Application of proper orthogonal decomposition (POD) to design decomposition methods

A method for using Proper Orthogonal Decomposition (POD) to build approximation models intended for design applications has been developed that incorporate the governing equations of a system. The technique uses a series of observations or snapshots of a system to build a linear basis for approximating other solutions of interest. Scalar coefficients of the basis functions are computed from the governing equations of the physical system using a weighted residual method. For representing highly non-linear phenomena such as shocks in transonic aerodynamics the method can be incorporated in a dynamic domain decomposition technique in which the vast majority of the computational domain is represented by POD and the remaining small subdomain is represented at full order. In a complementary method the ability of a small number of scalar coefficients to represent a high-fidelity aerodynamic or structural simulation is used to reduce the bandwidth or order of interaction between disciplines in decomposition algorithms for multidisciplinary design. Order reduction makes decomposition algorithms, which often have a cost highly dependent on the number of interaction variables, more suitable for use with high-fidelity models. Because full order analyses are not eliminated, the approximation can be monitored and adapted to yield accurate solutions with computationally costs competitive with more tightly coupled methods.