Abstract
In this work is proposed the use of a numerical strategy based on the operator splitting technique, for solving a mathematical model for the population of the golden mussel in its adult stage, larval stage and algae (its food source) in aquatic environments, presented in [1, 19]. The model is composed of three unsteady and nonlinear advective-diffusive-reactive equations for species dynamics and the Navier-Stokes equations to simulate the water velocity field. We employ the operator splitting technique in order to effectively handle the reaction terms and the stiff processes associated with the model. The numerical methodology solves the transport problem in two stages: first, given the velocity field, we solve the advective-diffusive problem to obtain the densities of larvae, algae and mussels; then, we use this first step approximation as initial condition for solving the system of ordinary differential equations for the reactions terms. The new numerical formulation is then used in a 3D simulation of golden mussel proliferation in a section of the Pereira Barreto channel (Brazil), with a focus on population control actions. Preliminary results are discussed, as well as other considerations related to numerical strategy.
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Acknowledgements
Research carried out within the scope of the project “Control of the Golden Mussel Infestation by Genetic Induction of Infertility” (PD-10381-0419/2019) with funding from CTG Brasil, SPIC Brasil and Tijoá Energia, within their ANEEL Research & Development Programs.
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Azevedo, R.Z.S. et al. (2023). A Numerical Scheme for Solving a Mathematical Model Derived from Larvae-Algae-Mussel Interactions. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023 Workshops. ICCSA 2023. Lecture Notes in Computer Science, vol 14112. Springer, Cham. https://doi.org/10.1007/978-3-031-37129-5_14
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