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Levelset based fluid topology optimization using the extended finite element method

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Abstract

This study focuses on finding the optimal layout of fluidic devices subjected to incompressible flow at low Reynolds numbers. The proposed approach uses a levelset method to describe the fluid-solid interface geometry. The flow field is modeled by the incompressible Navier–Stokes equations and discretized by the extended finite element method (XFEM). The no-slip condition along the fluid-solid interface is enforced via a stabilized Lagrange multiplier method. Unlike the commonly used porosity approach, the XFEM approach does not rely on a material interpolation scheme, which allows for more flexibility in formulating the design problems. Further, it mitigates shortcomings of the porosity approach, including spurious pressure diffusion through solid material, strong dependency of the accuracy of the boundary enforcement with respect to the model parameters which may affect the optimization results, and poor boundary resolution. Numerical studies verify that the proposed method is able to recover optimization results obtained with the porosity approach. Further, it is demonstrated that the XFEM approach yields physical results for problems that cannot be solved with the porosity approach.

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Acknowledgments

The authors acknowledge the support of the National Science Foundation under grants DMI-0729529 and EFRI-1038305. The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organization.

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  1. Center for Aerospace Structures, University of Colorado at Boulder, Boulder, CO, USA

    Sebastian Kreissl & Kurt Maute

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  1. Sebastian Kreissl
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  2. Kurt Maute
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Correspondence to Kurt Maute.

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Kreissl, S., Maute, K. Levelset based fluid topology optimization using the extended finite element method. Struct Multidisc Optim 46, 311–326 (2012). https://doi.org/10.1007/s00158-012-0782-8

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