Using a Galerkin Method to Calculate the Velocity of Vortex Wake Sheets

Mathew Topper, David Forehand, Ian Bryden

Research output: Contribution to conferencePaper

Abstract / Description of output

Boundary element methods are commonly used in the fields of aeronautics and hydrodynamics to calculate flows about bluff and lifting bodies. When lifting bodies are considered, a vortex sheet, emanating from the lifting body’s trailing edge, must be included in the model in order to correctly account for the lift. Low order discretisations, particularly for unsteady simulations, do not calculate sufficiently accurate velocities on these sheets, which then leads to instabilities and erroneous solutions. As such, many efforts have been made to develop boundary element lifting solutions using higher order discretisations. For the vortex wake sheet, only the difference in potential between the top and bottom of the sheet is known and thus differentiating this quantity does not provide the required average of the velocity between the top and bottom of the sheet. The only available method to calculate the velocity of a vortex sheet is to directly differentiate the boundary integral equation producing a hypersingular boundary integral equation. Recent work has shown that a Galerkin limiting technique can be used to calculate the solution to the hyper-singular boundary integral equation at the edges and corners of high order piecewise elements in three dimensions. This paper considers the application of the aforementioned Galerkin method to solving for the velocity on vortex wake sheets in boundary element methods. Results will be presented along with a discussion of various improvements that can be made in order to enhance the stability of the method.
Original languageEnglish
Number of pages6
Publication statusPublished - 2011
EventIABEM 2011 - Brescia, Italy
Duration: 5 Sept 20118 Sept 2011


ConferenceIABEM 2011


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