Block-centered finite difference methods for general Darcy-Forchheimer problems

Block-centered finite difference methods are constructed to solve the general Darcy-Forchheimer problems with Neumann boundary conditions, in which the velocity and pressure can be approximated simultaneously. We demonstrate that with sufficiently smooth analytical solution, the errors for both pressure and velocity in discrete L2-norms are second-order accurate on a nonuniform rectangular grid. Numerical experiments carried out using the scheme show the consistency of the convergence rates of our method with the theoretical analysis.