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-conditionindependent. 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-conditionindependent reduced order model.Boundary-conditionindependent 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.

Multi-port dynamic compact thermal models of dual-chip package using model order reduction and metaheuristic optimization

“…Only few works have been proposed for the construction of boundary-condition-independent DCTMs [20,21]. These works use proper orthogonal decomposition (POD) method, which was developed for computational fluid dynamics and requires large set of time-consuming transient thermal simulations of the detailed model.…”

BFC-POD-ROM Aided Fast Thermal Scheme Determination for China’s Secondary Dong-Lin Crude Pipeline with Oils Batching Transportation

“…The temperature fields at representative instances under various sampling conditions should be put into the sampling matrix. Suppose L kinds of sampling conditions are sampled and, for every condition, the temperature field at each time instance is obtained with a total number, K. Considering the ith condition, if the temperature fields in each time instance are sampled, the sampling matrix for the ith condition can be constructed as Equation (13). Similarly, for each condition, a sampling matrix for it can be obtained.…”