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

• Published in: Theoretical and computational fluid dynamics Vol. 30; no. 4; pp. 363 - 385
• Main Authors: Nelson, Daniel A., Jacobs, Gustaaf B., Kopriva, David A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2016; Springer; Springer Nature B.V
• Subjects: Aerodynamics; Airfoils; Boundaries; Classical and Continuum Physics; Computational fluid dynamics; Computational Science and Engineering; Engineering; Engineering Fluid Dynamics; Finite element method; Flow velocity; Mathematical analysis; Navier-Stokes equations; Numerical analysis; Original Article; Physics; Simulation; Viscosity; Viscous drag; High-order curved boundaries; Discontinuous-Galerkin spectral element methods; Direct numerical simulation; Low Reynolds number airfoil flow
• ISSN: 0935-4964; 1432-2250
• DOI: 10.1007/s00162-016-0388-7

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.