A pseudo-compressibility method developed by Rogers is used to solve the incompressible Navier-Stokes equation. Numerical flux is scattered through 3rd order Roe scheme and the 2nd order Harten-Yee TVD scheme separately. In order to accelerate convergence, several implicit methods(ADI-LU, LGS, LU-SGS) are accepted. Efficiency of different methods are shown as a classical flowfield around a cylinder in low Re(Re=200). Roe scheme is used to simulate two low speed unsteady problems:Low Re flowfield around a rotational cylinder(ω=1) and flowfield around a pitching NACA0015 airfoil with identical pitching rate.

A high accuracy and resolution finite difference method is first used to simulate numerically the compressible wake shear layers induced by flat plates with different thicknesses. The new method is named the Fu-Ma UCD5-SCD6 hybrid compact scheme. The fully two-dimensional compressible Navier-Stokes equations are directly solved. Based on the Steger-Warming flux-splitting technique, the convective terms are discretized by using the fifth-order upwind compact difference method, while the dissipative terms are discretized by using sixth-order symmetric compact difference method. A third-order Rung-Kutta method is selected for time marching. At convective Mach number M_c=0.3, four flat plate thicknesses and three upper incoming Mach numbers are considered. In all cases, the self-excited large scale vortex coherent structures are captured successfully, and their spatial evolution such as eddy rollup and pairing is investigated. Results show that the flat plate thickness can obviously affect the coherent structures. Increasing the flat plate thickness can accelerate the vortex rollup and enhance mixing. Moreover, for the same convective Mach number, increasing incoming Mach number can delay the vortex rollup and damp the vortex pairing. This can somehow be attributed to the well-known compressibility effect.