Numerical Methods with Adaptive Artificial Viscosity for Solving Navier−Stokes Equations

A numerical method for solving two-dimensional problems of a viscous compressible gas based on Navier–Stokes equations with the introduction of adaptive artificial viscosity is presented. The proposed method is implemented for areas of the general form on triangular grids. The method of the adaptive artificial viscosity is taken as the basis of the proposed numerical method and ensures the monotonicity of the solutions, even in the presence of shock waves. The artificial viscosity (introduced into the difference scheme) is constructed in such a way that it is absent in the boundary layer where the dynamic viscosity acts. The viscosity is determined from the conditions of the fulfillment of the maximum principle. The series of calculations of an external flow around a cylinder for various Reynolds and Mach numbers is described.