On the use of conformal mapping for the computation of hydrodynamic forces acting on bodies of arbitrary shape in viscous flow. Part 1: simply connected body

Some aspects of the force and moment computations in incompressible and viscous flows are revisited. The basic idea was developed in Quartapelle and Napolitano (AIAA J. 21:991–913, 1983). They formulated the way to compute the force and moment without explicitly calculating the pressure. The princip...

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Bibliographic Details
Published in:Journal of engineering mathematics 2008-02, Vol.60 (2), p.209-220
Main Authors: Scolan, Yves-Marie, Etienne, Stéphane
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Engineering Sciences
Fluids mechanics
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Mechanics
Theoretical and Applied Mechanics
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Summary:Some aspects of the force and moment computations in incompressible and viscous flows are revisited. The basic idea was developed in Quartapelle and Napolitano (AIAA J. 21:991–913, 1983). They formulated the way to compute the force and moment without explicitly calculating the pressure. The principle is to project Navier–Stokes equations on a set of functions. Surprisingly these functions have a meaning in potential theory. They are precisely the solutions which give the added masses and added moment of inertia for potential flow. By revisiting this problem for two-dimensional flows in unbounded liquid, a general identity giving the added masses and added moment of inertia is formulated. To this end a conformal-mapping technique is used to transform the fluid domain. Once the potential solution has been obtained, the projection method by Quartapelle and Napolitano is implemented. In addition an a posteriori computation of the pressure is described. Applications illustrate the present study.
ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-007-9158-2