousands and simulation time period can be tens of years and the high-order accuracy can be promised in numerical data. Precise analysis is present for simplified models of this type and that provides a tool to solve the international famous problem.
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.