Turbulent calculations of locally implicit scheme on three-dimensional unstructured meshes

A locally implicit scheme with an anisotropic dissipation model on three-dimensional unstructured tetrahedral mesh is developed to study the transonic, turbulent flow around an ONERA M6 wing. In the Cartesian coordinate system, three-dimensional, unsteady Favre-averaged Navier-Stokes equations and a two-equation k-epsilon turbulence model are solved using a cell-centered finite volume algorithm. This scheme is locally implicit, but globally explicit and is unconditionally stable under local linearized analysis. To assess the accuracy of the present flow solver on unstructured tetrahedrons, the transonic, turbulent flow around an ONERA M6 wing is investigated. After comparing the calculated pressure coefficient distributions at different spanwise cross sections with those of related numerical and experimental results, the accuracy of the present 3-D flow solver on unstructured tetrahedral mesh is confirmed. The capability of shock capturing at different wing spanwise cross sections is demonstrated. The triple shock wave structure is also depicted on the upper wing surface.