Algebraic turbulence modeling for unstructured and adaptive meshes

An algebraic turbulence model, based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background turbulence meshes. At each time step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more compli- cated flows, such as confluent boundary layers and wakes. The model is used in conjunction with an efficient unstructured multigrid finite-element Navier-Stokes solver, in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data. HE use of unstructured mesh techniques for computa- tional fluid dynamics (CFD) problems has become more widespread in recent years, due to the flexibility they afford in discretizing arbitrarily complex geometries, and due to the possibility they offer in resolving highly localized flow phenomena through the use of adaptive meshing. However, research on unstructured mesh techniques for CFD has con- centrated almost exclusively on the solution of the Euler equa- tions in two or three dimensions. For viscous flow calculations about nonsimple geometries, hybrid meshes have generally been employed,1'3 where a thin structured mesh is placed in the boundary-layer and wake regions, and an unstructured mesh is constructed in the outer inviscid region of the flowfield. Besides leading to an increase in coding complexity, this type of compromise limits the generality of the unstruc- tured mesh approach in dealing with arbitrarily complex geometries, such as multiple-body geometries with close toler- ances, where confluent boundary layers or wakes may occur, and complicates the task of performing adaptive meshing in the inviscid as well as viscous regions of flow. It appears that the difficulties associated with generating highly stretched unstructured meshes, which are required for efficiently resolv- ing viscous shear layers, as well as the efficient implementa- tion of a turbulence model on such meshes, has generally im- peded the use of fully unstructured meshes for viscous flows. The use of unstructured meshes throughout the entire flowfield is advocated in the present work. Previous work by the author has shown how a highly stretched unstructured mesh, suitable for high Reynolds number viscous flow calcula- tions, may be constructed4 and has also discussed the develop- ment of an efficient unstructured Navier-Stokes solver for laminar flows.5 This paper is, thus, concerned with the effi- cient implementation of a turbulence model for computing high Reynolds number turbulent flows using fully unstruc- tured meshes.