Galerkin Method For Miscible Displacement In Porous Media With Edge-bottom Water And Application

In this paper,the reservoir driven by incompressible and miscible two phases in porous media is considered.We focus on the equations coupled by pressure(P)and concentration(C):(?)We consider the appropriate Robin boundary and initial conditions,and do the semi discrete scheme analysis and convergence analysis of pressure and concentration respectively.The Robin boundary and initial condition in the above problems are not closed boundary.Compared with the actual application,the water outside the reservoir area flows through the boundary,which has certain reference significance for the actual application of the reservoir.In this paper,based on the above coupled equations,using the third boundary condition,the Galerkin finite element scheme and its convergence analysis are given.The first chapter mainly introduces the research background,research review and research significance of this paper,focusing on the mathematical model format of the research problem.In the second chapter,Galerkin finite element method and preparatory knowledge are described,and the preliminary error estimates are made.In the third chapter,the pressure equation and concentration equation are analyzed by semi-discrete scheme and convergence respectively,and the error order is obtained.The fourth chapter introduces the model and algorithm of the actual numerical simulation,and carries on the experimental calculation example.The fifth chapter summarizes the content of this paper and prospects the results.