AConservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem  

作　　者：Changfeng Li Yirang Yuan Aijie Cheng Huailing Song 

机构地区：[1]School of Economics,Shandong University,Jinan,Shandong 250100,China [2]Institute of Mathematics,Shandong University,Jinan,Shandong 250100,China [3]College of Mathematics and Econometrics,Hunan University,Changsha,Hunan 410082,China

出　　处：《Advances in Applied Mathematics and Mechanics》2022年第6期1246-1275,共30页应用数学与力学进展（英文）

基　　金：the Natural Science Foundation of Shandong Province(Grant No.ZR2021MA019);Natural Science Foundation of Hunan Province(Grant No.2018JJ2028);National Natural Science Foundation of China(Grant No.11871312).

摘　　要：A kind of conservative upwind method is discussed for chemical oil recovery displacement in porous media.The mathematical model is formulated by a nonlinear convection-diffusion system dependent on the pressure,Darcy velocity,concentration and saturations.The flow equation is solved by a conservative block-centered method,and the pressure and Darcy velocity are obtained at the same time.The concentration and saturations are determined by convection-dominated diffusion equations,so an upwind approximation is adopted to eliminate numerical dispersion and nonphysical oscillation.Block-centered method is conservative locally.An upwind method with block-centered difference is used for computing the concentration.The saturations of different components are solved by the method of upwind fractional step difference,and the computational work is shortened significantly by dividing a three-dimensional problem into three successive one-dimensional problems and using the method of speedup.Using the variation discussion,energy estimates,the method of duality,and the theory of a priori estimates,we complete numerical analysis.Finally,numerical tests are given for showing the computational accuracy,efficiency and practicability of our approach.

关 键 词：Chemical oil recovery upwind block-centered difference fractional step difference elemental conservation convergence analysis. 

分 类 号：O17[理学—数学]