Reduced basis steady Smagorinsky turbulence model for forced convection flow: application to the thermal comfort optimisation of cloisters

Abstract In this paper, we address the construction of reduced basis (RB) turbulence models for thermal air flow, as a tool to design optimal thermal comfort-oriented spaces in the architectural design of buildings. We consider thermal turbulent flow, modelled by the Smagorinsky LES turbulence model with forced convection, plus the internal energy conservation equation. We assume that the flow takes place in a transition space in buildings with some geometrical complexity, actually a cloister. We approximate this model by a stable discretisation using the finite element method using FreeFem++, leading to the full order model (FOM). We build mathematically based a posteriori error indicators for both velocity-pressure and temperature. On this basis, we construct a RB turbulence model for the targeted 2D thermal flow. We obtain speed-up rates of computation time of nearly 150 with respect to the FOM. We then apply the RB model to the optimal thermal comfort design of a cloister in typically hot climates. We determine the geometry of the cloister that allows the smallest deviation of the temperature with respect to a given comfort temperature: the corridors must be as wide and low as possible.