Shape optimization of 3D viscous flow fields

Katamine, Eiji; Nagatomo, Yuya; Azegami, Hideyuki

doi:10.1080/17415970802166352

Cited by 10 publications

(3 citation statements)

References 11 publications

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“…Subsequently, J. Haslinger and R. A. Makinen [4], B. Mohammadi and O. Pironneau [5], and M. Moubachir and J. P. Zolesio [6] constructed fundamental frameworks of flow-field shape-optimization problems. Recently, many researchers are examining the topic [7][8][9][10]. Efficient but accurate numerical methods must be used for such flow computations within an optimization process.…”

Section: Introductionmentioning

confidence: 99%

Optimal Design by Adaptive Mesh Refinement on Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition

Nakazawa

Nakajima

2019

IIS

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This paper presents optimal design using Adaptive Mesh Refinement (AMR) with shape optimization method. The method suppresses time periodic flows driven only by the non-stationary boundary condition at a sufficiently low Reynolds number using Snapshot Proper Orthogonal Decomposition (Snapshot POD). For shape optimization, the eigenvalue in Snapshot POD is defined as a cost function. The main problems are non-stationary Navier-Stokes problems and eigenvalue problems of POD. An objective functional is described using Lagrange multipliers and finite element method. Two-dimensional cavity flow with a disk-shaped isolated body is adopted. The non-stationary boundary condition is defined on the top boundary and non-slip boundary condition respectively for the side and bottom boundaries and for the disk boundary. For numerical demonstration, the disk boundary is used as the design boundary. Using H 1 gradient method for domain deformation, all triangles over a mesh are deformed as the cost function decreases. To avoid decreasing the numerical accuracy based on squeezing triangles, AMR is applied throughout the shape optimization process to maintain numerical accuracy equal to that of a mesh in the initial domain. The combination of eigenvalues that can best suppress the time periodic flow is investigated.

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Section: Introductionmentioning

confidence: 99%

Optimal Design by Adaptive Mesh Refinement on Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition

Nakazawa

Nakajima

2019

IIS

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“…This reshaping method is referred to as the traction method. Applications of the traction method to the shape optimization problems for stationary Navier-Stokes problems were presented in previous studies [11,12]. Another method by which to overcome the irregularity of the shape derivatives for a moving boundary was proposed using the Laplace operator on the boundary [5].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution to shape optimization problems for non-stationary Navier-Stokes problems

et al. 2010

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The present paper describes a numerical solution of shape optimization problems for nonstationary Navier-Stokes problems. As a concrete example, we consider the problem of finding the shape of an obstacle in a flow field in order to minimize the energy loss integral for an assigned time interval. The primary goal of the present paper is to demonstrate the evaluation of the shape derivative of the energy loss. The traction method is used for the reshaping algorithm. Numerical results show that the shapes of the circle obstacle converge to wedge shapes for the cases of Reynolds numbers of 100 and 250.

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“…This method has been applied to many shape optimization problems, such as elastic problems (Azegami et al, 1995;Shimoda et al, 1996), heat conduction problems (Katamine et al, 2001(Katamine et al, , 2003, and viscous flow problems (Katamine and Azegami, 1994;Katamine et al, 2005Katamine et al, , 2007Katamine et al, , 2009) in mechanical engineering. The traction method applies the gradient method of a distributed system and uses the shape gradient function of the domain variation that is theoretically derived from the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Shape design of heat convection fields based on the adjoint method

Katamine

2018

Mechanical Engineering Reviews

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The utilization of shape design to improve heat transfer characteristics in heat convection fields is an important subject in engineering. This review paper explains a numerical solution for the shape design problems involving steady and unsteady heat convection fields. Reshaping for the shape design is carried out by traction method, which is proposed as an approach to solving shape optimization problems. The traction method is a shape optimization method with some advantages such as deformation analysis of pseudo-elastic bodies can be used in the shape update analysis and smoothness in shape update can be maintained. In steady-state heat convection fields, shape design problems that control the temperature distribution in the sub-domains of the heat convection field are introduced. The square integration error between the actual temperature distribution and the target temperature distribution in the specified sub-domains is employed as the objective functional for the shape design. In unsteady heat convection fields, two shape design problems are shown; these problems also involve control of the temperature distribution in sub-domains of the field. In the first problem, in a manner similar to the steady-state problem, the square integration error of the sub-domains during the specified period of time is used as the objective functional. In the second problem, a multi-objective shape design problem that utilizes a normalized objective functional is formulated for the problem to prescribe the temperature distribution and the total dissipated energy minimization problem. The shape gradient of these shape design problems for steady and unsteady fields is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Numerical analysis programs for shape design problems using the traction method are developed, and the validity of the demonstrated method is confirmed by results of 2D numerical analyses.

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Shape optimization of 3D viscous flow fields

Cited by 10 publications

References 11 publications

Optimal Design by Adaptive Mesh Refinement on Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition

Optimal Design by Adaptive Mesh Refinement on Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition

Numerical solution to shape optimization problems for non-stationary Navier-Stokes problems

Shape design of heat convection fields based on the adjoint method

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