Multi-component flow in porous media involves localized phenomena that could be due to several features, such as concentration fronts, wells or geometry of the media. Our approach to treating the localized phenomena is to use high-resolution discretization methods in combination with adaptive mesh refinement (AMR). The purpose of AMR is to concentrate the computational work near the regions of interest in the flow. When properly designed, AMR can significantly reduce the computational effort required to obtain a desired level of accuracy in the simulation. Necessarily, AMR requires appropriate techniques for communication between length scales in a hierarchy. The selection of appropriate scaling rules as well as computationally efficient data structures is essential to the success of the overall method. However, the emphasis here is on the development of e.cient techniques for solving linear systems that arise in the numerical discretization of an elliptic equation for the incompressible pressure field. In this paper, the combined AMR technique has been applied to a two-component single-phase model for miscible flooding. Numerical results are discussed in one-dimensional and two-dimensional. © 2002 Elsevier Science Ltd. All rights reserved.