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

Garcke, Harald; Hinze, Michael; Kahle, Christian; Lam, Kei Fong

doi:10.1007/s10444-018-9586-8

Cited by 24 publications

(17 citation statements)

References 34 publications

(72 reference statements)

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“…Deng et al [58] used an Ersatz-material level set method to optimise two-phase flow, using with a phase field approach for the fluid-fluid interface. Garcke et al [59] extended their phase field approach to Navier-Stokes flow, presenting both in-depth mathematical analysis and optimisation results for minimum drag and maximum lift problems. Alonso et al [60] used a density-based approach to design laminar rotating swirl flow devices using a rotating axisymmetric model.…”

Section: Steady Laminar Flowmentioning

confidence: 99%

“…Of these 31 papers, 11 use an Ersatz-material, 11 use an adapted approach and only nine use a surface-capturing discretisation method. Lastly, the rest of the papers are distributed as follows: 5 using BESO [168,169,172,173,177]; 2 using phase field [42,59]; 1 using a discrete surface representation [63]; 1 using a geometry-projection method [138]; and 2 utilising the topological gradient [46,74]. Figure 6 shows the distribution of papers in these overall methods.…”

Section: Design Representationsmentioning

confidence: 99%

“…With 61 papers treating steady-state incompressible fluid flow only, it is proposed that the community not spend more time on this, especially for minimum dissipated energy and pressure drop. A large range of methods have been applied to these energy-based functionals, with only a minority of papers treating more complex objective functionals such as flow distribution and uniformity [33,50], diodicity [43,53,64,68,70,91], minimum drag and maximum lift [29,59].…”

Section: Steady-state Laminar Incompressible Flowmentioning

confidence: 99%

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A Review of Topology Optimisation for Fluid-Based Problems

Alexandersen

Andreasen

2020

Fluids

185

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This review paper provides an overview of the literature for topology optimisation of fluid-based problems, starting with the seminal works on the subject and ending with a snapshot of the state of the art of this rapidly developing field. “Fluid-based problems” are defined as problems where at least one governing equation for fluid flow is solved and the fluid–solid interface is optimised. In addition to fluid flow, any number of additional physics can be solved, such as species transport, heat transfer and mechanics. The review covers 186 papers from 2003 up to and including January 2020, which are sorted into five main groups: pure fluid flow; species transport; conjugate heat transfer; fluid–structure interaction; microstructure and porous media. Each paper is very briefly introduced in chronological order of publication. A quantititive analysis is presented with statistics covering the development of the field and presenting the distribution over subgroups. Recommendations for focus areas of future research are made based on the extensive literature review, the quantitative analysis, as well as the authors’ personal experience and opinions. Since the vast majority of papers treat steady-state laminar pure fluid flow, with no recent major advancements, it is recommended that future research focuses on more complex problems, e.g., transient and turbulent flow.

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Section: Steady Laminar Flowmentioning

confidence: 99%

Section: Design Representationsmentioning

confidence: 99%

Section: Steady-state Laminar Incompressible Flowmentioning

confidence: 99%

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A Review of Topology Optimisation for Fluid-Based Problems

Alexandersen

Andreasen

2020

Fluids

185

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“…However, numerical methods also for this approach encounter problems in situations where the sought shape needs to develop kinks and/or corners. This approach is proposed in Borrvall and Petersson (2003), and in a couple of papers investigated for hydrodynamic shape optimization problems Garcke et al (2015Garcke et al ( , 2016Garcke et al ( , 2018.…”

Section: Introductionmentioning

confidence: 99%

A novel p-harmonic descent approach applied to fluid dynamic shape optimization

Müller

Kühl

Siebenborn

et al. 2021

Struct Multidisc Optim

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We introduce a novel method for the implementation of shape optimization for non-parameterized shapes in fluid dynamics applications, where we propose to use the shape derivative to determine deformation fields with the help of the $$p-$$ p - Laplacian for $$p > 2$$ p > 2 . This approach is closely related to the computation of steepest descent directions of the shape functional in the $$W^{1,\infty }-$$ W 1 , ∞ - topology and refers to the recent publication Deckelnick et al. (A novel $$W^{1,\infty}$$ W 1 , ∞ approach to shape optimisation with Lipschitz domains, 2021), where this idea is proposed. Our approach is demonstrated for shape optimization related to drag-minimal free floating bodies. The method is validated against existing approaches with respect to convergence of the optimization algorithm, the obtained shape, and regarding the quality of the computational grid after large deformations. Our numerical results strongly indicate that shape optimization related to the $$W^{1,\infty }$$ W 1 , ∞ -topology—though numerically more demanding—seems to be superior over the classical approaches invoking Hilbert space methods, concerning the convergence, the obtained shapes and the mesh quality after large deformations, in particular when the optimal shape features sharp corners.

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“…(2019) the authors derive a coupled thermal fluid-structure model and in Deng, Liu & Wu (2017) and Garcke et al. (2018) a phase field model was used to describe the interface. Phase-field models have seen the most development in this area, due in part to the fact that solutions are quickly varying but continuous and allow for a standard approach through adjoint-based methods.…”

Section: Introductionmentioning

confidence: 99%