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In this work we study coupled incompressible viscous flow and advective-diffusive trans- port of a scalar. Both the Navier-Stokes and transport equations are solved using an Eulerian approach. The SUPG/PSPG stabilized finite element formulation is applied for the governing equations. The implementation is held using the libMEsh finite element library which provides support for parallel adaptive mesh refinement and coarsening. The Rayleigh-B ́enard natural convection and the planar lock-exchangedoi:10.19153/cleiej.15.3.1 fatcat:qeydz2znabcijlcvayo373scmu