On Modified Numerical Schemes in Vortex Element Method for 2D Flow Simulation Around Airfoils

Authors: Ilia Marchevsky, Victoriya Moreva

Abstract:

The problem of incompressible steady flow simulation around an airfoil is discussed. For some simplest airfoils (circular, elliptical, Zhukovsky airfoils) the exact solution is known from complex analysis. It allows to compute the intensity of vortex layer which simulates the airfoil. Some modifications of the vortex element method are proposed and test computations are carried out. It-s shown that the these approaches are much more effective in comparison with the classical numerical scheme.

Keywords: Vortex element method, vortex layer, integral equation, ill-conditioned matrix.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075913

References:

[1] I. K. Lifanov, S. M. Belotserkovskii Methods of Discrete Vortices. CRC Press, 1993.
[2] S. N. Kempka, M. W. Glass, J. S. Peery, J. H. Strickland Accuracy Considerations for Implementing Velocity Boundary Conditions in Vorticity Formulations. SANDIA REPORT SAND96-0583, UC-700, 1996.
[3] G.-H. Cottet, P. Koumoutsakos Vortex methods: theory and practice. Cambridge University Press, 2000.
[4] G. Ya. Dynnikova Vortex Motion in Two-Dimensional Viscous Fluid Flows. Fluid Dynamics, 38/5, 2003, P. 670-678.
[5] R. I. Lewis Vortex Element Methods For Fluid Dynamic Analysis Of Engineering Systems. Cambridge University Press, 2005.
[6] M. E. Makarova Steady Inviscid Incompressible Flow Simulation Around An Airfoil. Proc. of Bauman Moscow State Technical University, Natural Sciences Series, Spec. issue ÔÇÿApplied Mathematics-, 2011, P. 63-74 (in Russian).