Simulation of 3D phytoplankton dynamics: competition in light-limited environments

In this paper we study the dynamics of phytoplankton in a competition context. Current models are formulated as 1D integro-partial differential equations of advection-diffusion-reaction type. Here we include horizontal effects (water flow and horizontal diffusion). Due to the stiffness of the discretized system we selected an implicit integration method. However, the resulting implicit relations are extremely expensive to solve, caused by the strong coupling of the components. This coupling originates from the three spatial dimensions, the interaction of the various species and the integral term. To reduce the amount of work in the linear algebra part, we used an Approximate Matrix Factorization technique. The performance of the complete algorithm is demonstrated on the basis of two test examples. It turns out that the property of A-stability is very useful for this application.