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Construction of reduced-order models (ROMs) for hyperbolic conservation lawsis notoriously challenging mainly due to the translational property andnonlinearity of the governing equations. While the Lagrangian framework for ROMconstruction resolves the translational issue, it is valid only before a shockforms. Once that occurs, characteristic lines cross each other and projectionfrom a high-fidelity model space onto a ROM space distorts a moving grid,resulting in numerical instabilities. We address this grid distortion issue bydeveloping a physics-aware dynamic mode decomposition (DMD) method based onhodograph transformation. The latter provides a map between the originalnonlinear system and its linear counterpart, which coincides with the Koopmanoperator. This strategy is consistent with the spirit of physics-aware DMDs inthat it retains information about shock dynamics. Several numerical examplesare presented to validate the proposed physics-aware DMD approach toconstructing accurate ROMs.

Dynamic Mode Decomposition for Construction of Reduced-Order Models of Hyperbolic Problems with Shocks