Reduced-order modeling: new approaches for computational physics

In this paper, we review the development of new reduced-order modeling techniques and discuss their applicability to various problems in computational physics. Emphasis is given to methods based on Volterra series representations, the proper orthogonal decomposition, and harmonic balance. Results are reported for different nonlinear systems to provide clear examples of the construction and use of reduced-order models (ROMs), particularly in the multi-disciplinary field of computational aeroelasticity. Unsteady aerodynamic and aeroelastic behaviors of two-dimensional and three-dimensional geometries are described. Large increases in computational efficiency are obtained through the use of ROMs, thereby justifying the initial computational expense of constructing these models and motivating their use for multi-disciplinary design analysis.