On Local and Global Species Conservation Errors for Nonlinear Ecological Models and Chemical Reacting Flows

Advection-controlled and diffusion-controlled oscillatory chemical reactions appear in various areas of life sciences, hydrogeological systems, and contaminant transport. In this conference paper, we analyze whether the existing numerical formulations and commercial packages provide physically meaningful values for concentration of the chemical species for two popular oscillatory chemical kinetic schemes. The first one corresponds to the chlorine dioxide-iodine-malonic acid reaction while the second one is a simplified version of Belousov-Zhabotinsky reaction of a non-linear chemical oscillator. The governing equations for species balance are presented based on the theory of interacting continua. This results in a set of coupled non-linear partial differential equations. Obtaining analytical solutions is not practically viable. Moreover, it is well-known in literature that if the local dynamics becomes complex, the range of possible dynamic behavior in the presence of diffusion and advection becomes practically unlimited. We resort to numerical solutions, which are obtained using two popular stabilized formulations: Streamline Upwind/Petrov Galerkin and Galerkin/Least Squares. In order to make the computational analysis tractable, an estimate on the range of system-dependent parameters is obtained based on model reduction performed on the strong-form of the governing equations. Finally, we quantify the errors in satisfying the local and global species balance for various realistic benchmark problems. Through these representative numerical examples, we shall demonstrate the need and importance of developing locally conservative non-negative numerical formulations for chaotic and oscillatory chemically reacting systems.Copyright © 2015 by ASME

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