Orthogonal Locality Preserving model reduction and flow separation control for incompressible Navier Stokes equations

Abstract

Orthogonal Locality Preserving Projections (OLPP) are locally linear but globally nonlinear projection maps that arise by solving a variational problem, which optimally preserves the neighborhood structure of the state dynamics. OLPP projects the data in a way that preserves a certain affinity graph where graph nodes are the snapshots from numerical solutions. The edges can be defined by talking some number of nearest neighbor nodes to every state or alternatively by including all neighbors within a defined radius around the states. In this paper we design an OLPP POD model order reduction technique for an incompressible Navier-Stokes system that governs the velocity and pressure behavior of a fluid passing through the NACA 0015 airfoil with periodic boundary conditions. We first compute the optimal POD basis functions and show the reduced order system, then we compute the OLPP reduced system. Finally we present the flow separation problem.