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A new model order reduction approach is proposed for parametric steady-statenonlinear fluid flows characterized by shocks and discontinuities whose spatiallocations and orientations are strongly parameter dependent. In this method,solutions in the predictive regime are approximated using a linearsuperposition of parameter dependent basis. The sought after parametricreduced-basis are obtained by transporting the snapshots in a spatially andparametrically dependent transport field. Key to the proposed approach is theobservation that the transport fields are typically smooth and continuous,despite the solution themselves not being so. As a result, the transport fieldscan be accurately expressed using a low-order polynomial expansion. Similar totraditional projection-based model order reduction approaches, the proposedmethod is formulated mathematically as a residual minimization problem for thegeneralized coordinates. The proposed approach is also integrated withwell-known hyper-reduction strategies to obtain significant computationalspeed-ups. The method is successfully applied to the reduction of a parametric1-D flow in a converging-diverging nozzle, a parametric 2-D supersonic flowover a forward facing step and a parametric 2-D jet diffusion flame in acombustor.

Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter dependent shocks