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- Title
Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method.
- Authors
Dai, Xiaoxia; Zhang, Chengwei; Zhang, Ye; Gulliksson, Mårten
- Abstract
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.
- Subjects
TOPOLOGY; NAVIER-Stokes equations; MATHEMATICAL optimization; LAGRANGIAN mechanics; MULTIPLIERS (Mathematical analysis); SET theory
- Publication
Structural & Multidisciplinary Optimization, 2018, Vol 57, Issue 6, p2193
- ISSN
1615-147X
- Publication type
Article
- DOI
10.1007/s00158-017-1850-x