A boundary element method for the numerical investigation of near-wall fluid flow with vortex method simulation - Khatir, Z. (Engineering analysis with boundary elements, 2004)
When using discrete vortex methods to model incompressible fluid flow over a body of arbitrary geometry, it is necessary to construct an irrotational field to impose the impermeability condition at the surface of the object. In order to achieve this impermeability, a boundary integral equation based on the single- layer representation for the velocity potential is used. This three-dimensional exterior Neumann problem is specifically formulated in terms of a source/sink boundary integral equation. The solution to this integral equation is then coupled with an interpolation procedure which smoothes the transition between near-wall and interior regimes. We describe the numerical scheme embedding this strategy and discuss its accuracy and efficiency. For validation purposes, we consider the potential and vortical flow past a sphere, for which an analytical solution and the commonly used method of images are available. This is then followed by a second example of potential flow past a compliant wall including a check on leakage proving the numerical procedure to be effective. Finally, the newly developed algorithm is also tested against the method of images when conducting vortex flow calculations over a flat plate. Numerical results demonstrating the versatility of the method are presented when studying near- wall turbulence and show good agreement with experimental observations.