A combined boundary integral and vortex method for the numerical study of three-dimensional fluid flow systems

Abstract

Vortex methods using vorticity–velocity formulations have become an increasingly powerful and popular means of studying complex fluid flow systems. The problem of combining an integral equation method and grid-free discrete vortex method (DVM) when studying three-dimensional wall-bounded flows is considered. While the normal boundary condition is satisfied by means of a boundary integral equation (BIE), we also consider the problem of recovering pressure from given vorticity and velocity fields when using Lagrangian DVMs in terms of a BIE. For validation purposes, vortical flow past a sphere and past a flat plate are considered, for which the commonly used method of images is available. Results of near-wall boundary-layer flow simulations are then presented as an illustration of the numerical scheme. The importance of hairpin vortices is highlighted. Finally, results on wall compliance fluid flow are displayed emphasizing the versatility of the numerical method.

Keywords:

• boundary integral method
• discrete vortex method
• three-dimensional grid-free fluid flow simulation
• near-wall boundary layer
• turbulence flow structures

2010 AMS Subject Classifications :

• 31A10
• 76M23
• 35Q30
• 76F40
• 76F65

Acknowledgements

The authors dedicate this work in the memory of Prof. Peter W. Carpenter. They also thank the referees who improved the clarity of this paper with their valuable comments. The first author thank Prof. H.M. Thompson for his support and his valuable comments on this paper.