Theoretical and Computational Fluid Dynamics

, Volume 30, Issue 4, pp 363–385 | Cite as

Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier–Stokes solver

  • Daniel A. Nelson
  • Gustaaf B. Jacobs
  • David A. Kopriva
Original Article
First Online:
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Accepted:

Abstract

The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier–Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

Keywords

Discontinuous-Galerkin spectral element methods High-order curved boundaries  Direct numerical simulation Low Reynolds number airfoil flow 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Daniel A. Nelson
    • 1
  • Gustaaf B. Jacobs
    • 1
  • David A. Kopriva
    • 2
  1. 1.San Diego State UniversitySan DiegoUSA
  2. 2.The Florida State UniversityTallahasseeUSA

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