Simulation of three-dimensional phytoplankton dynamics: comptetion in light-limited environments

  • Authors:

  • N. N. Pham Thi;J. Huisman;B. P. Sommeijer

  • Affiliations:

  • Center for Mathematics and Computer Science (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;Aquatic Microbiology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 127, 1018 WS Amsterdam, The Netherlands;Center for Mathematics and Computer Science (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2005

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Abstract

In this paper, we develop computational methods for a three-dimensional model of competition for light between phytoplankton species. The competing phytoplankton populations are exposed to both horizontal and vertical mixing. The vertical light-dependence of phytoplankton photosynthesis implies that the three-dimensional model is formulated in terms of integro-partial differential equations that require an efficient numerical solution technique.Due to the stiffness of the discretized system we select 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 use an Approximate Matrix Factorization technique.The performance of the complete algorithm is demonstrated on the basis of two test examples. It turns out that unconditional stability (i.e., A-stability) is a very useful property for this application.