Archives of Current Research International

The transport of carbon dioxide (CO₂) through reactive porous media involves the simultaneous interplay of molecular diffusion, bulk advection, and concentration-dependent chemical reactions. Accurate modelling of this system requires numerical schemes that are computationally efficient and rigorously verified for stability and consistency. This paper analyses the numerical properties of an explicit finite difference scheme applied to a dimensionless reaction–diffusion–advection (RDA) equation that incorporates both a linear reactive source term and a linear sink term. Starting from the standard three-point central-difference stencil in space and a symmetric Du Fort–Frankel leap-frog update in time, the complete matrix representation of the discrete system is derived. Stability is then examined using the matrix eigenvalue method: the amplification matrix G = A⁻¹B is constructed, and its eigenvalues are computed numerically in MATLAB for a physically representative set of parameters. All eight eigenvalues obtained lie strictly inside the unit circle, indicating that the scheme is numerically stable and that perturbations do not grow in time for the tested configuration. Consistency is verified through a formal Taylor series expansion of the discrete stencil about the exact solution, from which the local truncation error (LTE) is derived and shown to be O(h², k²), indicating second-order accuracy in both space and time. By invoking the Lax Equivalence Theorem, the scheme is interpreted as convergent to the exact solution of the governing PDE as the grid is refined. These findings support the use of the proposed discretisation for simulating CO₂ transport dynamics within the assumptions of the model.