Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows

TL;DR

This paper introduces a Lagrangian basis method for reducing the complexity of convection-dominated nonlinear fluid flows by capturing wave-like solutions with low-rank structures using global basis functions.

Contribution

It proposes a novel projection-based model reduction approach that approximates flow evolution in the Lagrangian frame, enabling efficient compression of wave-like solutions.

Findings

Wave-like solutions exhibit low-rank structure in the Lagrangian framework

Global basis functions effectively approximate both flow state and domain position

Method successfully reduces several representative convection-dominated flow problems

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.