An Efficient Chorin–Temam Projection Proper Orthogonal Decomposition Based Reduced-Order Model for Nonstationary Stokes Equations

Improvement of Reduced Order Modeling based on Proper Orthogonal Decomposition

This report focuses on improving the stability as well as the approximation properties of Reduced Order Models (ROM) based on Proper Orthogonal Decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier-Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is...

Mixed Finite Element Formulation and Error Estimates Based on Proper Orthogonal Decomposition for the Nonstationary Navier-Stokes Equations

In this paper, proper orthogonal decomposition (POD) is used for model reduction of mixed finite element (MFE) for the nonstationary Navier–Stokes equations and error estimates between a reference solution and the POD solution of reduced MFE formulation are derived. The basic idea of this reduction technique is that ensembles of data are first compiled from transient solutions computed equation...

A reduced-order model for a bubbling fluidized bed based on proper orthogonal decomposition

This paper presents the development of a reduced-order model (ROM) for dynamics of fluidized beds, based on the proper orthogonal decomposition (POD) method. Several implementations of this ROM were developed for a two-dimensional bubbling fluidized bed using numerical results from a full computational fluid dynamics (CFD) simulation of the bed. The solutions of the ROM were used to investigate...

Proper Orthogonal Decomposition for Reduced Order Control of Partial Differential Equations

Numerical models of PDE systems can involve very large matrix equations, but feedback controllers for these systems must be computable in real time to be implemented on physical systems. Classical control design methods produce controllers of the same order as the numerical models. Therefore, reduced order control design is vital for practical controllers. The main contribution of this research...

Proper Orthogonal Decomposition for Reduced Order Feedback Control of Partial Differential Equations