Approximation of compressible flows by a reduced order model

Abstract

In this paper we discuss the possible advantages and inherent draw-backs of a reduced order model for compressible flows of practical interest. The models considered include Euler and Navier-Stokes equations. Turbulent flows are also investigated, and the model of turbulence evolution is based on the κ − ε formulation with wall laws. The reduced order model is constructed from a set of basis functions determined by proper orthogonal decomposition (POD). The POD basis functions are used to filter, at each time step, the solution obtained from a finite-volume code. Three test cases are discussed: unsteady Euler flow about an oscillating airfoil, laminar vortex shedding from a NACA-0012 airfoil at incidence, and finally turbulent vortex shedding from a square cylinder.