Cizmas, Paul G2015-12-012017-04-072015-12-012017-04-072013-122013-11-08http://hdl.handle.net/1969.1/151757This dissertation presents a proper orthogonal decomposition (POD) method that uses dynamic basis functions. The dynamic functions are of a prescribed form and do not explicitly depend on time but rather on parameters associated with flow unsteadiness. This POD method has been developed for modeling nonlinear flows with deforming meshes but can also be applied to fixed meshes. The method is illustrated for subsonic and transonic flows with fixed and deforming meshes. This method properly captured flow nonlinearities and shock motion for cases in which the classical POD method failed. Additionally, this dissertation presents a novel approach for assessing the number of basis functions used in POD. POD results are compared between subsonic and transonic flows for several cases. It is demonstrated that in order to determine the number of basis functions, it is better to assess the variation of individual energy values, as opposed to the cumulative energy values. Finally, for off-reference flow conditions, interpolation is performed on a tangent space to a Grassmann manifold, and the effect of interpolation order is investigated.enProper orthogonal decompositionReduced-order modelingDeforming meshDynamic basis functionsComputational fluid dynamicsGrassmann manifoldThesis