POD-based observer for estimation in Navier–Stokes flow

In this paper, we propose a POD-based technique that is suitable for the design of reliable observers for the estimation of velocity field and contaminant flow for Navier–Stokes flow. POD modes are constructed using the method snapshot. Karhunen–Loeve (Galerkin) projection to develop a reduced-order model obtained by projecting the velocity field onto the most important POD modes. The resulting finite-dimensional dynamical system is suitable for the design of nonlinear observers. The estimate of the velocity field is then used to estimate the concentration field of a contaminant from the 2D advection–diffusion equation. The prime application considered is the estimation of airflow and contaminant flow in building systems. A 2D simulation example is provided to demonstrate the applicability of the technique.