Topical Problems of Fluid Mechanics


Institute of Thermomechanics AS CR, v.v.i.	CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics	MIO Université du Sud Toulon Var - AMU - CNRS - IRD	Czech Pilot centre ERCOFTAC

The Boundary Integral Equation Solution in Vortex Methods with the Airfoil Surface Line Discretization into Curvilinear Panels
K. Kuzmina, I. Marchevsky
Abstract:
The boundary integral equation with respect to the vortex sheet intensity, which arises in meshless Lagrangian vortex methods, is considered. Two approaches to airfoil surface line discretization are considered for numerical solution of the integral equation: with rectilinear and curvilinear panels. For both approaches, numerical schemes with piecewise-constant and piecewise-linear representation of the numerical solution are developed. It is shown that the numerical scheme with curvilinear panels and piecewise-linear solution approximation permits to provide the second order of accuracy not only for the solution of the boundary integral equation, but also for the velocity field reconstruction in the flow domain in neighborhood of the airfoil surface. Other schemes (with piecewise-constant numerical solution or with rectilinear panels) provide only the first order of accuracy for velocity field reconstruction.
Keywords:
vortex method, boundary integral equation, vortex sheet, Galerkin approach, curvilinear panels.

Fulltext: PDF DOI: https://doi.org/10.14311/TPFM.2019.019

In Proceedings Topical Problems of Fluid Mechanics 2019, Prague, 2019 Edited by David Šimurda and Tomáš Bodnár, pp. 131-138 ISBN 978-80-87012-69-7 (Print) ISSN 2336-5781 (Print)