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.
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
