A gradient-based shape optimization scheme via isogeometric exact reanalysis

2018 ◽  
Vol 35 (8) ◽  
pp. 2696-2721 ◽  
Author(s):  
Chensen Ding ◽  
Xiangyang Cui ◽  
Guanxin Huang ◽  
Guangyao Li ◽  
K.K. Tamma ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Shape Optimization ◽  
Difference Method ◽  
Computer Aided Design ◽  
Content Type ◽  
Optimization Framework ◽  
Computer Aided ◽  
Gradient Based ◽  
The Finite Difference Method

PurposeThis paper aims to propose a gradient-based shape optimization framework in which traditional time-consuming conversions between computer-aided design and computer-aided engineering and the mesh update procedure are avoided/eliminated. The scheme is general so that it can be used in all cases as a black box, no matter what the objective and/or design variables are, whilst the efficiency and accuracy are guaranteed.Design/methodology/approachThe authors integrated CAD and CAE by using isogeometric analysis (IGA), enabling the present methodology to be robust and accurate. To overcome the difficulty in evaluating the sensitivities of objective and/or constraint functions by analytic method in some cases, the authors adopt the finite difference method to calculate these sensitivities, thereby providing a universal approach. Moreover, to further eliminate the inefficiency caused by the finite difference method, the authors advance the exact reanalysis method, the indirect factorization updating (IFU), to exactly and efficiently calculate functions and their sensitivities, which guarantees its generality and efficiency at the same time.FindingsThe proposed isogeometric gradient-based shape optimization using our IFU approach is reliable and accurate, as well as general and efficient.Originality/valueThe authors proposed a gradient-based shape optimization framework in which they first integrate IGA and the proposed exact reanalysis method for applicability to structural response and sensitivity analysis.

Natural convection inside a C-shaped nanofluid-filled enclosure with localized heat sources

2014 ◽  
Vol 24 (8) ◽  
pp. 1954-1978 ◽  
Author(s):  
M.A. Mansour ◽  
M.A. Bakeir ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Volume Fraction ◽  
Cu Nanoparticles ◽  
Content Type ◽  
The Finite Difference Method

Purpose – The purpose of this paper is to investigate natural convection fluid flow and heat transfer inside C-shaped enclosures filled with Cu-Water nanofluid numerically using the finite difference method. Design/methodology/approach – In this investigation, the finite difference method is employed to solve the governing equations with the boundary conditions. Central difference quotients were used to approximate the second derivatives in both the X and Y directions. Then, the obtained discretized equations are solved using a Gauss-Seidel iteration technique. Findings – It was found from the obtained results that the mean Nusselt number increased with increase in Rayleigh number and volume fraction of Cu nanoparticles regardless aspect ratio of the enclosure. Moreover the obtained results showed that the rate of heat transfer increased with decreasing the aspect ratio of the cavity. Also, it was found that the rate of heat transfer increased with increase in nanoparticles volume fraction. Also at low Rayleigh numbers, the effect of Cu nanoparticles on enhancement of heat transfer for narrow enclosures was more than that for wide enclosures. Originality/value – This paper is relatively original for considering C-shaped cavity with nanofluids.

A Software Tool for Determining Steady-State Temperature Distributions in a Square Domain by the Finite-Difference Method

2007 ◽  
Vol 35 (4) ◽  
pp. 305-315
Author(s):  
K. A. Oladejo ◽  
D. A. Adetan ◽  
O. A. Bamiro
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Computer Aided Design ◽  
Linear Equations ◽  
Analytical Techniques ◽  
Software Tool ◽  
Transfer Equations ◽  
The Finite Difference Method

This paper presents the development of an interactive program (called SSTDD) to solve two-dimensional conduction heat transfer equations in a square domain using the finite-difference method. The development of the tool (based on a computer-aided design package), on a Visual BASIC 6.0 platform, involved the application of the heat transfer equations and the appropriate boundary conditions to a square domain. The finite-difference method was used to express the elliptic differential equation in a form suitable for numerical solution. The system of linear equations generated was solved by the Gauss–Seidel iterative technique. The SSTDD model was tested by using problems solved by conventional analytical techniques. The results generated by the model and the analytical method were in good agreement. Hence the model can be used to solve practical engineering problems, with good accuracy, and also as a demonstration tool to students in the area of design and heat transfer of mechanical engineering.

Modelling of a desiccant rotor by using the collocation method

2013 ◽  
Vol 24 (1) ◽  
pp. 201-220 ◽  
Author(s):  
Marcello Aprile ◽  
Mario Motta
Keyword(s):  
Mass Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Heat And Mass Transfer ◽  
Collocation Method ◽  
Difference Method ◽  
Transfer Problem ◽  
Operating Conditions ◽  
Content Type ◽  
The Finite Difference Method

Purpose – This article aims to develop a fast numerical method for solving the one-dimensional heat and mass transfer problem within a desiccant rotor. Design/methodology/approach – The collocation method is used for discretizing the axial dimension and reducing the number of dependent variables. The resulting system of equation is then solved through backward differentiation formulas. Findings – The numerical results obtained here focus on verifying the accuracy and the computation time of the proposed method with respect to the finite difference method. The proposed numerical solution method resulted faster than, and as much accurate as, the finite difference method, over a large range of operating conditions that are of interest in desiccant cooling applications. Research limitations/implications – For heat and mass transfer analysis, constant average transfer coefficients are used. The results are calculated for NTU between 2 and 15 and for Le number between 0.5 and 2. Practical implications – The results can be used in designing desiccant heat exchangers and desiccant cooling systems including complex rotor arrangements. Originality/value – Different from other simplified solution techniques, the proposed method relies on few parameters that retain physical meaning and applies also to complex rotor configurations.

scholarly journals On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 70
Author(s):  
Farzad Mohebbi ◽  
Ben Evans
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Shape Optimization ◽  
Difference Method ◽  
Optimization Problems ◽  
Step Length ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Gradient Based

This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic shape optimization for an airfoil in steady inviscid transonic flows. The airfoil surfaces were parameterized using Bezier curves. The Bezier curve control points were considered as design variables and the finite-difference method was used to compute the gradient of the objective function (drag-to-lift ratio) with respect to the design variables. An exact explicit expression was derived for the step length in gradient-based shape optimization problems. It was shown that the derived step length was independent of the method used for calculating the gradient (adjoint method, finite-difference method, etc.). The obtained results reveal the accuracy of the derived step length.

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