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 nonlinear coupled system of two partial diierential equations: the pressure-velocity equation and the concentration equation. An iterative perturbation procedure is proposed and analyzed for the pressure-velocity equation, which is capable of producing as accurate velocity approximation as the mixed nite element method, and requires the solution of symmetric positive deenite linear systems. Only the velocity variable is involved in the linear systems and the pressure variable is obtained by substitution. The nite element spaces for our velocity and pressure variables need not satisfy the so-called Babuska-Brezzi condition. Trivially applying perturbation methods can only give an error O(), while our iterative scheme can improve the error to O(m) at the m-th iteration level, where is a small positive number. Thus the convergence rate of our iterative procedure is O(), and consequently a small number of iterations are required. Theoretical convergence analysis and numerical experiments are presented to show the eeciency and accuracy of our method.