Alter-and-Excite Approach for Reduced-Order Modeling of Diffusive and Convective Transport Phenomena

Abstract

Abstract. The Krylov subspace method is an efficient projection-based approach for reduced-order modeling (ROM) of large-scale linear systems common in computational fluid dynamics (CFD). It works by matching moments between a full-order model (FOM) and its ROM counterpart at specific interpolation points or shifts. However, its adoption is hindered by the need for high-dimensional operators from the CFD model. Recently, several methods have emerged to bypass this requirement for diffusive and convective transport problems. This paper interprets such attempts as a new branch of ROM techniques based on alter-and-excite (A&E) for improved identification, in contrast with traditional system-identification techniques relying solely on excitation for extraction of system information. In an A&E approach, the CFD model is iteratively both altered and excited to identify Krylov subspace basis vectors directly from system responses. Additionally, a novel A&E method is proposed for generating the Krylov subspace with complex conjugate shifts. It is shown that reformulating the CFD model as a multiphysics problem provides the necessary information for constructing a ROM based on real matrices when complex shifts are adopted. The study details the implementation and evaluation of the A&E method with complex conjugate shifts.