A STABLE GALERKIN REDUCED ORDER MODEL (ROM) FOR COMPRESSIBLE FLOW

Abstract

Abstract. A method for constructing stable Proper Orthogonal Decomposition (POD)/Galerkin reduced order models (ROMs) for compressible flow is described. The proposed model reduction technique differs from the approach taken in many applications in that the Galerkin projection step is applied to the continuous system of partial differential equations (PDEs), rather than a semi-discrete representation of these equations. It is demonstrated that the inner product used to define the Galerkin projection is intimately tied to the stability of the resulting model. For linearized conservation laws such as the linearized compressible Euler and linearized compressible Navier-Stokes equations, a symmetry transformation leads to a stable formulation for the inner product. Preservation of stability for the discrete implementation of the Galerkin projection is