For compressible two-phase displacement problem,the modified upwind finite difference fractionalsteps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplicationof difference operators,decomposition of high order difference operators,the theory of prior estimates and tech-niques are used.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.Thismethod has already been applied to the numerical simulation of seawater intrusion and migration-accumulationof oil resources.
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.
For the three-dimensional nonlinear two-phase displacement problem, the modified upwind finite difference fractional steps schenles were put forward. Some techniques, such as calculus of variations, induction hypothesis, decomposition of high order difference operators, the theory of prior estimates and techniques were used. Optimal order estimates were derived for the error in the approximation solution. These methods have been successfully used to predict the consequences of seawater intrusion and protection projects.
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.
Yirang YUANAijie CHENGDanping YANGChangfeng LIYunxin LIU
Numerical simulation of oil migration and accumulation is to describe the history of oil migration and accumulation in basin evolution. It is of great value in evaluation of oil resources and determination of the location and amount of oil deposits. Based on such actual conditions as the effects of fluid mechanics in porous media and 3-dimensional geology characteristics,a kind of modified method of second order upwind finite difference fractional steps implicit interactive scheme was put forward. As for the actual problem of Dongying hollow,Huimin hollow,Tanhai region and Yangxin hollow in Shengli Petroleum Oil Field,a numerical simulation test was carried out,and the result is basically coincident with the actual conditions. For the model problem,optimal order estimates were derived. Thus the well-known problem on oil resources was solved.
YUAN YiRang1 & HAN YuJi2 1 Institute of Mathematics,Shandong University,Ji’nan 250100,China
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.
