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Topology optimization of flow domains using the lattice Boltzmann method

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Abstract

We consider the optimal design of two- (2D) and three-dimensional (3D) flow domains using the lattice Boltzmann method (LBM) as an approximation of Navier-Stokes (NS) flows. The problem is solved by a topology optimization approach varying the effective porosity of a fictitious material. The boundaries of the flow domain are represented by potentially discontinuous material distributions. NS flows are traditionally approximated by finite element and finite volume methods. These schemes, while well established as high-fidelity simulation tools using body-fitted meshes, are effected in their accuracy and robustness when regular meshes with zero-velocity constraints along the surface and in the interior of obstacles are used, as is common in topology optimization. Therefore, we study the potential of the LBM for approximating low Mach number incompressible viscous flows for topology optimization. In the LBM the geometry of flow domains is defined in a discontinuous manner, similar to the approach used in material-based topology optimization. In addition, this non-traditional discretization method features parallel scalability and allows for high-resolution, regular fluid meshes. In this paper, we show how the variation of the porosity can be used in conjunction with the LBM for the optimal design of fluid domains, making the LBM an interesting alternative to NS solvers for topology optimization problems. The potential of our topology optimization approach will be illustrated by 2D and 3D numerical examples.

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Authors and Affiliations

  1. Center for Aerospace Structures, Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO, 80309–0429, USA

    Georg Pingen, Anton Evgrafov & Kurt Maute

Authors
  1. Georg Pingen
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  2. Anton Evgrafov
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  3. Kurt Maute
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Correspondence to Georg Pingen.

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Pingen, G., Evgrafov, A. & Maute, K. Topology optimization of flow domains using the lattice Boltzmann method. Struct Multidisc Optim 34, 507–524 (2007). https://doi.org/10.1007/s00158-007-0105-7

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  • DOI: https://doi.org/10.1007/s00158-007-0105-7

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