Abstract
Three-component systems of diffusion–reaction equations play a central role in the modelling and simulation of chemical processes in engineering, electro-chemistry, physical chemistry, biology, population dynamics, etc. A major question in the simulation of three-component systems is how to guarantee non-negative species distributions in the model and how to calculate them effectively. Current numerical methods to enforce non-negative species distributions tend to be cost-intensive in terms of computation time and they are not robust for big rate constants of the considered reaction. In this article, a method, as a combination of homotopy methods, modern augmented Lagrangian methods, and adaptive FEMs is outlined to obtain a robust and efficient method to simulate diffusion–reaction models with non-negative concentrations. Although in this paper the convergence analysis is not described rigorously, multiple numerical examples as well as an application to elctro-deposition from an aqueous Cu2+-(β-alanine) electrolyte are presented.
Highlights
Diffusion-reaction equations play a central role in the modelling and simulation of chemical processes, as the corresponding system describes the transport of multiple species w.r.t. diffusion and a single reaction
The resulting minimization problem can be treated with many methods such as quasi-Newton methods, cf. [17], SQP methods, cf. [18], penalty methods, cf. [19], augmented Lagrangian methods cf. [20,21,22], or PrimalDual Active-Set Strategies, cf. [23]
This section is devoted to the comparison of the augmented Lagrangian method, as described in this paper, with the classical augmented Lagrangian regime as described in [20,22] and the Primal-Dual Active-Set Strategy, as described in [23]
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The resulting minimization problem can be treated with many methods such as quasi-Newton methods, cf [17], SQP methods, cf [18], penalty methods, cf [19], augmented Lagrangian methods cf [20,21,22], or PrimalDual Active-Set Strategies, cf [23] This type of strategy (first discretization, solution) has the advantage to be, in comparison, easy, but have some problems in terms of efficiency, since those methods are iterative methods, due to a fixed triangulation T. As additional part of this article, a model for the static metal-deposition basing the complexation in a laminar boundary layer will be discussed, see Section 5.1, and numerically evaluated via the simulation methodology that is described in this article
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
