Control of Navier-Stokes equations by means of mode reduction

A Karhunen–Loève least-squares technique for optimization of geometry of a blunt body in supersonic flow

“…(48), the coordinates rðn; 0Þ and zðn; 0Þ are specified from the choice of b which fixes the body surface via the parameterization in Eqs. (30) and (31). The linear boundary conditions in Eq.…”

“…Independently, Park and Cho [22] developed a KL Galerkin model of a nonlinear heat equation for control or parameter estimation [23][24][25][26][27][28]. The KL Galerkin method has also been used to approximate Navier-Stokes solutions for flow control [29][30][31] applications. In order to avoid the difficulty of employing the Galerkin method for nonlinear problems, Theodoropulou et al [14] successfully implemented an orthogonal collocation method with numerical KL modes for the optimization of rapid thermal chemical vapor deposition systems in one dimension.…”

An input/output approach to the optimal transition control of a class of distributed chemical reactors

“…A direct use of CFD models for control design or dynamic optimization involves significant computational cost. Although application of advanced model reduction techniques to derive reduced-order models from the detailed partial differential equation (PDE) process models may work well in certain cases and lead to efficient dynamic optimization and control algorithms (see, for example, Armaou and Christofides, 1999Bendersky and Christofides, 2000;Christofides, 2001;Christofides and Daoutidis, 1997;Graham and Kevrekidis, 1996;Graham et al, 1999;Groetsch et al, 2006;Park and Lee, 2000), such a reduced-order model approach might require a huge amount of memory and computational cost when the CFD model consists of millions of grid points needed to accurately describe the process behavior. The reader may also refer to Raja et al (2000) and Varshney and Armaou (2006) for recent applications of model reduction and dynamic optimization to thin film deposition processes described by CFD equations and Balsa-Canto et al (2004 for further recent results on dynamic optimization and control of distributed parameter systems.…”

Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis

“…The use of POD analysis in control problems for partial differential equations has been considered in [1,17,18,25,26,27,30,31,35].…”