16 / 17
К.С. Кузьмина, И.К. Марчевский
108
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2016. № 6
points or on average on the panels. We applied higher order
of accuracy Gaussian quadrature formulas for approximate
integrals calculation. The results of the research show that
the developed scheme has higher accuracy order than the
previously known schemes. For some particular model
problems (flow around circular, elliptical and Zhukovsky
airfoils) this approach allows us to obtain solution with
accuracy
5
( )
O h
REFERENCES
[1] Lifanov I.K., Belotserkovsky S.M. Methods of discrete vortices. CRC, 1992.
[2] Cottet G.-H., Koumoutsakos P. Vortex methods: theory and practice. Cambridge Universi-
ty Press, 2000.
[3] Dynnikova
G.Ya.Vortex motion in two-dimensional viscous fluid flows.
Fluid Dynamics
,
2003, vol. 38, no. 5, pp. 670–678.
[4] Kalugin V.T., Mordvintcev G.G., Popov V.M. Modelirovanie protsessov obtekaniya i up-
ravleniya aerodinamicheskimi kharakteristikami letatel'nykh apparatov [Modeling of the flow
and the aerodynamic characteristics control for aircrafts]. Moscow, MGTU im. N.E. Baumana
Publ., 2011. 527 p.
[5] Andronov P.R., Guvernyuk S.V., Dynnikova
G.Ya. Vikhrevye metody rascheta nes-
tatsionarnykh gidrodimamicheskikh nagruzok [Vortex methods for unsteady hydrodynamic
loads]. Moscow, MGU im. M.V. Lomonosova Publ., 2006.
[6] Ogami Y., Akamatsu T. Viscous flow simulation using the discrete vortex model — the
diffusion velocity method.
Comput. and Fluids
, 1991, vol. 19, no. 3/4, pp. 433–441.
[7] Kuzmina K.S., Marchevsky I.K. On numerical schemes in 2D vortex element method for
flow simulation around moving and deformable airfoils.
Proc. of Summer School-Conference
“Advanced Problems in Mechanics 2014”
. St. Petersburg, 2014. pp. 335–344.
Available at:
http://www.ipme.ru/ipme/conf/APM2014/2014-PDF/2014-335.pdf[8] Kuzmina K.S., Marchevsky I.K., Moreva V.S. On the accuracy of numerical schemes for
flow simulation around airfoils with angle point.
Nauka i obrazovanie
.
MGTU im. N.E. Bau-
mana
[Science & Education of the Bauman MSTU. Electronic Journal], 2015, no. 2,
pp. 234–249. DOI: 10.7463/0215.0756954
Available at:
http://technomag.neicon.ru/en/doc/756954.html[9] Kempka S.N., Glass M.W., Peery J.S., Strickland J.H. Accuracy considerations for imple-
menting velocity boundary conditions in vorticity formulations. SANDIA REPORT SAND96-
0583 UC-700, 1996.
[10] Moreva V.S. Matematicheskoe modelirovanie obtekaniya profiley s ispol'zovaniem no-
vykh raschetnykh skhem metoda vikhrevykh elementov. Diss. kand. fiz.-mat. nauk [Mathe-
matical modeling of flow of profiles using the new calculation schemes of vortex element
method. Cand. phys.-math. sci. diss.]. Moscow, 2013.
[11] Marchevsky I.K., Moreva V.S. Vortex element method for 2D flow simulation with tangent
velocity components on airfoil surface.
ECCOMAS 2012. V European Congress on Computational
Methods in Applied Sciences and Engineering, e-Book Full Papers
, 2012, pp. 5952–5965.