A Spectral/Finite-Difference Algorithm for Direct Numerical Simulation of Spatially Growing Compressible Boundary Layer Transition

A numerical scheme is developed to directly simulate laminar-turbulent transition in spatially evolving compressible boundary layer flows. It employs a Fourier collocation method in the periodic spanwise direction, and sixth order central-difference (Pade) schemes in the nonperiodic streamwise and wall-normal directions. Emphasis has been given to the boundary condition treatment, especially at the inflow and outflow boundaries.At the boundaries, the flow field is first decomposed into three parts: the basic flow, the prescribed perturbation and the remaining disturbance. At the far field boundary, there is no prescribed perturbation and a non-reflecting characteristic boundary condition is applied to the disturbance part. At the supersonic section of the inflow boundary, the disturbance part is zero and all the variables of the basic flow and the prescribed perturbation are imposed. At the subsonic section, the basic flow and the prescribed perturbation are imposed while a characteristic boundary condition is applied to the disturbance part which allows out-going waves to pass the boundary with minimum reflection. At the outflow boundary, three treatments have been tested: characteristic-based boundary condition, buffer domain approach and sponge layer approach. Extensive code validation has been carried out. The simulations of linear two- and three-dimensional instability waves are compared with results from linear stability theory (LST) and parabolized stability equations (PSE). The simulations of nonlinear waves are compared with other spatial DNS codes. Results have shown that two outflow treatments perform best: characteristic boundary conditions combined with a sponge layer and buffer domain approach plus a sponge layer. No visible inflow and outflow coupling or wave reflection is present