The fundamental theory of NND (Non-oscillatory, containing no free parameters and dissipative) schemes is discussed. The way of constructing NND schemes for hyperbolic conservation laws is shown. Extensions of NND schemes to finite difference method, finite element method, finite spectral method and finite volume method are described. Problems on grid generation, difference scheme construction and treatment of boundary conditions are analyzed. Results of using various NND schemes and their extensions in the study of model problems and aerodynamic applications are shown.
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