Domain Decomposition Strategy for Combining Nonlinear and Linear Reduced-Order Models

Increasingly ubiquitous reliance on expensive, high-fidelity numerical simulations has led to the emergence of reduced-order modeling as an effective method to predict high-dimensional, spatially discretized field outputs in an efficient manner. This study presents a method to construct parametric, nonintrusive reduced-order models (ROMs) by leveraging domain decomposition (DD) to enable using multiple dimension reduction (DR) techniques within different spatial subdomains of the field to construct a single predictive ROM. To enforce smoothness of solutions across subdomains, points at domain interfaces are reconstructed using the data-driven gappy proper orthogonal decomposition method. The method is assessed on three high-dimensional test cases with shocks, including one with two-dimensional turbulent flow around the RAE2822. Results show that fully nonlinear ROMs predict fields more accurately in the vicinity of discontinuous features compared to their linear counterparts, which are more accurate in regions that are far from these discontinuities. Furthermore, irrespective of the DR method, DD-based ROMs outperformed their global counterparts in all test cases. Finally, models that used a combination of DR methods simultaneously showed superior performance near shockwaves and a significant improvement in total error compared to existing approaches that employ a single DR method in all subdomains.