The locally implicit scheme and a rigid-deformable dynamic mesh algorithm are introduced to solve the unsteady Navier-Stokes equations with Baldwin-Lomax turbulence model in the Cartesian coordinate system. In this scheme, a new treatment of viscous flux function is developed on the quadrilateral-triangular meshes. To validate the present scheme, the viscous flow over an oscillating flat plate is studied. By using the above solution approach, turbulent flows around transonic oscillating cascade of four biconvex blades with different oscillation amplitudes and interblade phase angles are investigated. From the distributions of magnitude and phase angle of the first harmonic dynamic pressure difference coefficient, which include the experimental data and numerical results obtained by linearized theory, Euler and Navier-Stokes solvers, the present solution approach is reliable and acceptable. The instantaneous pressure and/or Mach number contours indicate the effects of oscillation amplitude and interblade phase angle on the unsteady flow phenomena, such as vortex-shedding, pressure waves, shocks and boundary layer interactions.

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