In this thesis, 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 arise from solutions of linear transport equations. Key to the proposed approach is the observation that the optimal transport velocities 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 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
