A chebyshev spectral framework for solving coupled flow–diffusion equations with nonlinear transport effects
Ghuson S. Abed1
Department of Media Technology and Communication Engineering,College of Engineering, University of Information Technology and Communications (UOITC), Baghdad,Iraq1
Corresponding Author : Ghuson S. Abed
Received : 05-February-2026; Revised : 24-August-2026; Accepted : 26-August-2026
Abstract
The process of nonlinear flow–diffusion appears in many physical systems and mathematical models, where gradient-driven diffusion alone is inadequate for describing transport processes because of flow-induced nonlinear effects. To address this issue, a framework based on the Chebyshev spectral method is developed. In the proposed framework, a spatial discretization is performed using Chebyshev polynomials and the spectral–Galerkin formulation. Also, a semi-implicit time-integration approach is utilized to transform the governing partial differential equation (PDE) into a solvable algebraic system. The results show improved spectral accuracy, exponential convergence, and a significant reduction in numerical diffusion when compared with traditional finite-difference schemes, along with stable steady-state performance over varying flow strengths. These results indicate that the proposed model is an efficient, robust, and flexible scheme for solving nonlinear flow–diffusion equations, with broad applicability across mathematical and physical problems, and the proposed scheme can be extended to more complex multidimensional problems.
Keywords
Nonlinear flow–diffusion equations, Chebyshev spectral method, Spectral–Galerkin method, Semi-implicit time integration, Spectral convergence, Numerical diffusion.
Cite this article
Abed GS. A chebyshev spectral framework for solving coupled flow–diffusion equations with nonlinear transport effects. International Journal of Advanced Technology and Engineering Exploration. 2026;13(141):349-364. DOI : 10.19101/IJATEE.2026.131340105
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