This paper presents the numerical-visual approach to hybrid finite-difference schemes design, optimization and verification. The proposed approach is based on multiple inverse problems solution and simultaneous construction of limitation surfaces for weight parameters of hybrid finite-difference scheme. Further analysis and transformation of these surfaces allow fast and effective optimization of hybrid finite-difference schemes properties. The way of practical application for this approach is considered for laminar and turbulent supersonic wake flow problem.

Mathematical modelling in actual problems of science and technics