An analysis of grid-clustering rules in a boundary layer using the numerical solution of the problem of viscous flow over a plate

The problem of the supersonic flow of a viscous compressible gas over a flat plate at a zero angle of attack was numerically studied. The two-dimensional Navier–Stokes equations were solved at various Reynolds numbers on adaptive grids with boundary-layer mesh refinement. Well-known grids constructed with the help of coordinate transformations eliminating boundary layers of various types were considered. The characteristics of numerical solutions (the value and order of the error, the value and order of the solution jump, and computation time) were analyzed in a series of numerical experiments. The advantages, shortcomings, and the applicability of each boundary layer mesh refinement rule for finding the numerical solution of this problem were discussed. The novelty of this work lies in the analysis of special adaptive grids and their use for solving problems applied in various fields of supersonic aero- and gas dynamics.