A Lagrangian-frame DMD that includes characteristic-line positions as Koopman observables yields accurate reduced-order models for shock-free advection-dominated PDEs.
These equations become highly nonlinear when advection velocity and/or diffusion coefficient depend (s) on a system state, e.g., in the case of multiphase flows in porous media [1]
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Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena
A Lagrangian-frame DMD that includes characteristic-line positions as Koopman observables yields accurate reduced-order models for shock-free advection-dominated PDEs.