Numerical analysis of finite element methods for miscible displacements in porous media

✍ Scribed by Sandra M. C. Malta; Abimael F. D. Loula

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 570 KB
• Volume: 14
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199807)14:4<519::aid-num5>3.0.co;2-n

✦ Synopsis

Finite element methods are used to solve a coupled system of nonlinear partial differential equations, which models incompressible miscible displacement in porous media. Through a backward finite difference discretization in time, we define a sequentially implicit time-stepping algorithm that uncouples the system at each time-step. The Galerkin method is employed to approximate the pressure, and accurate velocity approximations are calculated via a post-processing technique involving the conservation of mass and Darcy's law. A stabilized finite element (SUPG) method is applied to the convection-diffusion equation delivering stable and accurate solutions. Error estimates with quasi-optimal rates of convergence are derived under suitable regularity hypotheses. Numerical results are presented confirming the predicted rates of convergence for the post-processing technique and illustrating the performance of the proposed methodology when applied to miscible displacements with adverse mobility ratios.