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arXiv · 1908.03688

Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena

Hannah Lu·Daniel M. Tartakovsky
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Abstract

Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct reduced-order models (ROMs) in a variety of fields of science and engineering. Despite their popularity, both DMD and POD struggle to formulate accurate ROMs for advection-dominated problems because of the nature of SVD-based methods. We investigate this shortcoming of conventional POD and DMD methods formulated within the Eulerian framework. Then we propose a Lagrangian-based DMD method to overcome this so-called translational issues. Our approach is consistent with the spirit of physics-aware DMD since it accounts for the evolution of characteristic lines. Several numerical tests are presented to demonstrate the accuracy and efficiency of the proposed Lagrangian DMD method.

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Hannah Lu, Daniel M. Tartakovsky. 2019-08-10. Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena. https://doi.org/10.1016/j.jcp.2020.109229

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