A block‐centered finite difference method for Darcy–Forchheimer model with variable Forchheimer number

A block‐centered finite difference scheme is introduced to solve the nonlinear Darcy–Forchheimer equation with variable Forchheimer number, in which the velocity and pressure can be approximated simultaneously. For variable Forchheimer number the second‐order error estimates for both pressure and velocity are established on nonuniform rectangular grid. An iteration process is given to solve the nonlinear system. Numerical experiments using the scheme show the consistency of the convergence rates of the presented methods with the theoretical analysis. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1603–1622, 2015