The three dimensional time dependent compressible Navier Stokes equations are numerically solved to study spatially developing plane Poiseuille flows undergoing transition. For spatially developing DNS (Direct Numerical Simulation), NSCBC (Navier Stokes Characteristic Boundary Conditions) are employed in the streamwise (x) and the vertical (y) directions. High order compact finite difference scheme is used in the x and the y directions. A classical Fourier method is used in the periodic direction z. Unstable disturbances are obtained from the linear stability theory using a Chebyshev collocation method. Preliminary results for low (M = 0.1, 0.5) and high (M = 4.5) Mach numbers are presented. Numerical tests to validate the code and the boundary conditions are given. A pseudo shock wave is observed in the plane Poiseuille flow for M = 4.5 because of the effect of viscosity on a shock.
圧縮性平面Poiseuille流れにおける乱流遷移のDNS
