A Methodology for Projection-Based Model Reduction with Black-Box High-Fidelity Models

摘要

This paper presents a methodology that enables projection-based modelreduction for black-box high-fidelity models such as commercial CFD codes. Themethodology specifically addresses the situation where the high-fidelity modelmay be a black-box but there is complete knowledge of the governing equations.The main idea is that the linear operator matrix, resulting from thediscretization of the linear differential terms is approximated directly usinga suitable discretization method such as the Finite Volume Method and requiresonly the computational grid as input. In this regard, the governing equationsare first cast in terms of a set of scalar observables of the state variables,leading to a linear set of equations. By applying the snapshots of theobservables to the discrete linear operator, a right hand side vector isobtained, providing the necessary system matrices for the Galerkin projectionstep. This way an online database of ROMs are generated for various parametersnapshots which are then interpolated online to predict the state for newparameter instances. Finally, the reduced order model is posed as a non-linearconstrained optimization problem that can be solved at a significantly cheapercost compared to the full order model. The method is successfully demonstratedon on a canonical non-linear parametric PDE with exponential non-linearity,followed by the compressible inviscid ow past the NACA0012 airfoil. As a firststep, this paper focuses only on establishing feasibility of the method.