Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems

Abstract

A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power reactor cooling systems. Thermal mixing of different temperature coolants in T-junction pipes leads to temperature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume regime. Two different parametric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model. The first test case results to a computational speed-up factor of 374 while the second test case to one of 211.

Enhancing CFD predictions in shape design problems by model and parameter space reduction

“…For parametric time-dependent problems, a proper orthogonal decomposition approach can be applied to reduce the dimensionality of the system, as in [19,25]. In this work we propose a novel data-driven approach for parametric dynamical systems, combining dynamic mode decomposition (DMD) with active subspaces (AS) property.…”

A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

“…This is done in the so-called on-line stage, where two different approaches, namely PODI and PODP, can be used to obtain q POD pwq for any value of w [44]. PODI [34,33,7] is less intrusive than PODP [40,13,12] since it does not require any information from the finite element solver, as opposed to PODP, which requires the FE system matrices to be accessible. On the other hand, PODI requires the solution to have a smooth variation with the parameters in order to provide accurate results, while PODP offers an increased accuracy and robustness, especially as the smoothness of the solution decreases [44,36].…”

“…Several numerical techniques can be classified as ROMs. Some examples are Proper Generalised Decomposition (PGD) [10,28,11] and Proper Orthogonal Decomposition (POD) [8,25,44,9], whose variants include POD with interpolation (PODI) [34,33,7] and projection based POD (in the following PODP), also known as POD based Reduced Basis (RB) or POD-Galerkin [40,13,12]. One key difference between PGD and POD is the complexity of their implementation and the extent to which an existing FE solver must be modified to implement the corresponding ROM.…”

Bayesian identification of a projection-based reduced order model for computational fluid dynamics

“…From this perspective, both of methods have to be further improved. This is very much the key component in future attempts to deal with the problems that are of timeand parameter-dependent nature such as the one presented in [13]. Looking forward, further attempts could be addressing the accuracy of the POD modes, and their extension to a nonlinear setting.…”