AN ITERATIVE PERTURBATION METHOD FOR THE PRESSURE EQUATION IN THE SIMULATION OF MISCIBLE DISPLACEMENT IN POROUS-MEDIA

The miscible displacement problem in porous media is modeled by a nonl inear coupled system of two partial differential equations: the pressu re-velocity equation and the concentration equation. An iterative pert urbation procedure is proposed and analyzed for the pressure-velocity equation, which is capable of producing as accurate a velocity approxi mation as the mixed finite element method, and which requires the solu tion of symmetric positive definite linear systems. Only the velocity variable is involved in the linear systems, and the pressure variable is obtained by substitution. Trivially applying perturbation methods c an only give an error O(epsilon), while our iterative scheme can impro ve the error to O(epsilon(m)) at the mth iteration level, where epsilo n is a small positive number. Thus the convergence rate of our iterati ve procedure is O(epsilon), and consequently a small number of iterati ons is required. Theoretical convergence analysis and numerical experi ments are presented to show the efficiency and accuracy of our method.