Contribution to the modeling of complex systems described by partial differential equations: a 2D multi-agent model for convection-diffusion
Jean Marie Dembele
Cheikh Anta Diop University (Sénégal)
Cheikh Anta Diop University (Sénégal) - Pierre et Marie Curie University (France)
Last modified: November 2, 2007
The numerical simulation of fluid dynamics and transport phenomena described by partial differential equation has long used grid-based methods (finite element method, finite difference method,...). Nowadays, it is more and more often based on particle methods which are more efficient because they use a lagrangian approach (Smooth particle hydrodynamics, Vortex methods,...).Nevertheless, these particle methods still have limits in the management of the particle behavior when submitted to complex boundary conditions, and in the approximations through quadrature points;"the particle adaptation comes at the expense of the regularity of the particle distribution as particles move in order to adapt to the gradients of the flow field".
We propose here a contribution, with multi-agent modeling, to the simulation
of such systems.The particle-agents are inspired by particle elements (volume or mass) and have vicinity perception,capacity of rearrangement and evaluation of their mutual contribution. In order to compare our multi-agent system with the classical models, we implement a model in Netlogo (a multi-agent platform) to simulate the convection-diffusion transport in two dimension.