Simulation of the laminar–turbulent transition by applying hybrid difference schemes

A simple hybrid difference scheme applicable to shock wave flows is proposed. The scheme remains monotone near shock waves and switches to a low-dissipative nonmonotone difference scheme in smooth flow regions, thus controlling the amount of numerical dissipation. This is achieved by smoothly decreasing a monotonizing correction term down to the prescribed threshold value depending on an indicator of solution smoothness. As an example, the laminar–turbulent transition in a supersonic boundary layer over a flat plate at a Mach number of 3 is simulated. The numerical results are compared with those of other works based on dissipative and low-dissipative schemes. More specifically, we compare the spectral characteristics of disturbances in the linear and nonlinear development domains, the transient flow structure, and averaged boundary layer characteristics.