Robust reduced order modeling of heat transfer in a back step flow

We present a method to obtain reduced order models to calculate steady states in thermal systems of industrial interest. The method could be regarded as an evolution of the standard proper orthogonal decomposition (POD) method, in which the reduced model is obtained through standard Galerkin projection (whose application exhibits well known difficulties) on previously obtained POD modes. Instead of relying on a Galerkin projection, we use a genetic algorithm (GA) to minimize a conveniently defined residual for the (continuity, momentum, and energy) equations and boundary conditions. The method and its practical application are illustrated on a test problem that describes heat transfer in the recirculation region downstream of a backwards facing step.