Open AccessCost-Efficient Numerical Schemes for the Boundary Integral Equation Solution in 2D Vortex Methods
Author(s) -
Kseniia Kuzmina,
Ilia Marchevsky,
Victoriya Moreva,
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 - 10.1088/1742-6596/1348/1/012100
Subject(s) - airfoil , mathematics , piecewise , discontinuity (linguistics) , piecewise linear function , vortex , finite element method , galerkin method , mathematical analysis , constant (computer programming) , numerical analysis , vortex sheet , vorticity , computer science , mechanics , physics , thermodynamics , programming language
The problem of the flow simulation around airfoils using Lagrangian vortex methods is considered. Numerical schemes of the second order of accuracy for free vortex sheet intensity distribution along the airfoil are developed for smooth and non-smooth airfoils. The schemes are based on the Galerkin approach with piecewise-constant and piecewise-linear basis functions. The finite element method ideas are used and the resulting piecewise-linear scheme has the same numerical complexity as the scheme with piecewise-constant numerical solution. The modification of a FEM-type scheme is developed for non-smooth airfoils which permits to take into account the discontinuity of the solution at the specified points; its computational cost increases insignificantly.