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The impact of grid cell geometry on the accuracy of a high order discretization is studied. The issues of solution approximation are investigated on unstructured grids where grid cells are present that are almost degenerate. It will be demonstrated that high-order discretization schemes which employ compact discretization stencil are less sensitive to the geometry of a distorted grid in comparison with those over expanded stencils.

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The article represents the discussion of several separate directions of investigations, which are performed by TsAGI flight vehicles aerodynamics specialists at the time. There are some major trends of classical layout of route aircraft and also peculiarities of some prospective flight vehicles. Also there are some hypersonic vehicles aerodynamics questions examined along with problems of creation of civil supersonic transport aircraft. There is a description given for well-known and some newer methods of flow control for drag reduction.