Higher-order Unstructured Finite Volume Methods for Turbulent Aerodynamic Flows

Abstract

In this paper, we describe the steps for constructing a higher-order finite volume unstructured solver for turbulent aerodynamic flows. These include the strategies for curving the interior faces of a mesh, solution reconstruction on highly anisotropic meshes with curvature, robust implementation and coupling of a RANS turbulence model and efficient solution method. The solutions are verified by one of the verification test cases of the NASA Langley turbulence model resource. Also, the solutions and convergence behaviors are presented for fully turbulent flow over a flat plate and subsonic flow over the NACA 0012 airfoil. Our results show fast and efficient convergence for second-, third-and fourthorder solutions for the flat plate test case and second-and third-order solutions for the airfoil. In addition, the accuracy of the solution is reasonable on meshes with sufficient degrees of freedom in which the turbulence features are captured appropriately.

Turbulence Model Implementation and Verification in the SENSEI CFD Code

“…Commonly the turbulent flux is computed in an uncoupled fashion, which treats the turbulence equation as a scalar transport equation. However, many authors have pointed out the fault with this type of treatment [13,14]. In treating the turbulence equation as a scalar transport equation, the turbulence convects at a velocity, which does not account for the effect of the turbulence.…”

Implementation and Validation of Semi-Implicit WENO Schemes Using OpenFOAM®

“…This results in an overdetermined, linear least-squares problem. Physically, it corresponds to the minimization of the L 2 -norm of the error in predicting the averaged values of the polynomial in all cells of the stencil [10] …”