The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model
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Vallaghe-2014-The static condensat.pdf
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Author(s)
Vallaghé, Sylvain
Patera, Anthony T.
Date Issued
January 2014
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Vallaghé, Sylvain, and Anthony T. Patera. “The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model.” SIAM Journal on Scientific Computing 36, no. 3 (January 2014): B294–B320.© 2014, Society for Industrial and Applied Mathematics.
Version
Final published version
Abstract
We propose a new approach for the simulation of conjugate heat exchangers. First, we introduce a dimensionality-reduced mathematical model for conjugate (fluid-solid) heat transfer: in the fluid channels, we consider a mixed-mean temperature defined on one-dimensional filaments; in the solid we consider a detailed partial differential equation conduction representation. We then propose a Petrov--Galerkin finite element (FE) numerical approximation which provides suitable stability and accuracy for our mathematical model. We next apply the static condensation reduced basis element (scRBE) method: a domain synthesis approach with parametric model order reduction at the intradomain level to populate a Schur complement at the interdomain level. We first build a library of “components,” each corresponding to a subdomain with a simple fluid channel geometry; for each component, we prepare Petrov--Galerkin reduced basis bubble approximations (and error bounds). We then assemble the system equations by static condensation and solve for the temperature distribution in the full domain. System-level error bounds are derived from matrix perturbation arguments; we also introduce a new output error bound which is sharper than the original scRBE estimator. We present numerical results for a two-dimensional automotive radiator model which demonstrate the flexibility, accuracy, and computational efficiency of our approach.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1137/120887709
