Numerical methods with adaptive artificial viscosity for solving of the Navier–Stokes equations

A new numerical method for solving of two-dimensional problems of viscous compressible gas on the base of the Navier–Stokes equations is supposed in the paper. The method is implemented for areas of general view on triangular meshes. The method of adaptive artificial viscosity is used as base of the proposed numerical method and provides the monotony of solutions, even if there are shock waves. An artificial viscosity, introduced in the differential scheme, is constructed in this way that it is not in the boundary layer, where there is a dynamic viscosity. The viscosity is determined from the conditions of the maximum principle. The series of calculations of external flow around a cylinder for different Reynolds and Mach numbers is represented.