"Application of a numerical-analytical method of conformal mapping to mesh generation in a channel with riblets"
Grigoriev O.A. and Klyushnev N.V.

A numerical-analytical method of conformal mapping is proposed for mesh generation to study the Poiseuille flow stability in a channel with rectangular riblets. The proposed method is compared with the method used in SCPACK (Schwarz-Christoffel conformal map PACKage). The convergence is shown as the grid spacing tends to zero when calculating the main flow and the neutral curves. The numerical results obtained for wave and comb riblets are consistent. Using this numerical-analytical method to study the flow stability allows one to analyze more general cases of rectangular riblets.

Keywords: riblets, neutral stability curve, conformal mappings, theta-functions, Poiseuille flow.

  • Grigoriev O.A. – Institute of Numerical Mathematics, Russian Academy of Sciences; ulitsa Gubkina 8, Moscow, 119333, Russia; Graduate Student, e-mail: guelpho@mail.ru
  • Klyushnev N.V. – Institute of Numerical Mathematics, Russian Academy of Sciences; ulitsa Gubkina 8, Moscow, 119333, Russia; Graduate Student, e-mail: n_klyushnev@mail.ru