A high‐order compact upwind algorithm is developed for solving Navier‐Stokes equations in two‐space dimensions. The method is based on advection upstream splitting method and fourth‐order compact finite‐difference schemes. The convection flux terms of the Navier‐Stokes equations are discretized by a compact cell‐centered differencing scheme while the diffusion flux terms are discretized by a central fourth‐order compact scheme. The midpoint values of the flux functions required by the cell‐centered compact scheme are determined by a fourth‐order MUSCL approach. For steady‐state solutions; first‐order implicit time integration, with LU decomposition, is employed. Computed results for a laminar flow past a flat plate and the problem of shock‐wave boundary layer interaction are presented.
Mawlood, M.K., Basri, S., Asrar, W., Omar, A.A., Mokhtar, A.S. and Ahmad, M.M.H.M. (2004), "An AUSM‐based high‐order compact method for solving Navier‐Stokes equations", Aircraft Engineering and Aerospace Technology, Vol. 76 No. 3, pp. 299-304. https://doi.org/10.1108/00022660410536032
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