Analysis of a Finite Difference Scheme for a Slow, 3-D Permeable Boundary, Navier-Stokes Flow

Navier-Stokes equation. The expression is the nonlinear part of the equation and features in the approximation of the flow’s Reynold’s number (see Remarks 5.2(3), on page 721 of [2]). In other words, we discretize the linearized , non-homogeneous Navier-Stokes problem, representing the 3-D slow flow of a fluid. A typical example of a slow Navier-Stokes fluid flow is ground water through an aquifer. It is to be noted that the condition of non-homogeneity stems from our further application of the Sauer-Maritz boundary permeation model (see Section 2,on page 718 of [2]). This model is also applied in [4], [5] and [6]. The homogeneous version of the problem is discussed by O.A. Ladyzhenskya in [7].The derived scheme will then be tested for convergence and error stability. The theoretic analysis of the problem, as discussed in