https://www.cfd-online.com/W/index.php?title=Special:Contributions/Chb&feed=atom&limit=50&target=Chb&year=&month=CFD-Wiki - User contributions [en]2017-03-27T19:08:47ZFrom CFD-WikiMediaWiki 1.16.5https://www.cfd-online.com/Wiki/Gradient-based_methodsGradient-based methods2011-05-03T07:52:22Z<p>Chb: </p>
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<div>As its name means, gradient-based methods need the gradient of objective functions to design variables. The evaluation of gradient can be achieved by '''finite difference method''', '''linearized method''' or '''adjoint method'''. Both finite difference method and linearized method has a time-cost proportional to the number of design variables and not suitable for design optimization with a large number of design variables. Apart from that, finite difference method has a notorious disadvantage of subtraction cancellation and is not recommended for practical design application.<br />
<br />
Suppose a cost function <math>J</math> is defined as follows, <br />
<br />
<math>J=J(U,\alpha)</math><br />
<br />
where <math>U</math> and <math>\alpha</math> are the flow variable vector and the design variable vector respectively. <math>U</math> and <math>\alpha</math> are implicitly related through the flow equation, which is represented by a residual function driven to zero.<br />
<br />
<math>{R}(U(\alpha),\alpha)=0</math><br />
<br />
The sensitivity of the cost function <math>J</math> with respect to the design variables <math>\alpha</math>, that is <math>\frac{D J }{D \alpha_{i}}</math>, is needed for design purpose. The following is three main methods to obtain this sensitivity.<br />
<br />
Finite difference method is the most straightforward approach, where the sensitivity is calculated through finite difference, using different cost function values corresponding to different design variable input<br />
<br />
<math>\frac{DJ}{D\alpha_{i}}=\frac{J(\alpha_{i}+\delta \alpha)-J(\alpha_{i})}{\delta \alpha}</math><br />
<br />
The defect with this approach is that first of all, not efficient, because the computational cost is linearly proportional to the number of design variables which is practically too expensive. Second of all, the interval <math>\delta\alpha</math> is difficult to determine due to the concern of accuracy and machine error.<br />
<br />
<br />
Linearized method:<br />
<br />
[[Adjoint method]]:<br />
<br />
''Reference:Time-stepping for adjoint CFD codes from automatic differentiation, 2010, Faidon Christakopoulos, Dominic Jones and Jens D. Mueller''</div>Chbhttps://www.cfd-online.com/Wiki/Adjoint_methodAdjoint method2011-05-03T07:43:38Z<p>Chb: </p>
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<div>Adjoint method<br />
<br />
<br />
Some references which could be helpful:<br />
<br />
[1] Giannakoglou K.C., Papadimitriou D.I., "Chapter 4: Adjoint Methods for Shape Optimization", in Optimization and Computational Fluid Dynamics, Editors: D. Thevenin, G. Janiga, Springer-Verlag Berlin Heidelberg, 2008 (ISBN 978-3-540-72152-9).<br />
<br />
[2] O. Soto and R. Löhner, "On the Computation of Flow Sensitivities From Boundary Integrals", AIAA-04-0112 (2004).<br />
<br />
[3] C. Othmer, "A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows", Int. J. Num. Meth. Fluids, Vol. 58, pp. 861–877 (2008).<br />
<br />
[4] K. Morimoto, Y. Suzuki, N. Kasagi, "Optimal Shape Design of Compact Heat Exchangers Based on Adjoint Analysis of Momentum and Heat Transfer", J. Therm. Sci. Tech., Vol. 5, No. 1, pp.24-35 (2010).</div>Chbhttps://www.cfd-online.com/Wiki/Adjoint_methodAdjoint method2011-05-03T07:38:08Z<p>Chb: </p>
<hr />
<div>Adjoint method<br />
<br />
<br />
Some references which could be helpful:<br />
<br />
[1] Kyriakos C. Giannakoglou and Dimitrios I. Papadimitriou ,"Adjoint Methods for Shape Optimization", in Optimization and Computational Fluid Dynamics. Thévenin, Dominique; Janiga, Gábor (Eds.) 2008, XVI, 294 p. 149 illus.<br />
<br />
[2] O. Soto and R. Löhner, "On the Computation of Flow Sensitivities From Boundary Integrals", AIAA-04-0112 (2004).<br />
<br />
[3] C. Othmer, "A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows", Int. J. Num. Meth. Fluids, Vol. 58, pp. 861–877 (2008).<br />
<br />
[4] K. Morimoto, Y. Suzuki, N. Kasagi, "Optimal Shape Design of Compact Heat Exchangers Based on Adjoint Analysis of Momentum and Heat Transfer", J. Therm. Sci. Tech., Vol. 5, No. 1, pp.24-35 (2010).</div>Chbhttps://www.cfd-online.com/Wiki/Adjoint_methodAdjoint method2011-05-03T07:36:25Z<p>Chb: </p>
<hr />
<div>Adjoint method<br />
<br />
<br />
Some references which might be helpful:<br />
<br />
[1] Kyriakos C. Giannakoglou and Dimitrios I. Papadimitriou ,"Adjoint Methods for Shape Optimization", in Optimization and Computational Fluid Dynamics. Thévenin, Dominique; Janiga, Gábor (Eds.) 2008, XVI, 294 p. 149 illus.<br />
<br />
[2] O. Soto and R. Löhner, "On the Computation of Flow Sensitivities From Boundary Integrals", AIAA-04-0112 (2004).<br />
<br />
[3] C. Othmer, "A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows", Int. J. Num. Meth. Fluids, Vol. 58, pp. 861–877 (2008).<br />
<br />
[4] K. Morimoto, Y. Suzuki, N. Kasagi, "Optimal Shape Design of Compact Heat Exchangers Based on Adjoint Analysis of Momentum and Heat Transfer", J. Therm. Sci. Tech., Vol. 5, No. 1, pp.24-35 (2010).</div>Chbhttps://www.cfd-online.com/Wiki/Ahmed_bodyAhmed body2009-10-16T11:12:44Z<p>Chb: obsolete link removed</p>
<hr />
<div>== Brief Description ==<br />
[[Image:Ahmed.gif]]<br />
<br />
'''Fig. 1:''' Ahmed model. Dimensions are in mm (Fig. from [4])<br />
<br />
<br />
'''Description of the test case:'''<br />
The Ahmed body (Fig. 1) was first defined and its characteristics described in the experimental work of Ahmed [1]. Two configurations with slant angles of 25°and 35°are considered as a test case. For this configurations detailed LDA Measurements have been performed by Becker, Lienhart and Stoots [2,3] in the [[LSTM]] low-speed [[wind-tunnel]] with a cross-section of 1.87x1.4 m2 (width x height) with a bulk [[velocity]] of 40 m/s. The [[test-section]] of the [[wind-tunnel]] was 3/4 open (only ground plate present). The distance between the body and the plate representing the ground is 50 mm.<br />
In the experiment perform by the Ahmed [1], flow velocity was taken 60 m/s, Reynolds number was 4.29 million based on model length. <br />
<br />
== References: ==<br />
<br />
[1] S.R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984<br />
<br />
[2] H. Lienhart, S. Becker, Flow and Turbulence Structure in the Wake of a Simplified Car Model, SAE 2003 World Congress, SAE Paper 2003-01-0656, Detroit, Michigan, USA, 2003 <br />
<br />
[3] H. Lienhart, C. Stoots, S. Becker, Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model), DGLR Fach Symp. der AG STAB, Stuttgart University, 15-17 Nov., 2000 <br />
<br />
[4] C. Hinterberger, M. García-Villalba, W. Rodi, Large Eddy Simulation of flow around the Ahmed body. In "Lecture Notes in Applied and Computational Mechanics / The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains", R. McCallen, F. Browand, J. Ross (Eds.), Springer Verlag, ISBN: 3-540-22088-7, 2004 <br />
<br />
[5] S. Krajnovic, L. Davidson, Large eddy simulation of the flow around a simplified car model, SAE 2004 World Congress, SAE Paper 2004-01-0227, Detroit, Michigan, USA, 2004 <br />
<br />
[6] M. Minguez, R. Pasquetti, E. Serre, High-order large-eddy simulation of flow over the “Ahmed body” car model, Phys. Fluids, 20, 9, 2008<br />
<br />
<br />
{{stub}}</div>Chbhttps://www.cfd-online.com/Wiki/Ahmed_bodyAhmed body2005-11-21T09:47:36Z<p>Chb: </p>
<hr />
<div>[[Image:Ahmed.gif]]<br />
<br />
'''Fig. 1:''' Ahmed model. Dimensions are in mm (Fig. from [4])<br />
<br />
<br />
'''Description of the testcase:'''<br />
The Ahmed body (Fig. 1) was first defined and its characteristics described in the experimental work of Ahmed [1]. Two configurations with slant angles of 25°and 35°are considered as a test case. For this configurations detailed LDA Measurements have been performed by Becker, Lienhart and Stoots [2,3] in the LSTM low-speed wind-tunnel with a Cross-section of 1.87x1.4 m2 (width x height) with a bluk velocity of 40 m/s. The test-section of the wind-tunnel was 3/4 open (only ground plate present). The distance between the body and the plate representing the ground is 50 mm. <br />
<br />
A detailed test case description can be found [http://rz-ifh-pluto.rz.uni-karlsruhe.de/testcase/t4project.html here]<br />
<br />
'''References:'''<br />
<br />
[1] S.R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984<br />
<br />
[2] H. Lienhart, S. Becker, Flow and Turbulence Structure in the Wake of a Simplified Car Model, SAE 2003 World Congress, SAE Paper 2003-01-0656, Detroit, Michigan, USA, 2003 <br />
<br />
[3] H. Lienhart, C. Stoots, S. Becker, Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model), DGLR Fach Symp. der AG STAB, Stuttgart University, 15-17 Nov., 2000 <br />
<br />
[4] Hinterberger, M. Garcia-Villalba, W. Rodi, Large Eddy Simulation of flow around the Ahmed body. In "Lecture Notes in Applied and Computational Mechanics / The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains", R. McCallen, F. Browand, J. Ross (Eds.), Springer Verlag, ISBN: 3-540-22088-7, 2004 <br />
<br />
[5] S. Krajnovic, L. Davidson, Large eddy simulation of the flow around a simplified car model, SAE 2004 World Congress, SAE Paper 2004-01-0227, Detroit, Michigan, USA, 2004 <br />
<br />
<br />
{{stub}}</div>Chbhttps://www.cfd-online.com/Wiki/Ahmed_bodyAhmed body2005-11-21T09:43:45Z<p>Chb: </p>
<hr />
<div>[[Image:Ahmed.gif]]<br />
<br />
'''Fig. 1:''' Ahmed model. Dimensions are in mm (Fig. from [4])<br />
<br />
<br />
A detailed test case description can be found [http://rz-ifh-pluto.rz.uni-karlsruhe.de/testcase/t4project.html here]<br />
<br />
'''References:'''<br />
<br />
[1] S.R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984<br />
<br />
[2] H. Lienhart, S. Becker, Flow and Turbulence Structure in the Wake of a Simplified Car Model, SAE 2003 World Congress, SAE Paper 2003-01-0656, Detroit, Michigan, USA, 2003 <br />
<br />
[3] H. Lienhart, C. Stoots, S. Becker, Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model), DGLR Fach Symp. der AG STAB, Stuttgart University, 15-17 Nov., 2000 <br />
<br />
[4] Hinterberger, M. Garcia-Villalba, W. Rodi, Large Eddy Simulation of flow around the Ahmed body. In "Lecture Notes in Applied and Computational Mechanics / The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains", R. McCallen, F. Browand, J. Ross (Eds.), Springer Verlag, ISBN: 3-540-22088-7, 2004 <br />
<br />
[5] S. Krajnovic, L. Davidson, Large eddy simulation of the flow around a simplified car model, SAE 2004 World Congress, SAE Paper 2004-01-0227, Detroit, Michigan, USA, 2004 <br />
<br />
<br />
{{stub}}</div>Chbhttps://www.cfd-online.com/Wiki/Ahmed_bodyAhmed body2005-11-21T09:43:20Z<p>Chb: </p>
<hr />
<div>[[Image:Ahmed.gif]]<br />
'''Fig. 1:''' Ahmed model. Dimensions are in mm (Fig. from [4])<br />
<br />
<br />
A detailed test case description can be found [http://rz-ifh-pluto.rz.uni-karlsruhe.de/testcase/t4project.html here]<br />
<br />
'''References:'''<br />
<br />
[1] S.R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984<br />
<br />
[2] H. Lienhart, S. Becker, Flow and Turbulence Structure in the Wake of a Simplified Car Model, SAE 2003 World Congress, SAE Paper 2003-01-0656, Detroit, Michigan, USA, 2003 <br />
<br />
[3] H. Lienhart, C. Stoots, S. Becker, Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model), DGLR Fach Symp. der AG STAB, Stuttgart University, 15-17 Nov., 2000 <br />
<br />
[4] Hinterberger, M. Garcia-Villalba, W. Rodi, Large Eddy Simulation of flow around the Ahmed body. In "Lecture Notes in Applied and Computational Mechanics / The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains", R. McCallen, F. Browand, J. Ross (Eds.), Springer Verlag, ISBN: 3-540-22088-7, 2004 <br />
<br />
[5] S. Krajnovic, L. Davidson, Large eddy simulation of the flow around a simplified car model, SAE 2004 World Congress, SAE Paper 2004-01-0227, Detroit, Michigan, USA, 2004 <br />
<br />
<br />
{{stub}}</div>Chbhttps://www.cfd-online.com/Wiki/Ahmed_bodyAhmed body2005-11-21T09:42:53Z<p>Chb: </p>
<hr />
<div>[[Image:Ahmed.gif]]<br />
Fig. 1: Ahmed model. Dimensions are in mm (Fig. from [4])<br />
<br />
<br />
A detailed test case description can be found [http://rz-ifh-pluto.rz.uni-karlsruhe.de/testcase/t4project.html here]<br />
<br />
References: <br />
[1] S.R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984<br />
<br />
[2] H. Lienhart, S. Becker, Flow and Turbulence Structure in the Wake of a Simplified Car Model, SAE 2003 World Congress, SAE Paper 2003-01-0656, Detroit, Michigan, USA, 2003 <br />
<br />
[3] H. Lienhart, C. Stoots, S. Becker, Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model), DGLR Fach Symp. der AG STAB, Stuttgart University, 15-17 Nov., 2000 <br />
<br />
[4] Hinterberger, M. Garcia-Villalba, W. Rodi, Large Eddy Simulation of flow around the Ahmed body. In "Lecture Notes in Applied and Computational Mechanics / The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains", R. McCallen, F. Browand, J. Ross (Eds.), Springer Verlag, ISBN: 3-540-22088-7, 2004 <br />
<br />
[5] S. Krajnovic, L. Davidson, Large eddy simulation of the flow around a simplified car model, SAE 2004 World Congress, SAE Paper 2004-01-0227, Detroit, Michigan, USA, 2004 <br />
<br />
<br />
{{stub}}</div>Chbhttps://www.cfd-online.com/Wiki/Ahmed_bodyAhmed body2005-11-21T09:39:50Z<p>Chb: </p>
<hr />
<div>[[Image:Ahmed.gif]]<br />
Fig. 1: Ahmed model. Dimensions are in mm (Fig. from [4])<br />
<br />
<br />
A test case description can be found at<br />
<br />
[http://rz-ifh-pluto.rz.uni-karlsruhe.de/testcase/t4project.html Ahmed body test case]<br />
<br />
References: <br />
[1] S.R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984<br />
<br />
[2] H. Lienhart, S. Becker, Flow and Turbulence Structure in the Wake of a Simplified Car Model, SAE 2003 World Congress, SAE Paper 2003-01-0656, Detroit, Michigan, USA, 2003 <br />
<br />
[3] H. Lienhart, C. Stoots, S. Becker, Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model), DGLR Fach Symp. der AG STAB, Stuttgart University, 15-17 Nov., 2000 <br />
<br />
[4] Hinterberger, M. Garcia-Villalba, W. Rodi, Large Eddy Simulation of flow around the Ahmed body. In "Lecture Notes in Applied and Computational Mechanics / The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains", R. McCallen, F. Browand, J. Ross (Eds.), Springer Verlag, ISBN: 3-540-22088-7, 2004 <br />
<br />
[5] S. Krajnovic, L. Davidson, Large eddy simulation of the flow around a simplified car model, SAE 2004 World Congress, SAE Paper 2004-01-0227, Detroit, Michigan, USA, 2004 <br />
<br />
<br />
{{stub}}</div>Chbhttps://www.cfd-online.com/Wiki/File:Ahmed.gifFile:Ahmed.gif2005-11-21T09:36:26Z<p>Chb: Ahmed model. Dimensions are in mm.</p>
<hr />
<div>Ahmed model. Dimensions are in mm.</div>Chbhttps://www.cfd-online.com/Wiki/Ahmed_bodyAhmed body2005-11-21T07:45:28Z<p>Chb: </p>
<hr />
<div><br />
A test case description can be found at<br />
<br />
http://rz-ifh-pluto.rz.uni-karlsruhe.de/testcase/t4project.html</div>Chb