Boundary-condition-independent reduced-order modeling of 3D objects by the POD-Galerkin methodology

Abstract

The objective of the current work is to introduce the concept of boundary-condition-independent (BCI) reduced-order modeling (ROM) for complex electronic packages by the POD-Galerkin methodology. This work focuses on how the Proper Orthogonal Decomposition (POD)-Galerkin methodology can be used with the Finite Volume (FV) method to generate reduced-order models that are boundary-condition-independent. The method has been successfully implemented to generate boundary-condition-independent reduced-order thermal models for 1D and 2D objects. In this paper, the POD-Galerkin methodology is extended to generate a boundary-condition-independent model for a simple 3D object and a 3D object with a single heat source. Specific objectives of extending the methodology to 3D objects is to identify the correct number and type of snapshots used for constructing the reduced-order model and to identify the minimum number of POD basis vectors to generate the boundary-condition-independent reduced order model. Boundary-condition-independent reduced-order models generated for the 3D objects for isoflux boundary conditions show less than 4% relative error for a range of heat transfer coefficient of h = 1 W/m2K and h = 1000 W/m2K. The biggest advantage of this methodology is the potential of being integrated into commercial computational fluid dynamics software with minimal modifications.