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
This article discusses the enhanced oil recovery numerical simulation of the chemical-flooding (such as surfactallts, alcohol, polymers) composed of three-dimensional multicomponent, multiphase and incompressible mixe...This article discusses the enhanced oil recovery numerical simulation of the chemical-flooding (such as surfactallts, alcohol, polymers) composed of three-dimensional multicomponent, multiphase and incompressible mixed fluids. The mathematical model can be described as a coupled system of nonlinear partial differential equations with initialboundary value problerns. viom the actual conditions such as the effect of cross interference and the three-dimensional charederistic of large-scale science-engineering computation,this article puts forward a kind of characteristic finite element fractional step schemes and obtain the optimal order error estdriates in L2 norm. Thus we have thoroughly solved the well-known theoretical problem proppsed by a famous scientist, R. E. Ewing.展开更多
For the three-dimensional compressible multicomponent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting,cha...For the three-dimensional compressible multicomponent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting,characteristic method,calculus of variations,energy method,negative norm estimate,two kinds of test functions and the theory of prior estimates and techniques.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.These methods have been successfully used in oil-gas resources estimation,enhanced oil recovery simulation and seawater intrusion numerical simulation.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.
文摘This article discusses the enhanced oil recovery numerical simulation of the chemical-flooding (such as surfactallts, alcohol, polymers) composed of three-dimensional multicomponent, multiphase and incompressible mixed fluids. The mathematical model can be described as a coupled system of nonlinear partial differential equations with initialboundary value problerns. viom the actual conditions such as the effect of cross interference and the three-dimensional charederistic of large-scale science-engineering computation,this article puts forward a kind of characteristic finite element fractional step schemes and obtain the optimal order error estdriates in L2 norm. Thus we have thoroughly solved the well-known theoretical problem proppsed by a famous scientist, R. E. Ewing.
基金This research is supported by the Major State Research Program of China(Grant No.19990328),the National Natural Sciences Foundation of China(Grant Nos.19871051 and 19972039),the National Tackling Key Problems Program and the Doctorate Foundation of the S
文摘For the three-dimensional compressible multicomponent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting,characteristic method,calculus of variations,energy method,negative norm estimate,two kinds of test functions and the theory of prior estimates and techniques.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.These methods have been successfully used in oil-gas resources estimation,enhanced oil recovery simulation and seawater intrusion numerical simulation.
