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Applied mathematics, Fluids and plasma physics, Applied mechanics
In this paper we outline an expeditious numerical procedure to calculate the Stokes flow in a corner due to the rotation of a scraping circular boundary. The method is also applicable to other wedge geometries. We employ a collocation technique utilising a basis of eddy (similarity) functions introduced by Moffatt (1964) that allows us to satisfy automatically the governing equations for the streamfunction and all the boundary conditions on the surface of the wedge. The circular honing problem thereby becomes one-dimensional requiring only the satisfaction of conditions on the circular boundary. The advantage of using the Moffatt eddy functions as a basis in wedge geometry is clear and the technique greatly reduces many of the concerns with accuracy and time expenditure associated with alternative numerical methods. An investigation of the details of the eddy structure for our particular geometry is presented.
Hill, C.P.: Eddy Structures Induced Within a Wedge by a Honing Circular Arc, Theoretical and Computational Fluid Dynamics, Volume 15, Number 1 / September, 2001, pp.1-10.