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Abstract: An Eulerian/Lagrangian method for the numerical simulation of incompressible convection flows interacting with complex obstacles is developed in this article. This method is successfully validated on natural convection cases, a porous medium and the Sierpinski carpet. The ability of the model to take accurately into account complex topologies allows its application to natural convection in the Lascaux cave, in order to give information on velocities, temperature and moisture content values and to provide helpful details to the conservators of the cave. [Copyright &y& Elsevier]