Open AccessExact solutions of boundary integral equation arising in vortex methods for incompressible flow simulation around elliptical and Zhukovsky airfoils
Author(s) -
Kseniia Kuzmina,
Ilia Marchevsky,
Evgeniya Ryatina
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1348/1/012099
Subject(s) - airfoil , vortex , vortex sheet , conformal map , incompressible flow , potential flow , compressibility , mathematics , exact solutions in general relativity , flow (mathematics) , starting vortex , boundary value problem , integral equation , mathematical analysis , physics , mechanics , geometry , vortex ring , vorticity
The problem of 2D incompressible flow simulation around airfoils using vortex methods is considered. An exact solution for the boundary integral equation with respect to a free vortex sheet intensity at the airfoil surface line that arises in such problems is obtained. The exact solution is constructed for flows around elliptical and Zhukovsky airfoils using the theory of complex potentials and conformal mappings technique. It is possible to take into account the influence of singularities in the flow domain — point vortices which simulate vortex wake. The obtained exact solutions can be used to verify and estimate the accuracy of numerical schemes for the boundary integral equation solution: such procedure is also described in details.