Application of a Zonal Decomposition Algorithm, to Improve the Computational Operation Count of the Discrete Vortex Method Calculation. G.U. Aero Report 9711.

Taylor, I.J. and Vezza, M. (1997) Application of a Zonal Decomposition Algorithm, to Improve the Computational Operation Count of the Discrete Vortex Method Calculation. G.U. Aero Report 9711. Technical Report. Department of Aerospace Engineering, University of Glasgow.

Abstract

The vortex method has proved a very useful tool for analysing separated, incompressible flow around two dimensional bodies. The method utilises a grid free, Lagrangian approach, to discretise the vorticity field into a series of vortex particles. These particles are then tracked in time, using the Biot-Savart law to calculate the velocity field. This calculation requires the velocity of each vortex to be found as a sum over all other particles in the flow field. A Discrete Vortex Method (DVM) has been developed at the Department of Aerospace Engineering, University of Glasgow. Currently, this vortex method uses a direct summation technique, which although relatively simple, leads to a computational operation count proportional to the square of the number of particles. In calculations that use a large number of particles, such as bluff body models, the direct summation technique becomes prohibitively expensive. A new algorithm for the velocity calculation has now been included in the DVM and is presented in this report. The procedure uses a zonal decomposition algorithm for the velocity summation. This allows the effect of groups of particles on the velocity to be calculated using a single series expansion, thus significantly reducing the operation count of the calculation. The algorithm utilises a hierarchical technique, so that the largest possible group of particles is used for each series expansion. The resulting operation count is 0(N+NlogN), and therefore offers a significant improvement over the direct summation method.

• Item Type: Research Reports or Papers (Technical Report)
• Status: Published
• Glasgow Author(s) Enlighten ID: Vezza, Dr Marco and Taylor, Dr Ian
• Authors: Taylor, I.J., and Vezza, M.
• College/School: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• Publisher: Department of Aerospace Engineering, University of Glasgow
• Copyright Holders: Copyright © 1997
• Publisher Policy: Reproduced with the permission of the Department