Splitting methods for the numerical solution of multi-component mass transfer problems

• Published in: Mathematics and computers in simulation Vol. 152; pp. 1 - 14
• Main Authors: Juncu, Gheorghe, Nicola, Aurelian, Popa, Constantin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2018
• Subjects: Convection–diffusion equation; Finite differences; Multi-component diffusion; Splitting method; Ternary system; Convection–diffusion equation; Ternary system; Splitting method; Multi-component diffusion; Finite differences
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2018.05.001

In a multi-component system the diffusion of a certain species is dictated not only by its own concentration gradient but also by the concentration gradient of the other species. In this case, the mathematical model is a system of strongly coupled second order elliptic/parabolic partial differential equations. In this paper, we adapt the splitting method for numerical solution of multi-component mass transfer equations, with emphasis on the linear ternary systems. We prove the positive definiteness assumptions for the discrete problem matrices which ensure the stability of the method. The numerical experiments performed confirmed the theoretical results, and the results obtained show good numerical performances. •Splitting method for multi-component diffusion problems.•Linear ternary systems.•Extension to multi-component systems.•Numerical experiments.