A boundary element method for the numerical investigation of near-wall fluid flow with vortex method simulation

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...

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Published in:	Engineering analysis with boundary elements Vol. 28; no. 11; pp. 1405 - 1416
Main Author:	Khatir, Z.
Format:	Journal Article
Language:	English
Published:	Oxford Elsevier 01.11.2004
Subjects:	Boundary-integral methods Computational techniques Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) General theory Mathematical methods in physics Physics Irrotational flow Neumann problem 3D-boundary element method Boundary integral method Spheres Near-wall flow simulation Experimental study Surface states Leaks Image method Potential flow Vortex method Incompressible flow Integral equations Exterior problem Vortices Source sink boundary integral equation Modelling Vortex flow Incompressible fluid Boundary element method Flat plate Flow potential
ISSN:	0955-7997
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Abstract	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.
AbstractList	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.
Author	Khatir, Z.
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Keywords	Irrotational flow Neumann problem 3D-boundary element method Boundary integral method Spheres Near-wall flow simulation Experimental study Surface states Leaks Image method Potential flow Vortex method Incompressible flow Integral equations Exterior problem Vortices Source sink boundary integral equation Modelling Vortex flow Incompressible fluid Boundary element method Flat plate Flow potential
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SubjectTerms	Boundary-integral methods Computational techniques Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) General theory Mathematical methods in physics Physics
Title	A boundary element method for the numerical investigation of near-wall fluid flow with vortex method simulation
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