Von Neumann Stability Analysis of a Finite Difference Scheme for Unsteady Flow in a Fractured Confined Aquifer: Application and Validation

Abstract

Ensuring stability and accuracy is essential in numerical modeling of subsurface flow in fractured and heterogeneous media. This study investigates one-dimensional transient groundwater flow in a finite fractured confined aquifer using a double-porosity continuum approach, for which a finite difference scheme is developed employing the Crank-Nicolson method. The validity of the proposed scheme is assessed through detailed comparisons with an established analytical solution, demonstrating close agreement and confirming the accuracy of the numerical solution. In addition, von Neumann stability analysis is employed within a systematic framework to evaluate the stability of the scheme and to provide insight into its behavior across governing parameters. The stability condition is satisfied. The results show that the analytical and numerical solutions of the finite difference equations for the fractures exhibit the closest agreement for a specific value of α = Δ θ Δ λ 2 for all cases considered, where the amplification factor, G , attains its minimum.