Mathematical and numerical modeling for a bio-chemical aquarium

Based on bio-chemical ground we derive an aquarium mathematical model useful for predicting dangerous situations as well as for the startup cycle. This model is a basic step toward a more complex advection–diffusion–reaction model in 3D space variables: it defines the reaction part of the more complex partial differential equations model. For the numerical solution of our aquarium model we apply a low complexity second order method combined with a simple adaptive step-size selection procedure. The low accuracy and complexity of the resulting numerical algorithm are motivated because of the high complexity of the final 3D model. The reported numerical results, and comparisons with the know-how available in literature, show the validity of the proposed model.