A BROYDEN NUMERICAL KUTTA CONDITION FOR AN UNSTEADY PANEL METHOD

Article type: Research Article

Authors: Liu, Pengfei | Bose, Neil | Colbourne, Bruce

Affiliations: Institute for Marine Dynamics, National Research Council Canada, St. John's, Canada | Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John's, Canada

Abstract: In panel methods, numerical Kutta conditions are applied in order to ensure that pressure differences between the surfaces at the trailing edges of lifting surface elements are close to zero. Previous numerical Kutta conditions for 3-D panel methods have focused on use of the Newton-Raphson iterative procedure. For extreme unsteady motions, such as for oscillating hydrofoils or for a propeller behind a blockage, the Newton-Raphson procedure can have severe convergence difficulties. The Broyden iteration, a modified Newton-Raphson iteration procedure, is applied here to obtain improved convergence behavior. Using the Broyden iteration increases the reliability, robustness and in many cases computing efficiency for unsteady, multi-body interactive flows. This method was tested in a time domain code for an ice class propeller in both open water flow and during interaction with a nearby ice blockage. Predictions showed that the method was effective in these extreme flows.

Journal: International Shipbuilding Progress, vol. 49, no. 4, pp. 263-273, 2002