Reduced-Order Model for Unsteady Compressible Flow Based on POD-Galerkin Projection

Abstract

Italic textIn this paper, the reduced-order model (ROM) of unsteady compressible flow based on POD-Galerkin projection has been investigated. The Euler equation formulated with the conservative variables for compressible flow has been reformulated using modified primitive variables. The POD modes are computed using snapshot method and then an explicit quadratic ROM is constructed by applying the Galerkin projection to the modified Euler equation. Because of lacking any dissipation in POD-Galerkin projection, the flow calibration method is introduced to account for the numerical dissipation to stabilize the ROM. At last, the NACA0012 airfoil undergoing pitch harmonic oscillating in Mach number Mach = 0.755 is calculated as a test case. For this flow configuration, the calibrated coefficients of the ROM are almost the same as the initial guess which comes from POD-Galerkin projection; the differences are mostly focused on the linear Lij coefficients and quadratic Qijk coefficients.