Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows

Abstract

Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis functions are used to approximate both the state and the position of the Lagrangian computational domain. It is demonstrated that in this framework, certain wave-like solutions exhibit low-rank structure and thus, can be efficiently compressed using relatively few global basis. The proposed approach is successfully demonstrated for the reduction of several simple but representative problems.

References in corpus (4)

• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• Adaptive $h$-refinement for reduced-order models
• Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution Equations
• Projective and Coarse Projective Integration for Problems with Continuous Symmetries

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