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
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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.
KeywordsConformal mappings Simply connected bodies Two-dimensional flows
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