  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.
