A fully conservative block‐centered finite difference method for Darcy–Forchheimer incompressible miscible displacement problem. Issue 1 (13th June 2019)

• Record Type: Journal Article
• Authors: Li, Xiaoli; Rui, Hongxing
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 1(2020)
• Page Start: 66
• Page End: 85
• Publication Date: 2019-06-13
• Subjects: block‐centered finite difference -- Darcy–Forchheimer incompressible miscible displacement -- full mass conservation -- non‐uniform grids -- numerical experiments; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22400
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: In this paper, a block‐centered finite difference method is derived for the Darcy–Forchheimer incompressible miscible displacement problem in porous media by introducing an auxiliary flux variable to guarantee full mass conservation. Error estimates for the pressure, velocity, concentration, and auxiliary flux in different discrete norms are established rigorously and carefully on nonuniform grids. Finally, some numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis.