Centroidal Voronoi Tessellation-Based Reduced-Order Modeling of Complex Systems

Abstract

\noindent A reduced-order modeling methodology based on centroidal Voronoi tessellations (CVTs) is introduced. CVTs are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. For discrete data sets, CVTs are closely related to the h-means and k-means clustering techniques. A discussion of reduced-order modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed from snapshot sets and how they can be applied to the low-cost simulation of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples.