The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model
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 cons...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Society for Industrial and Applied Mathematics
2014
|
| Online Access: | http://hdl.handle.net/1721.1/89466 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1826199218077827072 |
|---|---|
| author | Vallaghé, Sylvain Patera, Anthony T. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Vallaghé, Sylvain Patera, Anthony T. |
| author_sort | Vallaghé, Sylvain |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:16:16Z |
| format | Article |
| id | mit-1721.1/89466 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:16:16Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/894662024-07-12T20:25:05Z The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model Vallaghé, Sylvain Patera, Anthony T. Massachusetts Institute of Technology. Department of Mechanical Engineering Patera, Anthony T. 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. United States. Office of Naval Research (ONR grant N00014-11-0713) 2014-09-12T17:01:02Z 2014-09-12T17:01:02Z 2014-01 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/89466 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. https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1137/120887709 SIAM Journal on Scientific Computing Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics |
| spellingShingle | Vallaghé, Sylvain Patera, Anthony T. The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model |
| title | The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model |
| title_full | The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model |
| title_fullStr | The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model |
| title_full_unstemmed | The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model |
| title_short | The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model |
| title_sort | static condensation reduced basis element method for a mixed mean conjugate heat exchanger model |
| url | http://hdl.handle.net/1721.1/89466 https://orcid.org/0000-0002-2631-6463 |
| work_keys_str_mv | AT vallaghesylvain thestaticcondensationreducedbasiselementmethodforamixedmeanconjugateheatexchangermodel AT pateraanthonyt thestaticcondensationreducedbasiselementmethodforamixedmeanconjugateheatexchangermodel AT vallaghesylvain staticcondensationreducedbasiselementmethodforamixedmeanconjugateheatexchangermodel AT pateraanthonyt staticcondensationreducedbasiselementmethodforamixedmeanconjugateheatexchangermodel |