A reduced-order finite element method based on proper orthogonal decomposition for the Allen-Cahn model

2021 ◽  
pp. 125103
Author(s):  
Huanrong Li ◽  
Zhengyuan Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Element Method

On Reduced Order Modeling of Transient Flows Using the Proper Orthogonal Decomposition

2012 ◽  
Author(s):  
Fariduddin Behzad ◽  
Brian T. Helenbrook ◽  
Goodarz Ahmadi
Keyword(s):  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Reduced Order Modeling ◽  
Orthogonal Decomposition ◽  
Basis Functions ◽  
Navier Stokes ◽  
Reduced Order ◽  
Split Method ◽  
Proper Orthogonal

Reduced-order modeling (ROM) of transient fluid flows using the proper orthogonal decomposition (POD) was studied. Particular attention was given to incompressible, unsteady flow over a two-dimensional NACA0015 airfoil in the laminar regime. When the airfoil sheds vortices, a transient blowing through a jet placed at the 10% chord location was imposed. POD modes were derived from the numerical solution of the flow obtained using an hp-finite element method. The ROM was obtained by a streamwise-upwind-Petrov-Galerkin (SUPG) projection of the incompressible Navier–Stokes equations onto the space spanned by the POD modes. The extraction of accurate POD-based reduced order model of this flow was explored using three different POD mode generation methods. The first approach was the split method, which superposes modes derived from simulations of the blowing jet with no flow and simulations of the baseline flow with no jet. The second method combined POD modes derived from simulations having both the jet and flow with modes obtained from simulation of only the flow. These modes were generated after the simulations reached the periodic state. The third and newly proposed approach was to generate a set of modes called “Generalized POD basis functions.” These modes were derived from simulations where the jet’s flow amplitude is varied slowly. For each method, the results were compared with detailed Finite Element solutions and the accuracy and efficiency of different methods were evaluated. The newly proposed “Generalized POD basis functions” approach predicted the transient response of the system most accurately.

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

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