Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis

Abstract

SUMMARYA method of reducing the number of degrees of freedom and the overall computing times in finite element method (FEM) has been devised. The technique is valid for linear problems and arbitrary temporal variation of boundary conditions. At the first stage of the method standard FEM time stepping procedure is invoked. The temperature fields obtained for the first few time steps undergo statistical analysis yielding an optimal set of globally defined trial and weighting functions for the Galerkin solution of the problem at hand. Simple matrix manipulations applied to the original FEM system produce a set of ordinary differential equations of a dimensionality greatly reduced when compared with the original FEM formulation. Using the concept of modal analysis the set is then solved analytically. Treatment of non-homogeneous initial conditions, time-dependent boundary conditions and controlling the error introduced by the reduction of the degrees of freedom are discussed. Several numerical examples are included for validation of the approach.

Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

“…Error propagation through the POD mode basis has been explored to some degree as far as implications to reduced-order models (see, e.g., Refs. [23][24][25][26]). The propagation of error through data-driven POD representations of turbulence remains a subject requiring development.…”

Reduced order models for thermal analysis : final report : LDRD Project No. 137807.

“…Similar techniques have recently been applied in standard thermal conduction problems e.g. [1][2][3][4][5] though the general use of ROM for heat transfer is not yet widespread. One major difficulty with the development of ROM for general thermal analysis is the need to include the very nonlinear effects of enclosure radiation in many applications.…”

“…[1][2][3][4][5][6]. Here a simple sketch of the attributes and procedure is provided to introduce the method for the particular applications of interest.…”

Interpolation of final geometry and result fields in process parameter space

“…The most popular is inverse analysis where based on the system response compared to its metamodel some of the systems parameters such as material properties may be identified [2,3,4]. The second group consists of direct problems where based on POD-RBF methodology calculation time is improved by coupling it with FEM [5,6] or where it is used to support the design process [7,8].…”