direct numerical simulation of supersonic and transonic compressible viscous flow by kinetic energy preserving scheme

present paper investigates the numerical solution of two-dimensional unsteady compressible navier-stokes equations by a new scheme based on the finite volume method. kinetic energy preserving (kep) scheme is introduced for solving the supersonic and transonic external compressible flow field on very fine grids (with a number of cells of the order of the reynolds number) without artificial dissipation terms even in place of shock waves. it should be noted that the solution of flow field with this scheme in this range of speed, is presented for the first time. by discretization of the governing equations based on kep scheme and elimination of dissipative effects, the direct numerical simulation (dns) of the flow is possible. the results of this solution for supersonic flow over flat plate and transonic flow over the airfoil at low reynolds numbers show that the kep method can be presented stable and non-oscillatory solution by no artificial dissipation even in areas with shock waves. therefore, the kep method can be used for dns of turbulent flows (without a modeling the turbulence phenomena itself).