Development of a Mathematical Model for Simulation of Macroalgae Farming in the Coastal Areas

Abstract

A mathematical model consisting of a system of three coupled partial differential equations (PDEs) was proposed to estimate the concentrations of nitrogen, phosphorous and macroalgae biomass in coastal open waters. However, some simplifying assumptions were used in the model to cope with the complexity of real conditions. For the macroalgae biomass, the system works as a batch mode, while input and output were accounted for nitrogen and phosphorous. The MATLAB pdepe feature, applying the finite element method was used in model solving and the simulation of model equations. The program was split into four functions that included the solver and post-processing of the results, a function containing the PDEs, a function setting the initial conditions, and one setting the boundary conditions. For model validation, the experimental measurement of nitrogen, phosphorous and macroalgae biomass concentrations of Bandar Abbas coastal open waters were analyzed by standard methods at three depths of 1, 5 and 10 m. The predictive values of the developed model demonstrated its applicability for the management of coastal macroalgae cultivation systems by assessing the impact of nitrogen and phosphorous strategies on the farming system.