research-article

Topology optimization of thermal fluid flows with an adjoint Lattice Boltzmann Method

Authors:

Florian Dugast,

Christophe Josset,

Lingai LuoAuthors Info & Claims

Volume 365, Issue C

Pages 376 - 404

https://doi.org/10.1016/j.jcp.2018.03.040

Published: 15 July 2018 Publication History

Abstract

This paper presents an adjoint Lattice Boltzmann Method (LBM) coupled with the Level-Set Method (LSM) for topology optimization of thermal fluid flows. The adjoint-state formulation implies discrete velocity directions in order to take into account the LBM boundary conditions. These boundary conditions are introduced at the beginning of the adjoint-state method as the LBM residuals, so that the adjoint-state boundary conditions can appear directly during the adjoint-state equation formulation. The proposed method is tested with 3 numerical examples concerning thermal fluid flows, but with different objectives: minimization of the mean temperature in the domain, maximization of the heat evacuated by the fluid, and maximization of the heat exchange with heated solid parts. This latter example, treated in several articles, is used to validate our method. In these optimization problems, a limitation of the maximal pressure drop and of the porosity (number of fluid elements) is also applied. The obtained results demonstrate that the method is robust and effective for solving topology optimization of thermal fluid flows.

Highlights

•

Topology optimization of thermal fluid flow problems using LBM and LSM.

•

Continuous adjoint-state problem in space and time.

•

New introduction of the LBM boundary conditions in the adjoint-state formulation.

•

Use of the LBM incompressible model to improve the forward problem accuracy and to simplify adjoint-states calculations.

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Cited By

Guan KMatsushima KNoguchi YYamada T(2023)Topology optimization for rarefied gas flow problems using density method and adjoint IP-DSMCJournal of Computational Physics10.1016/j.jcp.2022.111788474:COnline publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1016/j.jcp.2022.111788
Yoon GKim M(2023)Topology optimization for transient two-phase fluid systems with continuous behaviorFinite Elements in Analysis and Design10.1016/j.finel.2023.104017225:COnline publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1016/j.finel.2023.104017
Tanabe YYaji KUshijima K(2023)Topology optimization using the lattice Boltzmann method for unsteady natural convection problemsStructural and Multidisciplinary Optimization10.1007/s00158-023-03522-y66:5Online publication date: 13-Apr-2023
https://dl.acm.org/doi/10.1007/s00158-023-03522-y
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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 365, Issue C

Jul 2018

405 pages

ISSN:0021-9991

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Copyright © 2018.

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Academic Press Professional, Inc.

United States

Publication History

Published: 15 July 2018

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Cited By

Guan KMatsushima KNoguchi YYamada T(2023)Topology optimization for rarefied gas flow problems using density method and adjoint IP-DSMCJournal of Computational Physics10.1016/j.jcp.2022.111788474:COnline publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1016/j.jcp.2022.111788
Yoon GKim M(2023)Topology optimization for transient two-phase fluid systems with continuous behaviorFinite Elements in Analysis and Design10.1016/j.finel.2023.104017225:COnline publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1016/j.finel.2023.104017
Tanabe YYaji KUshijima K(2023)Topology optimization using the lattice Boltzmann method for unsteady natural convection problemsStructural and Multidisciplinary Optimization10.1007/s00158-023-03522-y66:5Online publication date: 13-Apr-2023
https://dl.acm.org/doi/10.1007/s00158-023-03522-y
Yodono TYaji KYamada TFuruta KIzui KNishiwaki S(2022)Topology optimization for the elastic field using the lattice Boltzmann methodComputers & Mathematics with Applications10.1016/j.camwa.2022.01.032110:C(123-134)Online publication date: 15-Mar-2022
https://dl.acm.org/doi/10.1016/j.camwa.2022.01.032

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