Drag minimization and lift maximization in laminar flows via topology optimization employing simple objective function expressions based on body force integration

Kondoh, Tsuguo; Matsumori, Tadayoshi; Kawamoto, Atsushi

doi:10.1007/s00158-011-0730-z

Cited by 59 publications

(50 citation statements)

References 7 publications

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“…This is also done in [7,25], but in the latter, the compressible Navier-Stokes equations are considered. We also mention [21], which utilises the approach of Borrvall and Petersson [4] and the volume integral formulation. The shape derivatives for general volume and boundary objective functionals in Navier-Stokes flow have been derived in [26].…”

Section: Notation and Problem Formulationmentioning

confidence: 99%

Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach

Garcke¹,

Hecht²,

Hinze³

et al. 2016

Interfaces Free Bound.

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We consider shape and topology optimization for fluids which are governed by the Navier-Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field method uses a Ginzburg-Landau functional in order to approximate a perimeter penalization. We focus on surface functionals and carefully introduce a new modelling variant, show existence of minimizers and derive first order necessary conditions. These conditions are related to classical shape derivatives by identifying the sharp interface limit with the help of formally matched asymptotic expansions. Finally, we present numerical computations based on a Cahn-Hilliard type gradient descent which demonstrate that the method can be used to solve shape optimization problems for fluids with the help of the new approach.

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Section: Notation and Problem Formulationmentioning

confidence: 99%

Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach

Garcke¹,

Hecht²,

Hinze³

et al. 2016

Interfaces Free Bound.

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show abstract

“…One approach to tackle shape optimization problems that can yield rigorous mathematical results is to employ a phase field approximation, similar in spirit to Bourdin and Chambolle [8] that was applied to topology optimization (see also [4,27,35,38] and the reference cited therein), and has been recently used for drag minimization in stationary Stokes flow [12] and in stationary Navier-Stokes flow [11,13,14,24].…”

Section: Phase Field Formulationmentioning

confidence: 99%

A phase field approach to shape optimization in Navier–Stokes flow with integral state constraints

et al. 2018

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We consider the shape optimization of an object in Navier-Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we extend the results of earlier works concerning the existence of optimal shapes and the derivation of first order optimality conditions. The control variable is a phase field function that prescribes the shape and topology of the object, while the state variables are the velocity and the pressure of the fluid. In our analysis, we cover a multitude of constraints which include constraints on the center of mass, the volume of the fluid region, and the drag of the object. Finally, we present numerical results of the optimization problem that is solved using the variable metric projection type (VMPT) method proposed by Blank and Rupprecht, where we consider one example of topology optimization without constraints and one example of maximizing the lift of the object with a state constraint, as well as a comparison with earlier results for the drag minimization.

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“…Historically, topology optimization was first introduced in a stiffness maximization problem and soon developed for applications in the field of structural mechanics such as vibration problems and compliant mechanism problems . Subsequently, topology optimization has been applied in various physics systems, such as thermal problems, fluid dynamics, acoustic problems, and electromagnetics . Topology optimization methods for multiphysics problems have also been proposed …”

Section: Introductionmentioning

confidence: 99%

A design method of spatiotemporal optical pulse using level‐set based time domain topology optimization

Yasuda

Yamada

Nishiwaki

2018

Numerical Meth Engineering

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Recently, two emerging areas of photonics research, ultrafast photonics, and nanophotonics have started to come together. One of the main problems in this field is the precise control of spatial and temporal profiles of the optical pulses.In this paper, we propose a design method for user-specified spatiotemporal optical pulses using a level set-based time-domain topology optimization method.In the proposed method, the optimization problem is formulated based on time domain Maxwell equations so that the spatiotemporal optical pulses can be treated directly. The objective function is defined using the envelope information of the pulses, and an efficient way to calculate this information, based on calculations of the complex electromagnetic field, is introduced. A level set-based topology optimization method is applied to obtain optimized configurations.Using the proposed method, the spatiotemporal user-specified pulse profiles can be designed by modifying the structural details of the nanostructures through which the pulses propagate. As a simple example, we demonstrate that the optimized structures focus optical pulses into a single or multiple focal points with a user-specified pulse-width. The results show that the proposed method is able to design highly controlled spatiotemporal optical pulses by engineering the nanophotonic structure. KEYWORDSfinite difference methods, level sets, topology design INTRODUCTIONNanophotonics and ultrafast photonics are main subjects of research in the current photonics research field. Nanophotonics is the study of the behavior of light on the nanometer scale and of the interaction of nanometer-scale objects with light. Nanophotonics is an emerging technology with many applications 1-4 such as surface-enhanced Raman scattering, near field optical microscopy, and metamaterials. On the other hand, ultrafast photonics is the study of light and its interaction with matter on short timescales of less than a picosecond. 5,6 The main interest in this field is to investigate the processes that occur in atoms, molecules, and solids, such as the dynamics of and correlations between electrons.Nanophotonics and ultrafast photonics, which developed independently, have recently started to merge. [7][8][9] In the vicinity of a nanostructure, ultrafast pulses drastically change their spatial and temporal profiles. In other words, the spatiotemporal optical pulse profile can be arbitrarily changed by adjusting the surrounding nanostructure. Spatially and temporally controlled ultrafast pulses potentially offer an efficient way to enhance light-matter interactions at the nanoscale and provide a promising platform for information processing.Int J Numer Methods Eng. 2019;117:605-622.wileyonlinelibrary.com/journal/nme

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Drag minimization and lift maximization in laminar flows via topology optimization employing simple objective function expressions based on body force integration

Cited by 59 publications

References 7 publications

Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach

Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach

A phase field approach to shape optimization in Navier–Stokes flow with integral state constraints

A design method of spatiotemporal optical pulse using level‐set based time domain topology optimization

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