Higher-order unstructured finite volume RANS solution of turbulent compressible flows

In this paper, we describe a higher-order finite volume solver for the RANS solution of turbulent compressible flows on unstructured meshes. Considering that higher-order least-squares reconstruction suffers from poor accuracy on highly anisotropic meshes with curvature, we propose a modification to this method which highly improves the accuracy of solution approximation and output quantities. In addition, robust implementation and coupling of a RANS turbulence model with a higher-order finite volume solver is described and an efficient solution strategy is adopted for the convergence to the steady-state solution. We present our results, ranging from second- to fourth-order, for the test case of turbulent flat plate, subsonic and transonic flows over two-dimensional airfoils and also turbulent flow over a multi-element configuration. These results are verified by comparison against well-established numerical and experimental values in the literature. Our results show the advantages of higher-order methods in obtaining a more accurate solution with fewer degrees of freedom and also fast and efficient convergence to the steady-state solutions.