Abstract
The purpose of this paper is to investigate the shape determination of a rigid body located in incompressible fluid flow in two dimensions. This state problem is controlled by the Stokes equations. The derivative of the cost functional is given by an adjiont method. The level set method is successfully utilized as the minimization algorithm. Since the level set method is implemented in an Eulerian framework, the computational cost is moderate. Finally, a numerical example is presented to illustrate the effectiveness and validity of the proposed algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Modhammadi, B., Pironneau, O.: Applied shape optimization for fluids. Clarendon Press, Oxford (2001)
Ito, K., Kunish, K., Li, Z.: Level-set function approach to an inverse interface problem. Inverse Problem 17, 1225–1242 (2001)
Allaire, G., Jouve, F., Toader, A.M.: A level-set method for shape optimization. C. R. Acad. Sci. Paris, Ser.I 334, 1125–1130 (2001)
Allair, G., Jouve, F., Toader, A.M.: Structural optimization using sensitivitity analysis and a level-set method. Journal of Computational Physics 194, 393–393 (2004)
Wang, M.Y., Wang, X.M., Guo, D.M.: A level set method for structural topology optimization. Comp. Meth. Appl. Mech. Eng. 192, 227–246 (2003)
Osher, S., Sethian, J.A.: Fronts propagating with curvature-cependent speed: algotithms based on Hamilton-Jacobi formulations. J. Comp. Phys. 79, 12–49 (1988)
Sethian, J.A.: Level set methods and fast marching methods: evolving intetfaces in computational geometry, fluid mechanics, computer vision and materials science. Cambridge University Press, Cambridge (1999)
Burger, M.: A level set method for inverse problems. Inverse Problem 17, 1327–1355 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhao, JP. (2011). Shape Determination of the Rigid Body Located in Incompressible Flow. In: Shen, G., Huang, X. (eds) Advanced Research on Computer Science and Information Engineering. CSIE 2011. Communications in Computer and Information Science, vol 152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21402-8_49
Download citation
DOI: https://doi.org/10.1007/978-3-642-21402-8_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21401-1
Online ISBN: 978-3-642-21402-8
eBook Packages: Computer ScienceComputer Science (R0)