POD and CVT-based reduced-order modeling of Navier–Stokes flows

A discussion of reduced-order modeling for complex systems such as fluid flows is given to provide a context for the construction and application of reduced-order bases. Reviews of the POD (proper orthogonal decomposition) and CVT (centroidal Voronoi tessellation) approaches to reduced-order modeling are provided, including descriptions of POD and CVT reduced-order bases, their construction from snapshot sets, and their application to the low-cost simulation of the Navier–Stokes system. Some concrete incompressible flow examples are used to illustrate the construction and use of POD and CVT reduced-order bases and to compare and contrast the two approaches to reduced-order modeling.