A Type Of Domain Decomposition Methods For Oil-Water Two Phases Miscible Displacement

The transport processes of fluids in porous medium arise in many different fields, including petroleum reservoir, the exploration and production of oil and gas fields, the contaminants in groundwater, seawater intrusion, and so on. In this dissertation, an efficient and accurate numerical approximate scheme is considered for oil-water two phases incompressible/compressible miscible displacement. This scheme is constructed by two methods. Standard mixed finite clement is used for the pressure equation. A parallel non-overlapping domain decomposition procedure combined with the characteristic method is presented for the concentration equation. By analysis, optimal order error estimates in L2-norm are derived for this scheme.The concentration equation of oil-water two phases incompressible or com-pressible miscible displacement is described as a convection-diffusion equation. It is effective to approximate the solutions of the convection-diffusion equation by using the method of characteristics. Combined with this method, a par-allel procedure is presented, which uses implicit Galerkin method in the sub-domains and simple explicit flux calculation on the inter-domain boundaries by integral mean method to predict the inner-boundary conditions. Thus, the parallelism can be achieved.Chapter1introduces the integral mean non-overlapping DDM combined with the characteristic method for oil-water two phases incompressible miscible displacement. In this chapter, a numerical approximate scheme is considered for in-compressible miscible displacement. According to the above methods, we use the integral mean non-overlapping DDM with the characteristic method for the concentration equation and standard mixed finite element method for the pressure equation. Optimal order error estimates in L2-norm are derived for this scheme.This chapter is divided into four sections. Section I introduces the back-grounds of the integral mean non-overlapping DDM. In Sections Ⅱ and Ⅲ. we introduce the mathematical model of the incompressible miscible displace-ment and build its parallel scheme. In Section IV, we analyze the optimal error estimates in L2norm for the scheme.Chapter2introduces the integral mean non-overlapping DDM combined with the characteristic method for compressible miscible displacement.In this chapter, we use the similar parallel Galcrkin domain decomposi-tion procedure as that of Chapter1for the model of compressible miscible displacement. We build the parallel scheme and also give the optimal order error estimates in L2-norm for this problem.This chapter is divided into three sections. Section I introduces the math-ematical model. In Sections11, we build the parallel scheme for compressible miscible displacement with characteristic method briefly. In Section III, we analyze the optimal order error estimates in L2-norm for the scheme.Chapter3introduces a generalized method and a numerical experiment.This chapter builds another generalized scheme of the parallel method-the extrapolation-integral mean non-overlapping DDM combined with the charac-teristic method. We use this method to solve the concentration equations in above two models. Then a numerical experiment for a convection-diffusion problem is given to illustrate the efficiency of our method.This chapter is divided into two sections. Section I builds the numerical schemes for the models of incompressible/compressible miscible displacement, respectively. Section II gives a numerical experiment, whose results show the valid of the integral mean non-overlapping DDM combined with the charac- toristic method for convection-diffusion equation.