  A new model order reduction approach is proposed for parametric steady-state
nonlinear fluid flows characterized by shocks and discontinuities whose spatial
locations and orientations are strongly parameter dependent. In this method,
solutions in the predictive regime are approximated using a linear
superposition of parameter dependent basis. The sought after parametric
reduced-basis are obtained by transporting the snapshots in a spatially and
parametrically dependent transport field. Key to the proposed approach is the
observation that the transport fields are typically smooth and continuous,
despite the solution themselves not being so. As a result, the transport fields
can be accurately expressed using a low-order polynomial expansion. Similar to
traditional projection-based model order reduction approaches, the proposed
method is formulated mathematically as a residual minimization problem for the
generalized coordinates. The proposed approach is also integrated with
well-known hyper-reduction strategies to obtain significant computational
speed-ups. The method is successfully applied to the reduction of a parametric
1-D flow in a converging-diverging nozzle, a parametric 2-D supersonic flow
over a forward facing step and a parametric 2-D jet diffusion flame in a
combustor.
