Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows
Abstract
Foundations of a new projectionbased 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 wavelike solutions exhibit lowrank 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.04343
 Bibcode:
 2017arXiv170104343M
 Keywords:

 Physics  Fluid Dynamics;
 Mathematics  Numerical Analysis;
 Physics  Computational Physics