A methodology for projection-based model reduction with black-box high-fidelity models

This paper presents a methodology that enables projection-based model reduction for black-box high-fidelity models such as commercial CFD codes. The methodology specifically addresses the situation where the high-fidelity model may be a black-box but there is complete knowledge of the governing equations. The main idea is that the linear operator matrix, resulting from the discretization of the linear differential terms (such as divergence and gradient) can be approximated directly using the computational grid and boundary conditions, which are always available. By applying the snapshot solutions onto the linear operator matrix, a vector representing all the non-linear terms and source terms is also extracted, providing the necessary system matrices for the Galerkin projection step. In this regard, the proposed methodology performs a direct finite volume discretization of the linear terms at a computational cost that varies linearly with the grid size. The method is applicable to unstructured grids with arbitrary polygonal cell types and to models with generalized non-linearities. The method is successfully demonstrated on model reduction of a simple linear PDE and a non-linear PDE with exponential non-linearity. As a first step, this paper focuses only on establishing feasibility of the method.