A high‐level programming‐language implementation of topology optimization applied to steady‐state Navier–Stokes flow

By Laurits Højgaard Olesen, Fridolin Okkels, Henrik Bruus. 2004

494 citations recorded by the source corpus.

We present a versatile high‐level programming‐language implementation of non‐linear topology optimization. Our implementation is based on the commercial software package FEMLAB, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady‐state Navier–Stokes flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes flow (Int. J. Num. Meth. Fluids 2003; 41:77–107). We analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as FEMLAB code in an appendix. Copyright © 2005 John Wiley & Sons, Ltd.

Subfields: Artificial Intelligence, Civil and Structural Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/33e77cced5da5548270b583492eb5709559bcd6f

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Citations in the corpus

Topology optimisation for natural convection problems (2014, methodology): “The same methodology was later extended to the Navier–Stokes equations [21, 22].”
Topology optimization using a mixed formulation: An alternative way to solve pressure load problems (2007, methodology): “For the sensitivity analysis COMSOL’s built-in automatic diﬀerentiation sets up the adjoint equations automatically (if needed) and the sensitivity information is found from the residual expressions for the design variable ﬁelds (see [25] for more details).”
A general formulation of structural topology optimization for maximizing structural stiffness (2011, background): “Analogous optimization problems can be found in optimal topological design of fluid flow channel ( Olesen et al. 2006 ).”
Topology optimization of heat conduction problems using the finite volume method (2006, background): “The seminal work Borrvall and Petersson (2003) has been extended to include the effect of inertia in Sigmund et al. (2003), Evgrafov (2004), Gersborg-Hansen et al. (2005a), and Olesen et al. (2005) , and new work on topology optimization of transport problems was presented in Thellner (2005).”
Topology Optimization of Turbulent Flows (2018, background): “Through testing, it has been found that selecting a sufficiently small Darcy number (Da ≈ 10−5 − 10−6) [43] is sufficient to yield nearly impermeable solidified regions.”
Parametric solutions involving geometry: A step towards efficient shape optimization (2014, background): “Particularly noteworthy is the work covered in [3, 4] where in order to characterize the topology of the domain, the design variables define a field (a function) which describes the geometry.”