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A fully coupled numerical methodology is developed for calculating the flow-structure interaction problems. The Roe scheme is extended to moving grid and used with the finite-volume method. The unsteady solutions march in time by using a dual-time stepping implicit unfactored line Gauss-Seidel iteration. The unsteady Navier-Stokes equations and the linear structural equations are fully coupled implicitly via successive iteration with pseudo time stepping. The moving mesh and mesh deformation strategy is based on two mesh zones, a fine mesh zone surrounding the solid body without mesh deformation and a coarse mesh zone surrounding the fine mesh zone and deforms with the solid object. This mesh deformation strategy can maintain the orthogonality of the mesh near the wall and save CPU time for re-meshing. The study cases presented include a vortex-induced oscillating cylinder, a forced pitching airfoil, and an elastically mounted transonic airfoil. For the elastic transonic airfoil, the flutter boundary is calculated. Other phenomena captured include the limit cycle oscillation (LCO) and the steady state flow conditions, under which the aerodynamic forces and moments are balanced by the structure. The computational results agree well with the experiments and the computed results of other researchers. The methodology is demonstrated to be accurate, robust and efficient.

SUMMARYA newly suggested E-CUSP upwind scheme is employed for the ÿrst time to calculate 3D ows of propulsion systems. The E-CUSP scheme contains the total energy in the convective vector and is fully consistent with the characteristic directions. The scheme is proved to have low di usion and high CPU e ciency. The computed cases in this paper include a transonic nozzle with circular-to-rectangular cross-section, a transonic duct with shock wave=turbulent boundary layer interaction, and a subsonic 3D compressor cascade. The computed results agree well with the experiments. The new scheme is proved to be accurate, e cient and robust for the 3D calculations of the ows in this paper.

A new efficient upwind scheme based on the concept of convective upwind and split pressure is developed. The upwinding of the convective term and the pressure split are consistent with their characteristic directions. The scheme has low diffusion to resolve accurately wall boundary layers and is able to capture crisp shock waves and exact contact discontinuities. The accuracy of the scheme is compared with other popularly used schemes including the Roe scheme, the Liou's latest advection upstream splitting method scheme (AUSM + + ), the Van Leer scheme, and the Van Leer-Hänel scheme. The new scheme is tested for the one-dimensional Sod shock tube problem, one-dimensional slowly moving contact surface, supersonic flat plate laminar boundary layer, a transonic nozzle with oblique shock waves and reflections that do not align with the mesh lines, and a transonic inlet diffuser with shock wave/turbulent boundary-layer interaction. The test cases show that the new scheme is accurate, robust, and efficient. Nomenclaturea = speed of sound D = numerical dissipation vector E = inviscid flux of quasi-one-dimensional Euler equations E , F , G = inviscid flux vectors in ξ, η, and ζ directions e = total energy per unit mass F = inviscid flux of quasi-one-dimensional Euler equations per unit area H = source term of quasi-one-dimensional Euler equations, total enthalpy J = transformation Jacobian l = control volume interface area vectors, l x i + l y j + l z k M = Mach number p = static pressure Q = conservative variable vector R , S , T = viscous flux vectors in ξ, η, and ζ directions S = cross-sectional area of one-dimensional duct T = right eigenvector matrix of the Jacobian matrix U = normal contravariant velocity in ξ direction U = conservative variable vector of quasi-one-dimensional Euler equations multiplied by duct area u, v, w = velocity in x, y, and z directions V = velocity vector, ui + vj + wk x, y, z = spatial coordinates in the Cartesian coordinate system γ = specific heat ratio = eigenvalue matrix of the Jacobian matrix ξ, η, ζ = spatial coordinates in the generalized coordinate system ρ = density Subscripts i = cell index L = left value R = right value t = time 1 2 = control interface position Superscripts c = convective n, n + 1 = time level index p = pressure + = upwind direction − = downwind directioñ = Roe's average = flux vectors of H convective upwind and split pressure schemes, flux vectors in three-dimensional generalized coordinates

The 3D compressible Navier-Stokes equations with Baldwin-Lomax turbulence model are solved to study the flow separation phenomenon in a NASA Transonic Flutter Cascade. The influence of the incidence angle and the inlet Mach number on the flow pattern in the cascade is numerically studied. When the incoming flow is subsonic, increasing the incidence angle generates a large separation region starting from the leading edge on the suction surface. Higher subsonic inlet Mach number results in a larger separation region. The separation region shrinks and moves downstream when the inlet Mach number is increased to supersonic due to the shock wave boundary layer interaction.