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Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method
School of Computing Science, Zhejiang University City College, Hangzhou, Zhejiang, People’s Republic of China.
School of Computing Science, Zhejiang University City College, Hangzhou, Zhejiang, People’s Republic of China.
Örebro University, School of Science and Technology. (Mathematics)ORCID iD: 0000-0003-4023-6352
Örebro University, School of Science and Technology.ORCID iD: 0000-0003-0332-2315
2017 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488Article in journal (Refereed) Epub ahead of print
Abstract [en]

This paper presents a piecewise constant level set method for the topology optimization of steady Navier- Stokes flow. Combining piecewise constant level set functions and artificial friction force, the optimization problem is formulated and analyzed based on a design variable. The topology sensitivities are computed by the adjoint method based on Lagrangian multipliers. In the optimization procedure, the piecewise constant level set function is updated by a new descent method, without the needing to solve the Hamilton-Jacobi equation. To achieve optimization, the piecewise constant level set method does not track the boundaries between the different materials but instead through the regional division, which can easily create small holes without topological derivatives. Furthermore, we make some attempts to avoid updating the Lagrangian multipliers and to deal with the constraints easily. The algorithm is very simple to implement, and it is possible to obtain the optimal solution by iterating a few steps. Several numerical examples for both two- and three-dimensional problems are provided, to demonstrate the validity and efficiency of the proposed method.

Place, publisher, year, edition, pages
Heidelberg, Germany: Springer, 2017.
Keyword [en]
Topology optimization, Piecewise constant, Level set method, Navier-Stokes equations, Finite element method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-64001DOI: 10.1007/s00158-017-1850-xOAI: oai:DiVA.org:oru-64001DiVA: diva2:1172409
Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-01-16Bibliographically approved

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Zhang, YeGulliksson, Mårten

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