A truncation error injection approach to viscous-inviscid interaction

A numerical procedure is presented which uses the truncation error injection methodology to efficiently achieve accurate approximations to complex problems having disparate length scales in the context of solving viscous, transonic flow over an airfoil. The truncation error distribution is estimated using the solution on a coarse grid. Local fine grids are formed which improve the resolution in regions of large truncation error. A fast fourth-order accurate scheme is presented for interpolating and relating the solutions between the generalized curvilinear coordinate systems of the local and global grids. It is shown that accurate solutions can be obtained on a global coarse grid with correction information obtained on local fine grids, which may or may not be topologically similar to the global grid as long as they are capable of resolving the local length scale. Dirichlet boundary conditions for the local grid yield the best results. The scheme also serves as the basis of a local refinement technique wherein a grid local to the nose of an airfoil is used to resolve a supersonic zone terminated by a shock and its interaction with a turbulent boundary layer. The solution on the local grid reveals details of the shock structure and a jet-like flow emanating from the root of the normal shock in the shock boundary layer interaction zone.