Journal ArticleDOI
Shape optimization of 3D viscous flow fields
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In this paper, a numerical solution technique for shape optimization problems of 3D viscous flow fields is presented, in which the traction method is applied by making use of a shape gradient.Abstract:
This article presents a numerical solution technique for shape optimization problems of steady-state, 3D viscous flow fields. In a previous study, the authors formulated shape optimization problems by considering the minimization of total dissipation energy in the domain of a viscous flow field, proposing a solution technique in which the traction method is applied by making use of a shape gradient. This approach was found to be effective for 2D problems for low Reynolds number flows. In the present study, the validity of the proposed solution technique is confirmed by extending its application to 3D problems.read more
Citations
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Journal ArticleDOI
Shape optimization of continua using NURBS as basis functions
TL;DR: In this article, the Galerkin method is applied to shape optimization problems of domains in which boundary value problems of partial differential equations are defined, and the finite element method using NURBS as basis functions in the GEM is applied.
Journal ArticleDOI
Numerical solution to shape optimization problems for non-stationary Navier-Stokes problems
TL;DR: Numerical results show that the shapes of the circle obstacle converge to wedge shapes for the cases of Reynolds numbers of 100 and 250, and the shape derivative of the energy loss is evaluated.
Journal ArticleDOI
Shape optimization of flow field improving hydrodynamic stability
Abstract: This paper presents a solution of a shape optimization problem of a flow field for delaying transition from a laminar flow to a turbulent flow. Mapping from an initial domain to a new domain is chosen as the design variable. Main problems are defined by the stationary Navier–Stokes problem and an eigenvalue problem assuming a linear disturbance on the solution of the stationary Navier–Stokes problem. The maximum value of the real part of the eigenvalue is used as an objective cost function. The shape derivative of the cost function is defined as the Frechet derivative of the cost function with respect to arbitrary variation of the design variable, which denotes the domain variation, and is evaluated using the Lagrange multiplier method. To obtain a numerical solution, we use an iterative algorithm based on the $$H^{1}$$
gradient method using the finite element method. To confirm the validity of the solution, a numerical example for two-dimensional Poiseuille flow with a sudden expansion is presented. Results reveal that a critical Reynolds number increases by the iteration of reshaping.
Journal ArticleDOI
Multi-Objective Shape Optimization in Forced Heat-Convection Fields
TL;DR: In this article, a multi-objective shape optimization problem using normalized objective functional is formulated for the total dissipated energy minimization problem and the temperature distribution prescribed problem in steady heat-convection fields.
Book ChapterDOI
Increasing the Critical Reynolds Number by Maximizing Energy Dissipation Problem
TL;DR: In this article, a two-dimensional lid-driven cavity flow was used as an objective cost function, and the domain volume was considered as a constraint cost function where the shape of the boundaries aside the top boundary was optimized.
References
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Journal ArticleDOI
Aerodynamic design via control theory
TL;DR: The purpose of the last three sections is to demonstrate by representative examples that control theory can be used to formulate computationally feasible procedures for aerodynamic design, Provided, therefore, that one can afford the cost of a moderate number of flow solutions.
Book
Introduction to shape optimization
Jan Sokołowski,Jean-Paul Zolésio +1 more
TL;DR: This book is motivated largely by a desire to solve shape optimization problems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems.
Book
Introduction to Shape Optimization: Shape Sensitivity Analysis
Jan Sokołowski,Jean-Paul Zolésio +1 more
TL;DR: In this article, modern functional analysis methods for the sensitivity analysis of some infinite-dimensional systems governed by partial differential equations are presented, and the main topics are treated in a general and systematic way.
Book
Optimal Shape Design for Elliptic Systems
TL;DR: The techniques of the calculus of variation and of optimization proved to be successful for several optimal shape design problems however these remain expensive both in the qualification of the engineers required to understand the method and in computing time.
Journal ArticleDOI
On optimum design in fluid mechanics
TL;DR: In this article, the change in energy dissipation due to a small hump on a body in a uniform steady flow is calculated, and the result is used in conjunction with the variational methods of optimal control to obtain the optimality conditions for four minimum-drag problems of fluid mechanics.