A uniform method for unsteady flows at arbitrary Mach number is developed.The preconditioned dual-time compressible Navier-Stokes equations for unsteady flows are obtained by incorporating a pseudo-time derivative term and preconditioning.The inviscid flux vectors and the viscous flux vectors are differentiated by a Roe-scheme of three-order and a general central difference scheme,respectively.A pseudo-time subiteration with an implicit ADI-LU scheme is implemented based on state-vector flux linearization.A two-order precision for physical-time step is achieved.Taking low speed flows as examples,the flow over a circular cylinder and the dynamic stall of the NACA0015 airfoil with identical pitching rate are simulated.Computed results agree with published results.It shows that the method simulates unsteady flows at arbitrary Mach number well.

Based on a static non-overlapped domain decomposition method,the problem is studied about the parallel implementation of a Harten-Yee implicit TVD difference algorithm on a MIMD multi-computers parallel system.The convergence and stability of the parallel processing techniques used here are manifested well through numerical simulation of the steady "super-supersonic" jet flow fields,and the parallel parameters obtained are promising.

Three-dimension, compressible, internal flow solution obtained using a modifiedBeam-Warming implicit factorization scheme is presented. Steady-state solution is obtained by solving numerically the full Navier-Stokes equations from given initial conditions until the time-dependent terms become negligible. The configuration considered is a rectangular cross-section, S-shaped centreline diffuser duct with an exit/inlet area ratio of 2.25. TheMach number at the duct entrance is 0.9 with a Raynolds number of 5.82×10⁵. Two regions of separated flow exist within the diffuser. The detail flow field especially the developement process of secondary velocity patterns in transverse plane are pressented. Comparing with the results ofRef.[1]. they have a good agreement. The secondary velocity patterns are more reasonable.

Some aerodynamic characteristics of an oscillating trail-edge flap were investigated by numerical simulation, such as the unsteady effect of flow field and flow field comparison between different frequences or amplitudes. The Euler equations were solved by LU-ADI algorithm, the grid is C type grid. The numerical results showed that: (1) with the oscillation of trail-edge flap, the shock strength and its location are nonlinear to the motion of the trail-edge flap, (2) the higher the reduced frequence, the less the influence to variable pressure jump, (3) with the increase of the amplitude, the variations of shock strength and its location become more seriously.

In this paper, LU-ADI scheme and Baldwin-Lomax turbulent model were applied to simulate turbulent transonic flow around twodimensional airfoils. By a series of numerical experiments, it is proven that the method used in this paper is successful and the numerical results are satisfactory.