A very high-order compact difference method for wall-bounded flows

In this paper, we formulate and analyze high-order compact finite difference schemes for the approximation of derivatives in boundary and near boundary computational nodes. It has been shown that the proposed schemes, although unstable for hyperbolic problems, turn out to be stable and accurate for the parabolic vorticity-stream function equation describing fluid flow problems. The results obtained for the Burggraf flow and the lid-driven cavity flows agree very well with the analytical solutions and literature data.