Optimization of unsteady incompressible Navier–Stokes flows using variational level set method

Deng, Yongbo; Zhang, Ping; Liu, Yongshun; Wu, Yihui; Liu, Zhenyu

doi:10.1002/fld.3721

Cited by 27 publications

(13 citation statements)

References 45 publications

(75 reference statements)

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“…The adjoint sensitivity analysis in the context of fluidic topology optimization has been used by Deng et al [5,14], Zhou et al [9] and Kreissl et al [11,15] using a finite element method for the Navier-Stokes problem. The adjoint analysis in the context of the lattice Boltzmann method was pioneered by Tekitek et al for the optimization of relaxation rates of a multiple-relaxation-time LBM [16].…”

Section: Introductionmentioning

confidence: 99%

Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method

Geier

Liu

et al. 2014

Computers & Mathematics with Applications

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a b s t r a c tA discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice Boltzmann method (LBM) with multiple-relaxation-times (MRT) is developed. The lattice Boltzmann fluid solver is supplemented by a porosity model using a Darcy force. The continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels. The adjoint LBM equation, which is used to compute the gradient of the optimization objective with respect to the design variables, is derived in moment space and found to be as simple as the original LBM. The moment based spatial momentum derivatives used to express the discrete objective functional (cost function) have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field. This is particularly useful if dissipation is a design criterion as demonstrated in this paper. The method is validated by a detailed comparison with results obtained by Borrvall et al. for Stokes flow. While their approach is only valid for Stokes flow (i.e. very low Reynolds numbers) our approach in its present form can in principle be applied for flows of different Reynolds numbers just like the Navier-Stokes equation based approaches. This point is demonstrated with a bending pipe example for various Reynolds numbers.

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Section: Introductionmentioning

confidence: 99%

Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method

Geier

Liu

et al. 2014

Computers & Mathematics with Applications

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“…Topology optimization, first proposed in Ref. 11 for structural mechanics, has been expanded to the field of fluid mechanics through the introduction of a source term into the Stokes, [12][13][14] laminar, 15 turbulent 8 steady and unsteady, 16 flow equations. This source term acts as a design variable for each grid cell and its corresponding field is controlled to minimize an objective function.…”

Section: Introductionmentioning

confidence: 99%

A Continuous Adjoint Framework for Shape and Topology Optimization and their Synergistic Use

Papoutsis‐Kiachagias

Koch

Gkaragounis

et al. 2018

2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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In fluid mechanics, two of the most widely used optimization approaches are shape and topology optimization, which are generally treated as mutually-exclusive. This paper presents a general continuous adjoint formulation for both shape and topology optimization, focusing on (a) crucial aspects of computing accurate shape sensitivity derivatives such as the differentiation of the turbulence model PDEs and the proper treatment of grid sensitivities and (b) a synergistic, sequential application of topology and shape optimization, in which topology is used to define a preliminary solution from which shape optimization can be initiated. To achieve this, a transition process is used to accurately represent and parameterize the topological solution with NURBS surfaces. The flow cases presented in this work and the in-house code pertaining to the optimization and transition process are implemented within OpenFOAM. Results from purely aerodynamic as well as multidisciplinary applications including Conjugate Heat Transfer (CHT) are presented.

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“…First proposed in [5] for the design of structural mechanics, topology optimization (TopO) has been expanded to the field of fluid mechanics through the introduction of a blockage term (β) into the Stokes [2,6,11] and laminar [10], turbulent [20] steady and unsteady, [15,8], flow equations. This blockage term acts as a design variable for each grid cell and its corresponding field is controlled to minimize an objective function.…”

Section: Introductionmentioning

confidence: 99%

Transition from adjoint level set topology to shape optimization for 2D fluid mechanics

2017

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Most optimization problems in the field of fluid mechanics can be classified as either topology or shape optimization. Although topology and shape have been considered mutually exclusive optimization methods since their inception, it is conceivable that they will find choicest solutions in tandem, with shape optimization refining a solution found by topology. However, linking the topology optimization problem to that of shape is not trivial and, to the authors' knowledge, has yet to be formally attempted. This paper proposes a novel transitional procedure that post-processes 2D adjoint topology solutions, fitting the interface between the solid and fluid topological domains to create a parameterized solution which can be used as either a CAD-compatible representation of the interface or a source for grid generation from which a shape optimization loop can be initialized. The interface to be fit can be extracted from any topological field with distinct fluid and solid domains, meaning that the proposed transition process is independent of the topology approach utilized. To conveniently describe the interface between the solid and fluid topological domains, the topology optimization process employed in this paper is filtered using the level set method. The interface is fit with non-uniform rational B-spline (NURBS) curves through application of sensitivities garnered from the solution of an auxiliary inverse design problem which aims at reducing the difference between signed-distance fields generated about both the NURBS curve being optimized and the section of interface being fit. The geometry defined by the fit NURBS curves is then (optionally) used to build a boundary-fitted grid on which a shape optimization loop is performed. The parameterized result of the topology to shape transition process is compared to that of shape optimization in 2D cases with internal, incompressible fluid flows.

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Optimization of unsteady incompressible Navier–Stokes flows using variational level set method

Cited by 27 publications

References 45 publications

Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method

Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method

A Continuous Adjoint Framework for Shape and Topology Optimization and their Synergistic Use

Transition from adjoint level set topology to shape optimization for 2D fluid mechanics

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