Rank-Adaptive Reduced-Order Modeling of 2D Incompressible Linearized Navier stokes equations with Time-Dependent Bases

Accurately and efficiently describing the response of transitional flows to external forcing has numerous applications. Solving such high-dimensional systems can be costly, and many current reduced-order modeling techniques fail to make faithful low-dimensional representations. Flow response to external forcing is typically high-dimensional when expressed by static modal reduction techniques; however, for transitional flows, this approach could be ineffective because many modes are required. In this presentation, we introduce a reduced-order modeling technique based on time-dependent bases (TDB-ROM) leveraging the discrete empirical interpolation method (DEIM). This computationally efficient approach effectively captures the instantaneous correlated structures and constructs a low-rank approximation. Additionally, we propose a rank-adaptive strategy to control the error of the low-rank decomposition.

To demonstrate the performance of the proposed technique, we apply it to a two-dimensional decaying isotropic turbulence flow subjected to a high-dimensional external forcing.