Dynamic mode decomposition for density-driven gravity current simulations

Resumo

In the present work, we evaluate the capability of the Dynamic Mode Decomposition method to extract
spatio-temporal coherent structures of density-driven gravity current simulations. The coupled problem is solved
using the finite element method, and DMD is applied in the concentration dataset instead of all the simulation data.
We generate reduced order models from the DMD with a different number of computed basis vectors and evaluate
their accuracy and performance to capture the dynamics from the original system. We also extend our analysis to
two relevant quantities of interest, the front position and mass conservation, testing the accuracy of the surrogate
models. We also evaluate three different implementations of the Singular Value Decomposition, the core procedure
in the DMD, in terms of performance and accuracy. Furthermore, we investigate the extrapolation ability of the
Dynamic Mode Decomposition and evaluate its accuracy when considering different initial conditions.