Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

This numerical study focuses on the use of the Modal Identification Method to build reduced models for problems of heat convection and diffusion. The principle is to minimize a cost function based on the difference between the outputs (velocity and/or temperature) of a detailed model and the outputs of a reduced one. The reduced model structure is defined from the partial differential equations governing fluid mechanics and heat transfer in the physical system. In this paper, an advection-diffusion problem is studied: forced heat convection is considered with an incompressible, stationary, laminar 2D flow. Physical properties of the fluid are temperature independent, hence velocity is independent of temperature. The system under consideration is a channel flow over a backward-facing step with a time-varying heat flux density applied upstream of the step. Three types of reduced models have been investigated: steady fluid mechanics only, unsteady heat transfer for a given constant Reynolds number, and unsteady heat transfer for any constant Reynolds number within the range [100:800]. In this last case, the thermal reduced model is weakly coupled to the fluid reduced one. Results show that reduced models fit very well with detailed ones, and allow a large decrease of computing time.